torch.nn

Parameters

class torch.nn.Parameter

A kind of Tensor that is to be considered a module parameter.

Parameters are Tensor subclasses, that have a very special property when used with Module s - when they’re assigned as Module attributes they are automatically added to the list of its parameters, and will appear e.g. in parameters() iterator. Assigning a Tensor doesn’t have such effect. This is because one might want to cache some temporary state, like last hidden state of the RNN, in the model. If there was no such class as Parameter, these temporaries would get registered too.

Parameters:

• data (Tensor) – parameter tensor.
• requires_grad (bool, optional) – if the parameter requires gradient. See Excluding subgraphs from backward for more details. Default: True

Containers

Module

class torch.nn.Module

Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes:

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
       x = F.relu(self.conv1(x))
       return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call to(), etc.

add_module(name, module)

Adds a child module to the current module.

The module can be accessed as an attribute using the given name.

Parameters:

• name (string) – name of the child module. The child module can be accessed from this module using the given name
• parameter (Module) – child module to be added to the module.

apply(fn)

Applies fn recursively to every submodule (as returned by .children()) as well as self. Typical use includes initializing the parameters of a model (see also torch-nn-init).

Parameters:fn (Module -> None) – function to be applied to each submodule Returns:self Return type:Module

Example:

>>> def init_weights(m):
        print(m)
        if type(m) == nn.Linear:
            m.weight.data.fill_(1.0)
            print(m.weight)

>>> net = nn.Sequential(nn.Linear(2, 2), nn.Linear(2, 2))
>>> net.apply(init_weights)
Linear(in_features=2, out_features=2, bias=True)
Parameter containing:
tensor([[ 1.,  1.],
        [ 1.,  1.]])
Linear(in_features=2, out_features=2, bias=True)
Parameter containing:
tensor([[ 1.,  1.],
        [ 1.,  1.]])
Sequential(
  (0): Linear(in_features=2, out_features=2, bias=True)
  (1): Linear(in_features=2, out_features=2, bias=True)
)
Sequential(
  (0): Linear(in_features=2, out_features=2, bias=True)
  (1): Linear(in_features=2, out_features=2, bias=True)
)

buffers(recurse=True)

Returns an iterator over module buffers.

Parameters:recurse (bool) – if True, then yields buffers of this module and all submodules. Otherwise, yields only buffers that are direct members of this module. Yields:torch.Tensor – module buffer

Example:

>>> for buf in model.buffers():
>>>     print(type(buf.data), buf.size())
<class 'torch.FloatTensor'> (20L,)
<class 'torch.FloatTensor'> (20L, 1L, 5L, 5L)

children()

Returns an iterator over immediate children modules.

Yields:Module – a child module

cpu()

Moves all model parameters and buffers to the CPU.

Returns:self Return type:Module

cuda(device=None)

Moves all model parameters and buffers to the GPU.

This also makes associated parameters and buffers different objects. So it should be called before constructing optimizer if the module will live on GPU while being optimized.

Parameters:device (int, optional) – if specified, all parameters will be copied to that device Returns:self Return type:Module

double()

Casts all floating point parameters and buffers to double datatype.

Returns:self Return type:Module

dump_patches = False

This allows better BC support for load_state_dict(). In state_dict(), the version number will be saved as in the attribute _metadata of the returned state dict, and thus pickled. _metadata is a dictionary with keys that follow the naming convention of state dict. See _load_from_state_dict on how to use this information in loading.

If new parameters/buffers are added/removed from a module, this number shall be bumped, and the module’s _load_from_state_dict method can compare the version number and do appropriate changes if the state dict is from before the change.

eval()

Sets the module in evaluation mode.

This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g. Dropout, BatchNorm, etc.

extra_repr()

Set the extra representation of the module

To print customized extra information, you should reimplement this method in your own modules. Both single-line and multi-line strings are acceptable.

float()

Casts all floating point parameters and buffers to float datatype.

Returns:self Return type:Module

forward(*input)

Defines the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

half()

Casts all floating point parameters and buffers to half datatype.

Returns:self Return type:Module

load_state_dict(state_dict, strict=True)

Copies parameters and buffers from state_dict into this module and its descendants. If strict is True, then the keys of state_dict must exactly match the keys returned by this module’s state_dict() function.

Parameters:

• state_dict (dict) – a dict containing parameters and persistent buffers.
• strict (bool, optional) – whether to strictly enforce that the keys in state_dict match the keys returned by this module’s state_dict() function. Default: True

modules()

Returns an iterator over all modules in the network.

Yields:Module – a module in the network

Note

Duplicate modules are returned only once. In the following example, l will be returned only once.

Example:

>>> l = nn.Linear(2, 2)
>>> net = nn.Sequential(l, l)
>>> for idx, m in enumerate(net.modules()):
        print(idx, '->', m)

0 -> Sequential (
  (0): Linear (2 -> 2)
  (1): Linear (2 -> 2)
)
1 -> Linear (2 -> 2)

named_buffers(prefix='', recurse=True)

Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.

Parameters:

• prefix (str) – prefix to prepend to all buffer names.
• recurse (bool) – if True, then yields buffers of this module and all submodules. Otherwise, yields only buffers that are direct members of this module.

Yields:

(string, torch.Tensor) – Tuple containing the name and buffer

Example:

>>> for name, buf in self.named_buffers():
>>>    if name in ['running_var']:
>>>        print(buf.size())

named_children()

Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.

Yields:(string, Module) – Tuple containing a name and child module

Example:

>>> for name, module in model.named_children():
>>>     if name in ['conv4', 'conv5']:
>>>         print(module)

named_modules(memo=None, prefix='')

Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.

Yields:(string, Module) – Tuple of name and module

Note

Duplicate modules are returned only once. In the following example, l will be returned only once.

Example:

>>> l = nn.Linear(2, 2)
>>> net = nn.Sequential(l, l)
>>> for idx, m in enumerate(net.named_modules()):
        print(idx, '->', m)

0 -> ('', Sequential (
  (0): Linear (2 -> 2)
  (1): Linear (2 -> 2)
))
1 -> ('0', Linear (2 -> 2))

named_parameters(prefix='', recurse=True)

Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.

Parameters:

• prefix (str) – prefix to prepend to all parameter names.
• recurse (bool) – if True, then yields parameters of this module and all submodules. Otherwise, yields only parameters that are direct members of this module.

Yields:

(string, Parameter) – Tuple containing the name and parameter

Example:

>>> for name, param in self.named_parameters():
>>>    if name in ['bias']:
>>>        print(param.size())

parameters(recurse=True)

Returns an iterator over module parameters.

This is typically passed to an optimizer.

Parameters:recurse (bool) – if True, then yields parameters of this module and all submodules. Otherwise, yields only parameters that are direct members of this module. Yields:Parameter – module parameter

Example:

>>> for param in model.parameters():
>>>     print(type(param.data), param.size())
<class 'torch.FloatTensor'> (20L,)
<class 'torch.FloatTensor'> (20L, 1L, 5L, 5L)

register_backward_hook(hook)

Registers a backward hook on the module.

The hook will be called every time the gradients with respect to module inputs are computed. The hook should have the following signature:

hook(module, grad_input, grad_output) -> Tensor or None

The grad_input and grad_output may be tuples if the module has multiple inputs or outputs. The hook should not modify its arguments, but it can optionally return a new gradient with respect to input that will be used in place of grad_input in subsequent computations.

Returns:a handle that can be used to remove the added hook by calling handle.remove() Return type:torch.utils.hooks.RemovableHandle

Warning

The current implementation will not have the presented behavior for complex Module that perform many operations. In some failure cases, grad_input and grad_output will only contain the gradients for a subset of the inputs and outputs. For such Module, you should use torch.Tensor.register_hook() directly on a specific input or output to get the required gradients.

register_buffer(name, tensor)

Adds a persistent buffer to the module.

This is typically used to register a buffer that should not to be considered a model parameter. For example, BatchNorm’s running_mean is not a parameter, but is part of the persistent state.

Buffers can be accessed as attributes using given names.

Parameters:

• name (string) – name of the buffer. The buffer can be accessed from this module using the given name
• tensor (Tensor) – buffer to be registered.

Example:

>>> self.register_buffer('running_mean', torch.zeros(num_features))

register_forward_hook(hook)

Registers a forward hook on the module.

The hook will be called every time after forward() has computed an output. It should have the following signature:

hook(module, input, output) -> None

The hook should not modify the input or output.

Returns:a handle that can be used to remove the added hook by calling handle.remove() Return type:torch.utils.hooks.RemovableHandle

register_forward_pre_hook(hook)

Registers a forward pre-hook on the module.

The hook will be called every time before forward() is invoked. It should have the following signature:

hook(module, input) -> None

The hook should not modify the input.

Returns:a handle that can be used to remove the added hook by calling handle.remove() Return type:torch.utils.hooks.RemovableHandle

register_parameter(name, param)

Adds a parameter to the module.

The parameter can be accessed as an attribute using given name.

Parameters:

• name (string) – name of the parameter. The parameter can be accessed from this module using the given name
• parameter (Parameter) – parameter to be added to the module.

state_dict(destination=None, prefix='', keep_vars=False)

Returns a dictionary containing a whole state of the module.

Both parameters and persistent buffers (e.g. running averages) are included. Keys are corresponding parameter and buffer names.

Returns:a dictionary containing a whole state of the module Return type:dict

Example:

>>> module.state_dict().keys()
['bias', 'weight']

to(*args, **kwargs)

Moves and/or casts the parameters and buffers.

This can be called as

to(device=None, dtype=None, non_blocking=False)

to(dtype, non_blocking=False)

to(tensor, non_blocking=False)

Its signature is similar to torch.Tensor.to(), but only accepts floating point desired dtype s. In addition, this method will only cast the floating point parameters and buffers to dtype (if given). The integral parameters and buffers will be moved device, if that is given, but with dtypes unchanged. When non_blocking is set, it tries to convert/move asynchronously with respect to the host if possible, e.g., moving CPU Tensors with pinned memory to CUDA devices.

See below for examples.

Note

This method modifies the module in-place.

Parameters:

• device (torch.device) – the desired device of the parameters and buffers in this module
• dtype (torch.dtype) – the desired floating point type of the floating point parameters and buffers in this module
• tensor (torch.Tensor) – Tensor whose dtype and device are the desired dtype and device for all parameters and buffers in this module

Returns:

self

Return type:

Module

Example:

>>> linear = nn.Linear(2, 2)
>>> linear.weight
Parameter containing:
tensor([[ 0.1913, -0.3420],
        [-0.5113, -0.2325]])
>>> linear.to(torch.double)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1913, -0.3420],
        [-0.5113, -0.2325]], dtype=torch.float64)
>>> gpu1 = torch.device("cuda:1")
>>> linear.to(gpu1, dtype=torch.half, non_blocking=True)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
        [-0.5112, -0.2324]], dtype=torch.float16, device='cuda:1')
>>> cpu = torch.device("cpu")
>>> linear.to(cpu)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
        [-0.5112, -0.2324]], dtype=torch.float16)

train(mode=True)

Sets the module in training mode.

This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g. Dropout, BatchNorm, etc.

Returns:self Return type:Module

type(dst_type)

Casts all parameters and buffers to dst_type.

Parameters:dst_type (type or string) – the desired type Returns:self Return type:Module

zero_grad()

Sets gradients of all model parameters to zero.

Sequential

class torch.nn.Sequential(*args)

A sequential container. Modules will be added to it in the order they are passed in the constructor. Alternatively, an ordered dict of modules can also be passed in.

To make it easier to understand, here is a small example:

# Example of using Sequential
model = nn.Sequential(
          nn.Conv2d(1,20,5),
          nn.ReLU(),
          nn.Conv2d(20,64,5),
          nn.ReLU()
        )

# Example of using Sequential with OrderedDict
model = nn.Sequential(OrderedDict([
          ('conv1', nn.Conv2d(1,20,5)),
          ('relu1', nn.ReLU()),
          ('conv2', nn.Conv2d(20,64,5)),
          ('relu2', nn.ReLU())
        ]))

ModuleList

class torch.nn.ModuleList(modules=None)

Holds submodules in a list.

ModuleList can be indexed like a regular Python list, but modules it contains are properly registered, and will be visible by all Module methods.

Parameters:modules (iterable, optional) – an iterable of modules to add

Example:

class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.linears = nn.ModuleList([nn.Linear(10, 10) for i in range(10)])

    def forward(self, x):
        # ModuleList can act as an iterable, or be indexed using ints
        for i, l in enumerate(self.linears):
            x = self.linears[i // 2](x) + l(x)
        return x

append(module)

Appends a given module to the end of the list.

Parameters:module (nn.Module) – module to append

extend(modules)

Appends modules from a Python iterable to the end of the list.

Parameters:modules (iterable) – iterable of modules to append

insert(index, module)

Insert a given module before a given index in the list.

Parameters:

• index (int) – index to insert.
• module (nn.Module) – module to insert

ModuleDict

class torch.nn.ModuleDict(modules=None)

Holds submodules in a dictionary.

ModuleDict can be indexed like a regular Python dictionary, but modules it contains are properly registered, and will be visible by all Module methods.

Parameters:modules (iterable, optional) – a mapping (dictionary) of (string: module) or an iterable of key/value pairs of type (string, module)

Example:

class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.choices = nn.ModuleDict({
                'conv': nn.Conv2d(10, 10, 3),
                'pool': nn.MaxPool2d(3)
        })
        self.activations = nn.ModuleDict([
                ['lrelu', nn.LeakyReLU()],
                ['prelu', nn.PReLU()]
        ])

    def forward(self, x, choice, act):
        x = self.choices[choice](x)
        x = self.activations[act](x)
        return x

clear()

Remove all items from the ModuleDict.

items()

Return an iterable of the ModuleDict key/value pairs.

keys()

Return an iterable of the ModuleDict keys.

pop(key)

Remove key from the ModuleDict and return its module.

Parameters:key (string) – key to pop from the ModuleDict

update(modules)

Update the ModuleDict with the key/value pairs from a mapping or an iterable, overwriting existing keys.

Parameters:modules (iterable) – a mapping (dictionary) of (string: Module`) or an iterable of key/value pairs of type (string, Module`)

values()

Return an iterable of the ModuleDict values.

ParameterList

class torch.nn.ParameterList(parameters=None)

Holds parameters in a list.

ParameterList can be indexed like a regular Python list, but parameters it contains are properly registered, and will be visible by all Module methods.

Parameters:parameters (iterable, optional) – an iterable of Parameter` to add

Example:

class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.params = nn.ParameterList([nn.Parameter(torch.randn(10, 10)) for i in range(10)])

    def forward(self, x):
        # ParameterList can act as an iterable, or be indexed using ints
        for i, p in enumerate(self.params):
            x = self.params[i // 2].mm(x) + p.mm(x)
        return x

append(parameter)

Appends a given parameter at the end of the list.

Parameters:parameter (nn.Parameter) – parameter to append

extend(parameters)

Appends parameters from a Python iterable to the end of the list.

Parameters:parameters (iterable) – iterable of parameters to append

ParameterDict

class torch.nn.ParameterDict(parameters=None)

Holds parameters in a dictionary.

ParameterDict can be indexed like a regular Python dictionary, but parameters it contains are properly registered, and will be visible by all Module methods.

Parameters:parameters (iterable, optional) – a mapping (dictionary) of (string : Parameter) or an iterable of key,value pairs of type (string, Parameter)

Example:

class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.params = nn.ParameterDict({
                'left': nn.Parameter(torch.randn(5, 10)),
                'right': nn.Parameter(torch.randn(5, 10))
        })

    def forward(self, x, choice):
        x = self.params[choice].mm(x)
        return x

clear()

Remove all items from the ParameterDict.

items()

Return an iterable of the ParameterDict key/value pairs.

keys()

Return an iterable of the ParameterDict keys.

pop(key)

Remove key from the ParameterDict and return its parameter.

Parameters:key (string) – key to pop from the ParameterDict

update(parameters)

Update the ParameterDict with the key/value pairs from a mapping or an iterable, overwriting existing keys.

Parameters:parameters (iterable) – a mapping (dictionary) of (string : Parameter) or an iterable of key/value pairs of type (string, Parameter)

values()

Return an iterable of the ParameterDict values.

Convolution layers

Conv1d

class torch.nn.Conv1d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)

Applies a 1D convolution over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C_{\text{in}}, L)\) and output \((N, C_{\text{out}}, L_{\text{out}})\) can be precisely described as:

\[\text{out}(N_i, C_{\text{out}_j}) = \text{bias}(C_{\text{out}_j}) + \sum_{k = 0}^{C_{in} - 1} \text{weight}(C_{\text{out}_j}, k) \star \text{input}(N_i, k) \]

where \(\star\) is the valid cross-correlation operator, \(N\) is a batch size, \(C\) denotes a number of channels, \(L\) is a length of signal sequence.

• stride controls the stride for the cross-correlation, a single number or a one-element tuple.

• padding controls the amount of implicit zero-paddings on both sides for padding number of points.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters, of size \(\left\lfloor\frac{C_\text{out}}{C_\text{in}}\right\rfloor\)

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution.

In other words, for an input of size \((N, C_{in}, L_{in})\), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments \((C_\text{in}=C_{in}, C_\text{out}=C_{in} \times K, ..., \text{groups}=C_{in})\).

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• in_channels (int) – Number of channels in the input image
• out_channels (int) – Number of channels produced by the convolution
• kernel_size (int or tuple) – Size of the convolving kernel
• stride (int or tuple, optional) – Stride of the convolution. Default: 1
• padding (int or tuple, optional) – Zero-padding added to both sides of the input. Default: 0
• dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
• groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True

Shape:

• Input: \((N, C_{in}, L_{in})\)

• Output: \((N, C_{out}, L_{out})\) where

  \[L_{out} = \left\lfloor\frac{L_{in} + 2 \times \text{padding} - \text{dilation} \times (\text{kernel\_size} - 1) - 1}{\text{stride}} + 1\right\rfloor \]

Variables:

• weight (Tensor) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size). The values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)
• bias (Tensor) – the learnable bias of the module of shape (out_channels). If bias is True, then the values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)

Examples:

>>> m = nn.Conv1d(16, 33, 3, stride=2)
>>> input = torch.randn(20, 16, 50)
>>> output = m(input)

Conv2d

class torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)

Applies a 2D convolution over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C_{\text{in}}, H, W)\) and output \((N, C_{\text{out}}, H_{\text{out}}, W_{\text{out}})\) can be precisely described as:

\[\text{out}(N_i, C_{\text{out}_j}) = \text{bias}(C_{\text{out}_j}) + \sum_{k = 0}^{C_{\text{in}} - 1} \text{weight}(C_{\text{out}_j}, k) \star \text{input}(N_i, k) \]

where \(\star\) is the valid 2D cross-correlation operator, \(N\) is a batch size, \(C\) denotes a number of channels, \(H\) is a height of input planes in pixels, and \(W\) is width in pixels.

• stride controls the stride for the cross-correlation, a single number or a tuple.

• padding controls the amount of implicit zero-paddings on both sides for padding number of points for each dimension.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters, of size: \(\left\lfloor\frac{C_\text{out}}{C_\text{in}}\right\rfloor\).

The parameters kernel_size, stride, padding, dilation can either be:

• a single int – in which case the same value is used for the height and width dimension
• a tuple of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution.

In other words, for an input of size \((N, C_{in}, H_{in}, W_{in})\), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments \((in\_channels=C_{in}, out\_channels=C_{in} \times K, ..., groups=C_{in})\).

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• in_channels (int) – Number of channels in the input image
• out_channels (int) – Number of channels produced by the convolution
• kernel_size (int or tuple) – Size of the convolving kernel
• stride (int or tuple, optional) – Stride of the convolution. Default: 1
• padding (int or tuple, optional) – Zero-padding added to both sides of the input. Default: 0
• dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
• groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True

Shape:

• Input: \((N, C_{in}, H_{in}, W_{in})\)

• Output: \((N, C_{out}, H_{out}, W_{out})\) where

  \[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[0] - \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[1] - \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor \]

Variables:

• weight (Tensor) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size[0], kernel_size[1]). The values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)
• bias (Tensor) – the learnable bias of the module of shape (out_channels). If bias is True, then the values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)

Examples:

>>> # With square kernels and equal stride
>>> m = nn.Conv2d(16, 33, 3, stride=2)
>>> # non-square kernels and unequal stride and with padding
>>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
>>> # non-square kernels and unequal stride and with padding and dilation
>>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2), dilation=(3, 1))
>>> input = torch.randn(20, 16, 50, 100)
>>> output = m(input)

Conv3d

class torch.nn.Conv3d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)

Applies a 3D convolution over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C_{in}, D, H, W)\) and output \((N, C_{out}, D_{out}, H_{out}, W_{out})\) can be precisely described as:

\[out(N_i, C_{out_j}) = bias(C_{out_j}) + \sum_{k = 0}^{C_{in} - 1} weight(C_{out_j}, k) \star input(N_i, k) \]

where \(\star\) is the valid 3D cross-correlation operator

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for padding number of points for each dimension.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters, of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\).

The parameters kernel_size, stride, padding, dilation can either be:

• a single int – in which case the same value is used for the depth, height and width dimension
• a tuple of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution.

In other words, for an input of size \((N, C_{in}, D_{in}, H_{in}, W_{in})\), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments \((in\_channels=C_{in}, out\_channels=C_{in} \times K, ..., groups=C_{in})\).

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• in_channels (int) – Number of channels in the input image
• out_channels (int) – Number of channels produced by the convolution
• kernel_size (int or tuple) – Size of the convolving kernel
• stride (int or tuple, optional) – Stride of the convolution. Default: 1
• padding (int or tuple, optional) – Zero-padding added to all three sides of the input. Default: 0
• dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
• groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True

Shape:

• Input: \((N, C_{in}, D_{in}, H_{in}, W_{in})\)

• Output: \((N, C_{out}, D_{out}, H_{out}, W_{out})\) where

  \[D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] - \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor \]
  \[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] - \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] - \text{dilation}[2] \times (\text{kernel\_size}[2] - 1) - 1}{\text{stride}[2]} + 1\right\rfloor \]

Variables:

• weight (Tensor) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size[0], kernel_size[1], kernel_size[2]) The values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)
• bias (Tensor) – the learnable bias of the module of shape (out_channels). If bias is True, then the values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)

Examples:

>>> # With square kernels and equal stride
>>> m = nn.Conv3d(16, 33, 3, stride=2)
>>> # non-square kernels and unequal stride and with padding
>>> m = nn.Conv3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(4, 2, 0))
>>> input = torch.randn(20, 16, 10, 50, 100)
>>> output = m(input)

ConvTranspose1d

class torch.nn.ConvTranspose1d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)

Applies a 1D transposed convolution operator over an input image composed of several input planes.

This module can be seen as the gradient of Conv1d with respect to its input. It is also known as a fractionally-strided convolution or a deconvolution (although it is not an actual deconvolution operation).

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for kernel_size - 1 - padding number of points. See note below for details.

• output_padding controls the additional size added to one side of the output shape. See note below for details.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters (of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\)).

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

The padding argument effectively adds kernel_size - 1 - padding amount of zero padding to both sizes of the input. This is set so that when a Conv1d and a ConvTranspose1d are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when stride > 1, Conv1d maps multiple input shapes to the same output shape. output_padding is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note that output_padding is only used to find output shape, but does not actually add zero-padding to output.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• in_channels (int) – Number of channels in the input image
• out_channels (int) – Number of channels produced by the convolution
• kernel_size (int or tuple) – Size of the convolving kernel
• stride (int or tuple, optional) – Stride of the convolution. Default: 1
• padding (int or tuple, optional) – kernel_size - 1 - padding zero-padding will be added to both sides of the input. Default: 0
• output_padding (int or tuple, optional) – Additional size added to one side of the output shape. Default: 0
• groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True
• dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1

Shape:

• Input: \((N, C_{in}, L_{in})\)

• Output: \((N, C_{out}, L_{out})\) where

  \[L_{out} = (L_{in} - 1) \times \text{stride} - 2 \times \text{padding} + \text{dilation} \times (\text{kernel\_size} - 1) + \text{output\_padding} + 1 \]

Variables:

• weight (Tensor) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1]). The values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)
• bias (Tensor) – the learnable bias of the module of shape (out_channels). If bias is True, then the values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)

ConvTranspose2d

class torch.nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)

Applies a 2D transposed convolution operator over an input image composed of several input planes.

This module can be seen as the gradient of Conv2d with respect to its input. It is also known as a fractionally-strided convolution or a deconvolution (although it is not an actual deconvolution operation).

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for kernel_size - 1 - padding number of points. See note below for details.

• output_padding controls the additional size added to one side of the output shape. See note below for details.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters (of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\)).

The parameters kernel_size, stride, padding, output_padding can either be:

• a single int – in which case the same value is used for the height and width dimensions
• a tuple of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

The padding argument effectively adds kernel_size - 1 - padding amount of zero padding to both sizes of the input. This is set so that when a Conv2d and a ConvTranspose2d are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when stride > 1, Conv2d maps multiple input shapes to the same output shape. output_padding is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note that output_padding is only used to find output shape, but does not actually add zero-padding to output.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• in_channels (int) – Number of channels in the input image
• out_channels (int) – Number of channels produced by the convolution
• kernel_size (int or tuple) – Size of the convolving kernel
• stride (int or tuple, optional) – Stride of the convolution. Default: 1
• padding (int or tuple, optional) – kernel_size - 1 - padding zero-padding will be added to both sides of each dimension in the input. Default: 0
• output_padding (int or tuple, optional) – Additional size added to one side of each dimension in the output shape. Default: 0
• groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True
• dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1

Shape:

• Input: \((N, C_{in}, H_{in}, W_{in})\)
• Output: \((N, C_{out}, H_{out}, W_{out})\) where

\[H_{out} = (H_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) + \text{output\_padding}[0] + 1 \]

\[W_{out} = (W_{in} - 1) \times \text{stride}[1] - 2 \times \text{padding}[1] + \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) + \text{output\_padding}[1] + 1 \]

Variables:

• weight (Tensor) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1]) The values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)
• bias (Tensor) – the learnable bias of the module of shape (out_channels) If bias is True, then the values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)

Examples:

>>> # With square kernels and equal stride
>>> m = nn.ConvTranspose2d(16, 33, 3, stride=2)
>>> # non-square kernels and unequal stride and with padding
>>> m = nn.ConvTranspose2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
>>> input = torch.randn(20, 16, 50, 100)
>>> output = m(input)
>>> # exact output size can be also specified as an argument
>>> input = torch.randn(1, 16, 12, 12)
>>> downsample = nn.Conv2d(16, 16, 3, stride=2, padding=1)
>>> upsample = nn.ConvTranspose2d(16, 16, 3, stride=2, padding=1)
>>> h = downsample(input)
>>> h.size()
torch.Size([1, 16, 6, 6])
>>> output = upsample(h, output_size=input.size())
>>> output.size()
torch.Size([1, 16, 12, 12])

ConvTranspose3d

class torch.nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)

Applies a 3D transposed convolution operator over an input image composed of several input planes. The transposed convolution operator multiplies each input value element-wise by a learnable kernel, and sums over the outputs from all input feature planes.

This module can be seen as the gradient of Conv3d with respect to its input. It is also known as a fractionally-strided convolution or a deconvolution (although it is not an actual deconvolution operation).

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for kernel_size - 1 - padding number of points. See note below for details.

• output_padding controls the additional size added to one side of the output shape. See note below for details.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters (of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\)).

The parameters kernel_size, stride, padding, output_padding can either be:

• a single int – in which case the same value is used for the depth, height and width dimensions
• a tuple of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

The padding argument effectively adds kernel_size - 1 - padding amount of zero padding to both sizes of the input. This is set so that when a Conv3d and a ConvTranspose3d are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when stride > 1, Conv3d maps multiple input shapes to the same output shape. output_padding is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note that output_padding is only used to find output shape, but does not actually add zero-padding to output.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• in_channels (int) – Number of channels in the input image
• out_channels (int) – Number of channels produced by the convolution
• kernel_size (int or tuple) – Size of the convolving kernel
• stride (int or tuple, optional) – Stride of the convolution. Default: 1
• padding (int or tuple, optional) – kernel_size - 1 - padding zero-padding will be added to both sides of each dimension in the input. Default: 0
• output_padding (int or tuple, optional) – Additional size added to one side of each dimension in the output shape. Default: 0
• groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True
• dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1

Shape:

• Input: \((N, C_{in}, D_{in}, H_{in}, W_{in})\)
• Output: \((N, C_{out}, D_{out}, H_{out}, W_{out})\) where

\[D_{out} = (D_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) + \text{output\_padding}[0] + 1 \]

\[H_{out} = (H_{in} - 1) \times \text{stride}[1] - 2 \times \text{padding}[1] + \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) + \text{output\_padding}[1] + 1 \]

\[W_{out} = (W_{in} - 1) \times \text{stride}[2] - 2 \times \text{padding}[2] + \text{dilation}[2] \times (\text{kernel\_size}[2] - 1) + \text{output\_padding}[2] + 1 \]

Variables:

• weight (Tensor) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1], kernel_size[2]) The values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)
• bias (Tensor) – the learnable bias of the module of shape (out_channels) If bias is True, then the values of these weights are sampled from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)

Examples:

>>> # With square kernels and equal stride
>>> m = nn.ConvTranspose3d(16, 33, 3, stride=2)
>>> # non-square kernels and unequal stride and with padding
>>> m = nn.ConvTranspose3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(0, 4, 2))
>>> input = torch.randn(20, 16, 10, 50, 100)
>>> output = m(input)

Unfold

class torch.nn.Unfold(kernel_size, dilation=1, padding=0, stride=1)

Extracts sliding local blocks from a batched input tensor.

Consider an batched input tensor of shape \((N, C, *)\), where \(N\) is the batch dimension, \(C\) is the channel dimension, and \(*\) represent arbitrary spatial dimensions. This operation flattens each sliding kernel_size-sized block within the spatial dimensions of input into a column (i.e., last dimension) of a 3-D output tensor of shape \((N, C \times \prod(\text{kernel\_size}), L)\), where \(C \times \prod(\text{kernel\_size})\) is the total number of values with in each block (a block has \(\prod(\text{kernel\_size})\) spatial locations each containing a \(C\)-channeled vector), and \(L\) is the total number of such blocks:

\[L = \prod_d \left\lfloor\frac{\text{spatial\_size}[d] + 2 \times \text{padding}[d] % - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor, \]

where \(\text{spatial\_size}\) is formed by the spatial dimensions of input (\(*\) above), and \(d\) is over all spatial dimensions.

Therefore, indexing output at the last dimension (column dimension) gives all values within a certain block.

The padding, stride and dilation arguments specify how the sliding blocks are retrieved.

• stride controls the stride for the sliding blocks.
• padding controls the amount of implicit zero-paddings on both sides for padding number of points for each dimension before reshaping.
• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

Parameters:

• kernel_size (int or tuple) – the size of the sliding blocks
• stride (int or tuple, optional) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
• padding (int or tuple, optional) – implicit zero padding to be added on both sides of input. Default: 0
• dilation (int or tuple, optional) – a parameter that controls the stride of elements within the neighborhood. Default: 1

• If kernel_size, dilation, padding or stride is an int or a tuple of length 1, their values will be replicated across all spatial dimensions.
• For the case of two input spatial dimensions this operation is sometimes called im2col.

Note

Fold calculates each combined value in the resulting large tensor by summing all values from all containing blocks. Unfold extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.

Warning

Currently, only 4-D input tensors (batched image-like tensors) are supported.

Shape:

• Input: \((N, C, *)\)
• Output: \((N, C \times \prod(\text{kernel\_size}), L)\) as described above

Examples:

>>> unfold = nn.Unfold(kernel_size=(2, 3))
>>> input = torch.randn(2, 5, 3, 4)
>>> output = unfold(input)
>>> # each patch contains 30 values (2x3=6 vectors, each of 5 channels)
>>> # 4 blocks (2x3 kernels) in total in the 3x4 input
>>> output.size()
torch.Size([2, 30, 4])

>>> # Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape)
>>> inp = torch.randn(1, 3, 10, 12)
>>> w = torch.randn(2, 3, 4, 5)
>>> inp_unf = torch.nn.functional.unfold(inp, (4, 5))
>>> out_unf = inp_unf.transpose(1, 2).matmul(w.view(w.size(0), -1).t()).transpose(1, 2)
>>> out = torch.nn.functional.fold(out_unf, (7, 8), (1, 1))
>>> # or equivalently (and avoiding a copy),
>>> # out = out_unf.view(1, 2, 7, 8)
>>> (torch.nn.functional.conv2d(inp, w) - out).abs().max()
tensor(1.9073e-06)

Fold

class torch.nn.Fold(output_size, kernel_size, dilation=1, padding=0, stride=1)

Combines an array of sliding local blocks into a large containing tensor.

Consider a batched input tensor containing sliding local blocks, e.g., patches of images, of shape \((N, C \times \prod(\text{kernel\_size}), L)\), where \(N\) is batch dimension, \(C \times \prod(\text{kernel\_size})\) is the number of values with in a block (a block has \(\prod(\text{kernel\_size})\) spatial locations each containing a \(C\)-channeled vector), and \(L\) is the total number of blocks. (This is exacly the same specification as the output shape of Unfold.) This operation combines these local blocks into the large output tensor of shape \((N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)\) by summing the overlapping values. Similar to Unfold, the arguments must satisfy

\[L = \prod_d \left\lfloor\frac{\text{output\_size}[d] + 2 \times \text{padding}[d] % - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor, \]

where \(d\) is over all spatial dimensions.

• output_size describes the spatial shape of the large containing tensor of the sliding local blocks. It is useful to resolve the ambiguity when multiple input shapes map to same number of sliding blocks, e.g., with stride > 0.

The padding, stride and dilation arguments specify how the sliding blocks are retrieved.

• stride controls the stride for the sliding blocks.
• padding controls the amount of implicit zero-paddings on both sides for padding number of points for each dimension before reshaping.
• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

Parameters:

• output_size (int or tuple) – the shape of the spatial dimensions of the output (i.e., input.sizes()[2:])
• kernel_size (int or tuple) – the size of the sliding blocks
• stride (int or tuple) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
• padding (int or tuple, optional) – implicit zero padding to be added on both sides of input. Default: 0
• dilation (int or tuple, optional) – a parameter that controls the stride of elements within the neighborhood. Default: 1

• If output_size, kernel_size, dilation, padding or stride is an int or a tuple of length 1 then their values will be replicated across all spatial dimensions.
• For the case of two output spatial dimensions this operation is sometimes called col2im.

Note

Fold calculates each combined value in the resulting large tensor by summing all values from all containing blocks. Unfold extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.

Warning

Currently, only 4-D output tensors (batched image-like tensors) are supported.

Shape:

• Input: \((N, C \times \prod(\text{kernel\_size}), L)\)
• Output: \((N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)\) as described above

Examples:

>>> fold = nn.Fold(output_size=(4, 5), kernel_size=(2, 2))
>>> input = torch.randn(1, 3 * 2 * 2, 1)
>>> output = fold(input)
>>> output.size()

Pooling layers

MaxPool1d

class torch.nn.MaxPool1d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)

Applies a 1D max pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C, L)\) and output \((N, C, L_{out})\) can be precisely described as:

\[out(N_i, C_j, k) = \max_{m=0, \ldots, \text{kernel\_size} - 1} input(N_i, C_j, stride \times k + m) \]

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points. dilation controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of what dilation does.

Parameters:

• kernel_size – the size of the window to take a max over
• stride – the stride of the window. Default value is kernel_size
• padding – implicit zero padding to be added on both sides
• dilation – a parameter that controls the stride of elements in the window
• return_indices – if True, will return the max indices along with the outputs. Useful for torch.nn.MaxUnpool1d later
• ceil_mode – when True, will use ceil instead of floor to compute the output shape

Shape:

• Input: \((N, C, L_{in})\)

• Output: \((N, C, L_{out})\), where

  \[L_{out} = \left\lfloor \frac{L_{in} + 2 \times \text{padding} - \text{dilation} \times (\text{kernel\_size} - 1) - 1}{\text{stride}} + 1\right\rfloor \]

Examples:

>>> # pool of size=3, stride=2
>>> m = nn.MaxPool1d(3, stride=2)
>>> input = torch.randn(20, 16, 50)
>>> output = m(input)

MaxPool2d

class torch.nn.MaxPool2d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)

Applies a 2D max pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C, H, W)\), output \((N, C, H_{out}, W_{out})\) and kernel_size \((kH, kW)\) can be precisely described as:

\[\begin{aligned} out(N_i, C_j, h, w) ={} & \max_{m=0, \ldots, kH-1} \max_{n=0, \ldots, kW-1} \\ & \text{input}(N_i, C_j, \text{stride[0]} \times h + m, \text{stride[1]} \times w + n) \end{aligned} \]

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points. dilation controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of what dilation does.

The parameters kernel_size, stride, padding, dilation can either be:

• a single int – in which case the same value is used for the height and width dimension
• a tuple of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension

Parameters:

• kernel_size – the size of the window to take a max over
• stride – the stride of the window. Default value is kernel_size
• padding – implicit zero padding to be added on both sides
• dilation – a parameter that controls the stride of elements in the window
• return_indices – if True, will return the max indices along with the outputs. Useful for torch.nn.MaxUnpool2d later
• ceil_mode – when True, will use ceil instead of floor to compute the output shape

Shape:

• Input: \((N, C, H_{in}, W_{in})\)

• Output: \((N, C, H_{out}, W_{out})\), where

  \[H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding[0]} - \text{dilation[0]} \times (\text{kernel\_size[0]} - 1) - 1}{\text{stride[0]}} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding[1]} - \text{dilation[1]} \times (\text{kernel\_size[1]} - 1) - 1}{\text{stride[1]}} + 1\right\rfloor \]

Examples:

>>> # pool of square window of size=3, stride=2
>>> m = nn.MaxPool2d(3, stride=2)
>>> # pool of non-square window
>>> m = nn.MaxPool2d((3, 2), stride=(2, 1))
>>> input = torch.randn(20, 16, 50, 32)
>>> output = m(input)

MaxPool3d

class torch.nn.MaxPool3d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)

Applies a 3D max pooling over an input signal composed of several input planes. This is not a test

In the simplest case, the output value of the layer with input size \((N, C, D, H, W)\), output \((N, C, D_{out}, H_{out}, W_{out})\) and kernel_size \((kD, kH, kW)\) can be precisely described as:

\[\begin{aligned} \text{out}(N_i, C_j, d, h, w) ={} & \max_{k=0, \ldots, kD-1} \max_{m=0, \ldots, kH-1} \max_{n=0, \ldots, kW-1} \\ & \text{input}(N_i, C_j, \text{stride[0]} \times k + d, \text{stride[1]} \times h + m, \text{stride[2]} \times w + n) \end{aligned} \]

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points. dilation controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of what dilation does.

The parameters kernel_size, stride, padding, dilation can either be:

• a single int – in which case the same value is used for the depth, height and width dimension
• a tuple of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension

Parameters:

• kernel_size – the size of the window to take a max over
• stride – the stride of the window. Default value is kernel_size
• padding – implicit zero padding to be added on all three sides
• dilation – a parameter that controls the stride of elements in the window
• return_indices – if True, will return the max indices along with the outputs. Useful for torch.nn.MaxUnpool3d later
• ceil_mode – when True, will use ceil instead of floor to compute the output shape

Shape:

• Input: \((N, C, D_{in}, H_{in}, W_{in})\)

• Output: \((N, C, D_{out}, H_{out}, W_{out})\), where

  \[D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] - \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor \]
  \[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] - \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] - \text{dilation}[2] \times (\text{kernel\_size}[2] - 1) - 1}{\text{stride}[2]} + 1\right\rfloor \]

Examples:

>>> # pool of square window of size=3, stride=2
>>> m = nn.MaxPool3d(3, stride=2)
>>> # pool of non-square window
>>> m = nn.MaxPool3d((3, 2, 2), stride=(2, 1, 2))
>>> input = torch.randn(20, 16, 50,44, 31)
>>> output = m(input)

MaxUnpool1d

class torch.nn.MaxUnpool1d(kernel_size, stride=None, padding=0)

Computes a partial inverse of MaxPool1d.

MaxPool1d is not fully invertible, since the non-maximal values are lost.

MaxUnpool1d takes in as input the output of MaxPool1d including the indices of the maximal values and computes a partial inverse in which all non-maximal values are set to zero.

Note

MaxPool1d can map several input sizes to the same output sizes. Hence, the inversion process can get ambiguous. To accommodate this, you can provide the needed output size as an additional argument output_size in the forward call. See the Inputs and Example below.

Parameters:

• kernel_size (int or tuple) – Size of the max pooling window.
• stride (int or tuple) – Stride of the max pooling window. It is set to kernel_size by default.
• padding (int or tuple) – Padding that was added to the input

Inputs:

• input: the input Tensor to invert
• indices: the indices given out by MaxPool1d
• output_size (optional): the targeted output size

Shape:

• Input: \((N, C, H_{in})\)

• Output: \((N, C, H_{out})\), where

  \[H_{out} = (H_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{kernel\_size}[0] \]

  or as given by output_size in the call operator

Example:

>>> pool = nn.MaxPool1d(2, stride=2, return_indices=True)
>>> unpool = nn.MaxUnpool1d(2, stride=2)
>>> input = torch.tensor([[[1., 2, 3, 4, 5, 6, 7, 8]]])
>>> output, indices = pool(input)
>>> unpool(output, indices)
tensor([[[ 0.,  2.,  0.,  4.,  0.,  6.,  0., 8.]]])

>>> # Example showcasing the use of output_size
>>> input = torch.tensor([[[1., 2, 3, 4, 5, 6, 7, 8, 9]]])
>>> output, indices = pool(input)
>>> unpool(output, indices, output_size=input.size())
tensor([[[ 0.,  2.,  0.,  4.,  0.,  6.,  0., 8.,  0.]]])

>>> unpool(output, indices)
tensor([[[ 0.,  2.,  0.,  4.,  0.,  6.,  0., 8.]]])

MaxUnpool2d

class torch.nn.MaxUnpool2d(kernel_size, stride=None, padding=0)

Computes a partial inverse of MaxPool2d.

MaxPool2d is not fully invertible, since the non-maximal values are lost.

MaxUnpool2d takes in as input the output of MaxPool2d including the indices of the maximal values and computes a partial inverse in which all non-maximal values are set to zero.

Note

MaxPool2d can map several input sizes to the same output sizes. Hence, the inversion process can get ambiguous. To accommodate this, you can provide the needed output size as an additional argument output_size in the forward call. See the Inputs and Example below.

Parameters:

• kernel_size (int or tuple) – Size of the max pooling window.
• stride (int or tuple) – Stride of the max pooling window. It is set to kernel_size by default.
• padding (int or tuple) – Padding that was added to the input

Inputs:

• input: the input Tensor to invert
• indices: the indices given out by MaxPool2d
• output_size (optional): the targeted output size

Shape:

• Input: \((N, C, H_{in}, W_{in})\)

• Output: \((N, C, H_{out}, W_{out})\), where

  \[H_{out} = (H_{in} - 1) \times \text{stride[0]} - 2 \times \text{padding[0]} + \text{kernel\_size[0]} \]
  \[W_{out} = (W_{in} - 1) \times \text{stride[1]} - 2 \times \text{padding[1]} + \text{kernel\_size[1]} \]

  or as given by output_size in the call operator

Example:

>>> pool = nn.MaxPool2d(2, stride=2, return_indices=True)
>>> unpool = nn.MaxUnpool2d(2, stride=2)
>>> input = torch.tensor([[[[ 1.,  2,  3,  4],
                            [ 5,  6,  7,  8],
                            [ 9, 10, 11, 12],
                            [13, 14, 15, 16]]]])
>>> output, indices = pool(input)
>>> unpool(output, indices)
tensor([[[[  0.,   0.,   0.,   0.],
          [  0.,   6.,   0.,   8.],
          [  0.,   0.,   0.,   0.],
          [  0.,  14.,   0.,  16.]]]])

>>> # specify a different output size than input size
>>> unpool(output, indices, output_size=torch.Size([1, 1, 5, 5]))
tensor([[[[  0.,   0.,   0.,   0.,   0.],
          [  6.,   0.,   8.,   0.,   0.],
          [  0.,   0.,   0.,  14.,   0.],
          [ 16.,   0.,   0.,   0.,   0.],
          [  0.,   0.,   0.,   0.,   0.]]]])

MaxUnpool3d

class torch.nn.MaxUnpool3d(kernel_size, stride=None, padding=0)

Computes a partial inverse of MaxPool3d.

MaxPool3d is not fully invertible, since the non-maximal values are lost. MaxUnpool3d takes in as input the output of MaxPool3d including the indices of the maximal values and computes a partial inverse in which all non-maximal values are set to zero.

Note

MaxPool3d can map several input sizes to the same output sizes. Hence, the inversion process can get ambiguous. To accommodate this, you can provide the needed output size as an additional argument output_size in the forward call. See the Inputs section below.

Parameters:

• kernel_size (int or tuple) – Size of the max pooling window.
• stride (int or tuple) – Stride of the max pooling window. It is set to kernel_size by default.
• padding (int or tuple) – Padding that was added to the input

Inputs:

• input: the input Tensor to invert
• indices: the indices given out by MaxPool3d
• output_size (optional): the targeted output size

Shape:

• Input: \((N, C, D_{in}, H_{in}, W_{in})\)

• Output: \((N, C, D_{out}, H_{out}, W_{out})\), where

  \[D_{out} = (D_{in} - 1) \times \text{stride[0]} - 2 \times \text{padding[0]} + \text{kernel\_size[0]} \]
  \[H_{out} = (H_{in} - 1) \times \text{stride[1]} - 2 \times \text{padding[1]} + \text{kernel\_size[1]} \]
  \[W_{out} = (W_{in} - 1) \times \text{stride[2]} - 2 \times \text{padding[2]} + \text{kernel\_size[2]} \]

  or as given by output_size in the call operator

Example:

>>> # pool of square window of size=3, stride=2
>>> pool = nn.MaxPool3d(3, stride=2, return_indices=True)
>>> unpool = nn.MaxUnpool3d(3, stride=2)
>>> output, indices = pool(torch.randn(20, 16, 51, 33, 15))
>>> unpooled_output = unpool(output, indices)
>>> unpooled_output.size()
torch.Size([20, 16, 51, 33, 15])

AvgPool1d

class torch.nn.AvgPool1d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)

Applies a 1D average pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C, L)\), output \((N, C, L_{out})\) and kernel_size \(k\) can be precisely described as:

\[\text{out}(N_i, C_j, l) = \frac{1}{k} \sum_{m=0}^{k} \text{input}(N_i, C_j, \text{stride} \times l + m)\]

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points.

The parameters kernel_size, stride, padding can each be an int or a one-element tuple.

Parameters:

• kernel_size – the size of the window
• stride – the stride of the window. Default value is kernel_size
• padding – implicit zero padding to be added on both sides
• ceil_mode – when True, will use ceil instead of floor to compute the output shape
• count_include_pad – when True, will include the zero-padding in the averaging calculation

Shape:

• Input: \((N, C, L_{in})\)

• Output: \((N, C, L_{out})\), where

  \[L_{out} = \left\lfloor \frac{L_{in} + 2 \times \text{padding} - \text{kernel\_size}}{\text{stride}} + 1\right\rfloor \]

Examples:

>>> # pool with window of size=3, stride=2
>>> m = nn.AvgPool1d(3, stride=2)
>>> m(torch.tensor([[[1.,2,3,4,5,6,7]]]))
tensor([[[ 2.,  4.,  6.]]])

AvgPool2d

class torch.nn.AvgPool2d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)

Applies a 2D average pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C, H, W)\), output \((N, C, H_{out}, W_{out})\) and kernel_size \((kH, kW)\) can be precisely described as:

\[out(N_i, C_j, h, w) = \frac{1}{kH * kW} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} input(N_i, C_j, stride[0] \times h + m, stride[1] \times w + n)\]

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points.

The parameters kernel_size, stride, padding can either be:

• a single int – in which case the same value is used for the height and width dimension
• a tuple of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension

Parameters:

• kernel_size – the size of the window
• stride – the stride of the window. Default value is kernel_size
• padding – implicit zero padding to be added on both sides
• ceil_mode – when True, will use ceil instead of floor to compute the output shape
• count_include_pad – when True, will include the zero-padding in the averaging calculation

Shape:

• Input: \((N, C, H_{in}, W_{in})\)

• Output: \((N, C, H_{out}, W_{out})\), where

  \[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[0] - \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[1] - \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor \]

Examples:

>>> # pool of square window of size=3, stride=2
>>> m = nn.AvgPool2d(3, stride=2)
>>> # pool of non-square window
>>> m = nn.AvgPool2d((3, 2), stride=(2, 1))
>>> input = torch.randn(20, 16, 50, 32)
>>> output = m(input)

AvgPool3d

class torch.nn.AvgPool3d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)

Applies a 3D average pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size \((N, C, D, H, W)\), output \((N, C, D_{out}, H_{out}, W_{out})\) and kernel_size \((kD, kH, kW)\) can be precisely described as:

\[\begin{aligned} \text{out}(N_i, C_j, d, h, w) ={} & \sum_{k=0}^{kD-1} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} \\ & \frac{\text{input}(N_i, C_j, \text{stride}[0] \times d + k, \text{stride}[1] \times h + m, \text{stride}[2] \times w + n)} {kD \times kH \times kW} \end{aligned} \]

If padding is non-zero, then the input is implicitly zero-padded on all three sides for padding number of points.

The parameters kernel_size, stride can either be:

• a single int – in which case the same value is used for the depth, height and width dimension
• a tuple of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension

Parameters:

• kernel_size – the size of the window
• stride – the stride of the window. Default value is kernel_size
• padding – implicit zero padding to be added on all three sides
• ceil_mode – when True, will use ceil instead of floor to compute the output shape
• count_include_pad – when True, will include the zero-padding in the averaging calculation

Shape:

• Input: \((N, C, D_{in}, H_{in}, W_{in})\)

• Output: \((N, C, D_{out}, H_{out}, W_{out})\), where

  \[D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] - \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor \]
  \[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] - \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] - \text{kernel\_size}[2]}{\text{stride}[2]} + 1\right\rfloor \]

Examples:

>>> # pool of square window of size=3, stride=2
>>> m = nn.AvgPool3d(3, stride=2)
>>> # pool of non-square window
>>> m = nn.AvgPool3d((3, 2, 2), stride=(2, 1, 2))
>>> input = torch.randn(20, 16, 50,44, 31)
>>> output = m(input)

FractionalMaxPool2d

class torch.nn.FractionalMaxPool2d(kernel_size, output_size=None, output_ratio=None, return_indices=False, _random_samples=None)

Applies a 2D fractional max pooling over an input signal composed of several input planes.

Fractional MaxPooling is described in detail in the paper Fractional MaxPooling by Ben Graham

The max-pooling operation is applied in \(kHxkW\) regions by a stochastic step size determined by the target output size. The number of output features is equal to the number of input planes.

Parameters:

• kernel_size – the size of the window to take a max over. Can be a single number k (for a square kernel of k x k) or a tuple (kh x kw)
• output_size – the target output size of the image of the form oH x oW. Can be a tuple (oH, oW) or a single number oH for a square image oH x oH
• output_ratio – If one wants to have an output size as a ratio of the input size, this option can be given. This has to be a number or tuple in the range (0, 1)
• return_indices – if True, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool2d(). Default: False

Examples

>>> # pool of square window of size=3, and target output size 13x12
>>> m = nn.FractionalMaxPool2d(3, output_size=(13, 12))
>>> # pool of square window and target output size being half of input image size
>>> m = nn.FractionalMaxPool2d(3, output_ratio=(0.5, 0.5))
>>> input = torch.randn(20, 16, 50, 32)
>>> output = m(input)

LPPool1d

class torch.nn.LPPool1d(norm_type, kernel_size, stride=None, ceil_mode=False)

Applies a 1D power-average pooling over an input signal composed of several input planes.

On each window, the function computed is:

\[f(X) = \sqrt[p]{\sum_{x \in X} x^{p}} \]

• At p = infinity, one gets Max Pooling
• At p = 1, one gets Sum Pooling (which is proportional to Average Pooling)

Note

If the sum to the power of p is zero, the gradient of this function is not defined. This implementation will set the gradient to zero in this case.

Parameters:

• kernel_size – a single int, the size of the window
• stride – a single int, the stride of the window. Default value is kernel_size
• ceil_mode – when True, will use ceil instead of floor to compute the output shape

Shape:

• Input: \((N, C, L_{in})\)

• Output: \((N, C, L_{out})\), where

  \[L_{out} = \left\lfloor\frac{L_{in} + 2 \times \text{padding} - \text{kernel\_size}}{\text{stride}} + 1\right\rfloor \]

Examples::

>>> # power-2 pool of window of length 3, with stride 2.
>>> m = nn.LPPool1d(2, 3, stride=2)
>>> input = torch.randn(20, 16, 50)
>>> output = m(input)

LPPool2d

class torch.nn.LPPool2d(norm_type, kernel_size, stride=None, ceil_mode=False)

Applies a 2D power-average pooling over an input signal composed of several input planes.

On each window, the function computed is:

\[f(X) = \sqrt[p]{\sum_{x \in X} x^{p}} \]

• At p = \(\infty\), one gets Max Pooling
• At p = 1, one gets Sum Pooling (which is proportional to average pooling)

The parameters kernel_size, stride can either be:

• a single int – in which case the same value is used for the height and width dimension
• a tuple of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension

Note

If the sum to the power of p is zero, the gradient of this function is not defined. This implementation will set the gradient to zero in this case.

Parameters:

• kernel_size – the size of the window
• stride – the stride of the window. Default value is kernel_size
• ceil_mode – when True, will use ceil instead of floor to compute the output shape

Shape:

• Input: \((N, C, H_{in}, W_{in})\)

• Output: \((N, C, H_{out}, W_{out})\), where

  \[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[0] - \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor \]
  \[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[1] - \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor \]

Examples:

>>> # power-2 pool of square window of size=3, stride=2
>>> m = nn.LPPool2d(2, 3, stride=2)
>>> # pool of non-square window of power 1.2
>>> m = nn.LPPool2d(1.2, (3, 2), stride=(2, 1))
>>> input = torch.randn(20, 16, 50, 32)
>>> output = m(input)

AdaptiveMaxPool1d

class torch.nn.AdaptiveMaxPool1d(output_size, return_indices=False)

Applies a 1D adaptive max pooling over an input signal composed of several input planes.

The output size is H, for any input size. The number of output features is equal to the number of input planes.

Parameters:

• output_size – the target output size H
• return_indices – if True, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool1d. Default: False

Examples

>>> # target output size of 5
>>> m = nn.AdaptiveMaxPool1d(5)
>>> input = torch.randn(1, 64, 8)
>>> output = m(input)

AdaptiveMaxPool2d

class torch.nn.AdaptiveMaxPool2d(output_size, return_indices=False)

Applies a 2D adaptive max pooling over an input signal composed of several input planes.

The output is of size H x W, for any input size. The number of output features is equal to the number of input planes.

Parameters:

• output_size – the target output size of the image of the form H x W. Can be a tuple (H, W) or a single H for a square image H x H. H and W can be either a int, or None which means the size will be the same as that of the input.
• return_indices – if True, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool2d. Default: False

Examples

>>> # target output size of 5x7
>>> m = nn.AdaptiveMaxPool2d((5,7))
>>> input = torch.randn(1, 64, 8, 9)
>>> output = m(input)
>>> # target output size of 7x7 (square)
>>> m = nn.AdaptiveMaxPool2d(7)
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)
>>> # target output size of 10x7
>>> m = nn.AdaptiveMaxPool2d((None, 7))
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)

AdaptiveMaxPool3d

class torch.nn.AdaptiveMaxPool3d(output_size, return_indices=False)

Applies a 3D adaptive max pooling over an input signal composed of several input planes.

The output is of size D x H x W, for any input size. The number of output features is equal to the number of input planes.

Parameters:

• output_size – the target output size of the image of the form D x H x W. Can be a tuple (D, H, W) or a single D for a cube D x D x D. D, H and W can be either a int, or None which means the size will be the same as that of the input.
• return_indices – if True, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool3d. Default: False

Examples

>>> # target output size of 5x7x9
>>> m = nn.AdaptiveMaxPool3d((5,7,9))
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> m = nn.AdaptiveMaxPool3d(7)
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)
>>> # target output size of 7x9x8
>>> m = nn.AdaptiveMaxPool3d((7, None, None))
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)

AdaptiveAvgPool1d

class torch.nn.AdaptiveAvgPool1d(output_size)

Applies a 1D adaptive average pooling over an input signal composed of several input planes.

The output size is H, for any input size. The number of output features is equal to the number of input planes.

Parameters:output_size – the target output size H

Examples

>>> # target output size of 5
>>> m = nn.AdaptiveAvgPool1d(5)
>>> input = torch.randn(1, 64, 8)
>>> output = m(input)

AdaptiveAvgPool2d

class torch.nn.AdaptiveAvgPool2d(output_size)

Applies a 2D adaptive average pooling over an input signal composed of several input planes.

The output is of size H x W, for any input size. The number of output features is equal to the number of input planes.

Parameters:output_size – the target output size of the image of the form H x W. Can be a tuple (H, W) or a single H for a square image H x H H and W can be either a int, or None which means the size will be the same as that of the input.

Examples

>>> # target output size of 5x7
>>> m = nn.AdaptiveAvgPool2d((5,7))
>>> input = torch.randn(1, 64, 8, 9)
>>> output = m(input)
>>> # target output size of 7x7 (square)
>>> m = nn.AdaptiveAvgPool2d(7)
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)
>>> # target output size of 10x7
>>> m = nn.AdaptiveMaxPool2d((None, 7))
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)

AdaptiveAvgPool3d

class torch.nn.AdaptiveAvgPool3d(output_size)

Applies a 3D adaptive average pooling over an input signal composed of several input planes.

The output is of size D x H x W, for any input size. The number of output features is equal to the number of input planes.

Parameters:output_size – the target output size of the form D x H x W. Can be a tuple (D, H, W) or a single number D for a cube D x D x D D, H and W can be either a int, or None which means the size will be the same as that of the input.

Examples

>>> # target output size of 5x7x9
>>> m = nn.AdaptiveAvgPool3d((5,7,9))
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> m = nn.AdaptiveAvgPool3d(7)
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)
>>> # target output size of 7x9x8
>>> m = nn.AdaptiveMaxPool3d((7, None, None))
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)

Padding layers

ReflectionPad1d

class torch.nn.ReflectionPad1d(padding)

Pads the input tensor using the reflection of the input boundary.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 2-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\))

Shape:

• Input: \((N, C, W_{in})\)
• Output: \((N, C, W_{out})\) where \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ReflectionPad1d(2)
>>> input = torch.arange(8, dtype=torch.float).reshape(1, 2, 4)
>>> input
tensor([[[0., 1., 2., 3.],
         [4., 5., 6., 7.]]])
>>> m(input)
tensor([[[2., 1., 0., 1., 2., 3., 2., 1.],
         [6., 5., 4., 5., 6., 7., 6., 5.]]])
>>> m(input)
tensor([[[2., 1., 0., 1., 2., 3., 2., 1.],
         [6., 5., 4., 5., 6., 7., 6., 5.]]])
>>> # using different paddings for different sides
>>> m = nn.ReflectionPad1d((3, 1))
>>> m(input)
tensor([[[3., 2., 1., 0., 1., 2., 3., 2.],
         [7., 6., 5., 4., 5., 6., 7., 6.]]])

ReflectionPad2d

class torch.nn.ReflectionPad2d(padding)

Pads the input tensor using the reflection of the input boundary.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))

Shape:

• Input: \((N, C, H_{in}, W_{in})\)

• Output: \((N, C, H_{out}, W_{out})\) where

  \(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\) \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ReflectionPad2d(2)
>>> input = torch.arange(9, dtype=torch.float).reshape(1, 1, 3, 3)
>>> input
tensor([[[[0., 1., 2.],
          [3., 4., 5.],
          [6., 7., 8.]]]])
>>> m(input)
tensor([[[[8., 7., 6., 7., 8., 7., 6.],
          [5., 4., 3., 4., 5., 4., 3.],
          [2., 1., 0., 1., 2., 1., 0.],
          [5., 4., 3., 4., 5., 4., 3.],
          [8., 7., 6., 7., 8., 7., 6.],
          [5., 4., 3., 4., 5., 4., 3.],
          [2., 1., 0., 1., 2., 1., 0.]]]])
>>> # using different paddings for different sides
>>> m = nn.ReflectionPad2d((1, 1, 2, 0))
>>> m(input)
tensor([[[[7., 6., 7., 8., 7.],
          [4., 3., 4., 5., 4.],
          [1., 0., 1., 2., 1.],
          [4., 3., 4., 5., 4.],
          [7., 6., 7., 8., 7.]]]])

ReplicationPad1d

class torch.nn.ReplicationPad1d(padding)

Pads the input tensor using replication of the input boundary.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 2-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\))

Shape:

• Input: \((N, C, W_{in})\)
• Output: \((N, C, W_{out})\) where \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ReplicationPad1d(2)
>>> input = torch.arange(8, dtype=torch.float).reshape(1, 2, 4)
>>> input
tensor([[[0., 1., 2., 3.],
         [4., 5., 6., 7.]]])
>>> m(input)
tensor([[[0., 0., 0., 1., 2., 3., 3., 3.],
         [4., 4., 4., 5., 6., 7., 7., 7.]]])
>>> # using different paddings for different sides
>>> m = nn.ReplicationPad1d((3, 1))
>>> m(input)
tensor([[[0., 0., 0., 0., 1., 2., 3., 3.],
         [4., 4., 4., 4., 5., 6., 7., 7.]]])

ReplicationPad2d

class torch.nn.ReplicationPad2d(padding)

Pads the input tensor using replication of the input boundary.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))

Shape:

• Input: \((N, C, H_{in}, W_{in})\)
• Output: \((N, C, H_{out}, W_{out})\) where \(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\) \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ReplicationPad2d(2)
>>> input = torch.arange(9, dtype=torch.float).reshape(1, 1, 3, 3)
>>> input
tensor([[[[0., 1., 2.],
          [3., 4., 5.],
          [6., 7., 8.]]]])
>>> m(input)
tensor([[[[0., 0., 0., 1., 2., 2., 2.],
          [0., 0., 0., 1., 2., 2., 2.],
          [0., 0., 0., 1., 2., 2., 2.],
          [3., 3., 3., 4., 5., 5., 5.],
          [6., 6., 6., 7., 8., 8., 8.],
          [6., 6., 6., 7., 8., 8., 8.],
          [6., 6., 6., 7., 8., 8., 8.]]]])
>>> # using different paddings for different sides
>>> m = nn.ReplicationPad2d((1, 1, 2, 0))
>>> m(input)
tensor([[[[0., 0., 1., 2., 2.],
          [0., 0., 1., 2., 2.],
          [0., 0., 1., 2., 2.],
          [3., 3., 4., 5., 5.],
          [6., 6., 7., 8., 8.]]]])

ReplicationPad3d

class torch.nn.ReplicationPad3d(padding)

Pads the input tensor using replication of the input boundary.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 6-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\), \(\text{padding\_front}\), \(\text{padding\_back}\))

Shape:

• Input: \((N, C, D_{in}, H_{in}, W_{in})\)
• Output: \((N, C, D_{out}, H_{out}, W_{out})\) where \(D_{out} = D_{in} + \text{padding\_front} + \text{padding\_back}\) \(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\) \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ReplicationPad3d(3)
>>> input = torch.randn(16, 3, 8, 320, 480)
>>> output = m(input)
>>> # using different paddings for different sides
>>> m = nn.ReplicationPad3d((3, 3, 6, 6, 1, 1))
>>> output = m(input)

ZeroPad2d

class torch.nn.ZeroPad2d(padding)

Pads the input tensor boundaries with zero.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))

Shape:

• Input: \((N, C, H_{in}, W_{in})\)
• Output: \((N, C, H_{out}, W_{out})\) where \(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\) \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ZeroPad2d(2)
>>> input = torch.randn(1, 1, 3, 3)
>>> input
tensor([[[[-0.1678, -0.4418,  1.9466],
          [ 0.9604, -0.4219, -0.5241],
          [-0.9162, -0.5436, -0.6446]]]])
>>> m(input)
tensor([[[[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
          [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
          [ 0.0000,  0.0000, -0.1678, -0.4418,  1.9466,  0.0000,  0.0000],
          [ 0.0000,  0.0000,  0.9604, -0.4219, -0.5241,  0.0000,  0.0000],
          [ 0.0000,  0.0000, -0.9162, -0.5436, -0.6446,  0.0000,  0.0000],
          [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
          [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000]]]])
>>> # using different paddings for different sides
>>> m = nn.ZeroPad2d((1, 1, 2, 0))
>>> m(input)
tensor([[[[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
          [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
          [ 0.0000, -0.1678, -0.4418,  1.9466,  0.0000],
          [ 0.0000,  0.9604, -0.4219, -0.5241,  0.0000],
          [ 0.0000, -0.9162, -0.5436, -0.6446,  0.0000]]]])

ConstantPad1d

class torch.nn.ConstantPad1d(padding, value)

Pads the input tensor boundaries with a constant value.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in both boundaries. If a 2-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\))

Shape:

• Input: \((N, C, W_{in})\)
• Output: \((N, C, W_{out})\) where \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ConstantPad1d(2, 3.5)
>>> input = torch.randn(1, 2, 4)
>>> input
tensor([[[-1.0491, -0.7152, -0.0749,  0.8530],
         [-1.3287,  1.8966,  0.1466, -0.2771]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000, -1.0491, -0.7152, -0.0749,  0.8530,  3.5000,
           3.5000],
         [ 3.5000,  3.5000, -1.3287,  1.8966,  0.1466, -0.2771,  3.5000,
           3.5000]]])
>>> m = nn.ConstantPad1d(2, 3.5)
>>> input = torch.randn(1, 2, 3)
>>> input
tensor([[[ 1.6616,  1.4523, -1.1255],
         [-3.6372,  0.1182, -1.8652]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000,  1.6616,  1.4523, -1.1255,  3.5000,  3.5000],
         [ 3.5000,  3.5000, -3.6372,  0.1182, -1.8652,  3.5000,  3.5000]]])
>>> # using different paddings for different sides
>>> m = nn.ConstantPad1d((3, 1), 3.5)
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  1.6616,  1.4523, -1.1255,  3.5000],
         [ 3.5000,  3.5000,  3.5000, -3.6372,  0.1182, -1.8652,  3.5000]]])

ConstantPad2d

class torch.nn.ConstantPad2d(padding, value)

Pads the input tensor boundaries with a constant value.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))

Shape:

• Input: \((N, C, H_{in}, W_{in})\)
• Output: \((N, C, H_{out}, W_{out})\) where \(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\) \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ConstantPad2d(2, 3.5)
>>> input = torch.randn(1, 2, 2)
>>> input
tensor([[[ 1.6585,  0.4320],
         [-0.8701, -0.4649]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  1.6585,  0.4320,  3.5000,  3.5000],
         [ 3.5000,  3.5000, -0.8701, -0.4649,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  1.6585,  0.4320,  3.5000,  3.5000],
         [ 3.5000,  3.5000, -0.8701, -0.4649,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000]]])
>>> # using different paddings for different sides
>>> m = nn.ConstantPad2d((3, 0, 2, 1), 3.5)
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
         [ 3.5000,  3.5000,  3.5000,  1.6585,  0.4320],
         [ 3.5000,  3.5000,  3.5000, -0.8701, -0.4649],
         [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000]]])

ConstantPad3d

class torch.nn.ConstantPad3d(padding, value)

Pads the input tensor boundaries with a constant value.

For N-dimensional padding, use torch.nn.functional.pad().

Parameters:padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 6-tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\), \(\text{padding\_front}\), \(\text{padding\_back}\))

Shape:

• Input: \((N, C, D_{in}, H_{in}, W_{in})\)
• Output: \((N, C, D_{out}, H_{out}, W_{out})\) where \(D_{out} = D_{in} + \text{padding\_front} + \text{padding\_back}\) \(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\) \(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)

Examples:

>>> m = nn.ConstantPad3d(3, 3.5)
>>> input = torch.randn(16, 3, 10, 20, 30)
>>> output = m(input)
>>> # using different paddings for different sides
>>> m = nn.ConstantPad3d((3, 3, 6, 6, 0, 1), 3.5)
>>> output = m(input)

Non-linear activations (weighted sum, nonlinearity)

ELU

class torch.nn.ELU(alpha=1.0, inplace=False)

Applies the element-wise function:

\[\text{ELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x) - 1)) \]

Parameters:

• alpha – the \(\alpha\) value for the ELU formulation. Default: 1.0
• inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.ELU()
>>> input = torch.randn(2)
>>> output = m(input)

Hardshrink

class torch.nn.Hardshrink(lambd=0.5)

Applies the hard shrinkage function element-wise:

\[\text{HardShrink}(x) = \begin{cases} x, & \text{ if } x > \lambda \\ x, & \text{ if } x < -\lambda \\ 0, & \text{ otherwise } \end{cases} \]

Parameters:lambd – the \(\lambda\) value for the Hardshrink formulation. Default: 0.5

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Hardshrink()
>>> input = torch.randn(2)
>>> output = m(input)

Hardtanh

class torch.nn.Hardtanh(min_val=-1.0, max_val=1.0, inplace=False, min_value=None, max_value=None)

Applies the HardTanh function element-wise

HardTanh is defined as:

\[\text{HardTanh}(x) = \begin{cases} 1 & \text{ if } x > 1 \\ -1 & \text{ if } x < -1 \\ x & \text{ otherwise } \\ \end{cases} \]

The range of the linear region \([-1, 1]\) can be adjusted using min_val and max_val.

Parameters:

• min_val – minimum value of the linear region range. Default: -1
• max_val – maximum value of the linear region range. Default: 1
• inplace – can optionally do the operation in-place. Default: False

Keyword arguments min_value and max_value have been deprecated in favor of min_val and max_val.

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Hardtanh(-2, 2)
>>> input = torch.randn(2)
>>> output = m(input)

LeakyReLU

class torch.nn.LeakyReLU(negative_slope=0.01, inplace=False)

Applies the element-wise function:

\[\text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x) \]

or

\[\text{LeakyRELU}(x) = \begin{cases} x, & \text{ if } x \geq 0 \\ \text{negative\_slope} \times x, & \text{ otherwise } \end{cases} \]

Parameters:

• negative_slope – Controls the angle of the negative slope. Default: 1e-2
• inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.LeakyReLU(0.1)
>>> input = torch.randn(2)
>>> output = m(input)

LogSigmoid

class torch.nn.LogSigmoid

Applies the element-wise function:

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.LogSigmoid()
>>> input = torch.randn(2)
>>> output = m(input)

PReLU

class torch.nn.PReLU(num_parameters=1, init=0.25)

Applies the element-wise function:

\[\text{PReLU}(x) = \max(0,x) + a * \min(0,x) \]

or

\[\text{PReLU}(x) = \begin{cases} x, & \text{ if } x \geq 0 \\ ax, & \text{ otherwise } \end{cases} \]

Here \(a\) is a learnable parameter. When called without arguments, nn.PReLU() uses a single parameter \(a\) across all input channels. If called with nn.PReLU(nChannels), a separate \(a\) is used for each input channel.

Note

weight decay should not be used when learning \(a\) for good performance.

Note

Channel dim is the 2nd dim of input. When input has dims < 2, then there is no channel dim and the number of channels = 1.

Parameters:

• num_parameters (int) – number of \(a\) to learn. Although it takes an int as input, there is only two values are legitimate: 1, or the number of channels at input. Default: 1
• init (float) – the initial value of \(a\). Default: 0.25

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Variables:weight (Tensor) – the learnable weights of shape (attr:num_parameters). The attr:dtype is default to

Examples:

>>> m = nn.PReLU()
>>> input = torch.randn(2)
>>> output = m(input)

ReLU

class torch.nn.ReLU(inplace=False)

Applies the rectified linear unit function element-wise \(\text{ReLU}(x)= \max(0, x)\)

Parameters:inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.ReLU()
>>> input = torch.randn(2)
>>> output = m(input)

ReLU6

class torch.nn.ReLU6(inplace=False)

Applies the element-wise function:

\[\text{ReLU6}(x) = \min(\max(0,x), 6) \]

Parameters:inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.ReLU6()
>>> input = torch.randn(2)
>>> output = m(input)

RReLU

class torch.nn.RReLU(lower=0.125, upper=0.3333333333333333, inplace=False)

Applies the randomized leaky rectified liner unit function, element-wise, as described in the paper:

Empirical Evaluation of Rectified Activations in Convolutional Network.

The function is defined as:

\[\text{RReLU}(x) = \begin{cases} x & \text{if } x \geq 0 \\ ax & \text{ otherwise } \end{cases} \]

where \(a\) is randomly sampled from uniform distribution \(\mathcal{U}(\text{lower}, \text{upper})\).

See: https://arxiv.org/pdf/1505.00853.pdf

Parameters:

• lower – lower bound of the uniform distribution. Default: \(\frac{1}{8}\)
• upper – upper bound of the uniform distribution. Default: \(\frac{1}{3}\)
• inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.RReLU(0.1, 0.3)
>>> input = torch.randn(2)
>>> output = m(input)

SELU

class torch.nn.SELU(inplace=False)

Applied element-wise, as:

\[\text{SELU}(x) = \text{scale} * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1))) \]

with \(\alpha = 1.6732632423543772848170429916717\) and \(\text{scale} = 1.0507009873554804934193349852946\).

More details can be found in the paper Self-Normalizing Neural Networks .

Parameters:inplace (bool, optional) – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.SELU()
>>> input = torch.randn(2)
>>> output = m(input)

CELU

class torch.nn.CELU(alpha=1.0, inplace=False)

Applies the element-wise function:

\[\text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x/\alpha) - 1)) \]

More details can be found in the paper Continuously Differentiable Exponential Linear Units .

Parameters:

• alpha – the \(\alpha\) value for the CELU formulation. Default: 1.0
• inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.CELU()
>>> input = torch.randn(2)
>>> output = m(input)

Sigmoid

class torch.nn.Sigmoid

Applies the element-wise function:

\[\text{Sigmoid}(x) = \frac{1}{1 + \exp(-x)} \]

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Sigmoid()
>>> input = torch.randn(2)
>>> output = m(input)

Softplus

class torch.nn.Softplus(beta=1, threshold=20)

Applies the element-wise function:

\[\text{Softplus}(x) = \frac{1}{\beta} * \log(1 + \exp(\beta * x)) \]

SoftPlus is a smooth approximation to the ReLU function and can be used to constrain the output of a machine to always be positive.

For numerical stability the implementation reverts to the linear function for inputs above a certain value.

Parameters:

• beta – the \(\beta\) value for the Softplus formulation. Default: 1
• threshold – values above this revert to a linear function. Default: 20

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Softplus()
>>> input = torch.randn(2)
>>> output = m(input)

Softshrink

class torch.nn.Softshrink(lambd=0.5)

Applies the soft shrinkage function elementwise:

\[\text{SoftShrinkage}(x) = \begin{cases} x - \lambda, & \text{ if } x > \lambda \\ x + \lambda, & \text{ if } x < -\lambda \\ 0, & \text{ otherwise } \end{cases} \]

Parameters:lambd – the \(\lambda\) value for the Softshrink formulation. Default: 0.5

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Softshrink()
>>> input = torch.randn(2)
>>> output = m(input)

Softsign

class torch.nn.Softsign

Applies the element-wise function:

\[\text{SoftSign}(x) = \frac{x}{ 1 + |x|} \]

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Softsign()
>>> input = torch.randn(2)
>>> output = m(input)

Tanh

class torch.nn.Tanh

Applies the element-wise function:

\[\text{Tanh}(x) = \tanh(x) = \frac{e^x - e^{-x}} {e^x + e^{-x}} \]

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Tanh()
>>> input = torch.randn(2)
>>> output = m(input)

Tanhshrink

class torch.nn.Tanhshrink

Applies the element-wise function:

\[\text{Tanhshrink}(x) = x - \text{Tanh}(x) \]

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Tanhshrink()
>>> input = torch.randn(2)
>>> output = m(input)

Threshold

class torch.nn.Threshold(threshold, value, inplace=False)

Thresholds each element of the input Tensor

Threshold is defined as:

\[y = \begin{cases} x, &\text{ if } x > \text{threshold} \\ \text{value}, &\text{ otherwise } \end{cases} \]

Parameters:

• threshold – The value to threshold at
• value – The value to replace with
• inplace – can optionally do the operation in-place. Default: False

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Output: \((N, *)\), same shape as the input

Examples:

>>> m = nn.Threshold(0.1, 20)
>>> input = torch.randn(2)
>>> output = m(input)

Non-linear activations (other)

Softmin

class torch.nn.Softmin(dim=None)

Applies the Softmin function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range (0, 1) and sum to 1

\[\text{Softmin}(x_{i}) = \frac{\exp(-x_i)}{\sum_j \exp(-x_j)} \]

Shape:

• Input: any shape
• Output: same as input

Parameters:dim (int) – A dimension along which Softmin will be computed (so every slice along dim will sum to 1). Returns:a Tensor of the same dimension and shape as the input, with values in the range [0, 1]

Examples:

>>> m = nn.Softmin()
>>> input = torch.randn(2, 3)
>>> output = m(input)

Softmax

class torch.nn.Softmax(dim=None)

Applies the Softmax function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range (0,1) and sum to 1

Softmax is defined as:

\[\text{Softmax}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)} \]

Shape:

• Input: any shape
• Output: same as input

Returns:a Tensor of the same dimension and shape as the input with values in the range [0, 1] Parameters:dim (int) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1).

Note

This module doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use LogSoftmax instead (it’s faster and has better numerical properties).

Examples:

>>> m = nn.Softmax()
>>> input = torch.randn(2, 3)
>>> output = m(input)

Softmax2d

class torch.nn.Softmax2d

Applies SoftMax over features to each spatial location.

When given an image of Channels x Height x Width, it will apply Softmax to each location \((Channels, h_i, w_j)\)

Shape:

• Input: \((N, C, H, W)\)
• Output: \((N, C, H, W)\) (same shape as input)

Returns:a Tensor of the same dimension and shape as the input with values in the range [0, 1]

Examples:

>>> m = nn.Softmax2d()
>>> # you softmax over the 2nd dimension
>>> input = torch.randn(2, 3, 12, 13)
>>> output = m(input)

LogSoftmax

class torch.nn.LogSoftmax(dim=None)

Applies the \(\log(\text{Softmax}(x))\) function to an n-dimensional input Tensor. The LogSoftmax formulation can be simplified as:

\[\text{LogSoftmax}(x_{i}) = \log\left(\frac{\exp(x_i) }{ \sum_j \exp(x_j)} \right) \]

Shape:

• Input: any shape
• Output: same as input

Parameters:dim (int) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1). Returns:a Tensor of the same dimension and shape as the input with values in the range [-inf, 0)

Examples:

>>> m = nn.LogSoftmax()
>>> input = torch.randn(2, 3)
>>> output = m(input)

AdaptiveLogSoftmaxWithLoss

class torch.nn.AdaptiveLogSoftmaxWithLoss(in_features, n_classes, cutoffs, div_value=4.0, head_bias=False)

Efficient softmax approximation as described in Efficient softmax approximation for GPUs by Edouard Grave, Armand Joulin, Moustapha Cissé, David Grangier, and Hervé Jégou.

Adaptive softmax is an approximate strategy for training models with large output spaces. It is most effective when the label distribution is highly imbalanced, for example in natural language modelling, where the word frequency distribution approximately follows the Zipf’s law.

Adaptive softmax partitions the labels into several clusters, according to their frequency. These clusters may contain different number of targets each. Additionally, clusters containing less frequent labels assign lower dimensional embeddings to those labels, which speeds up the computation. For each minibatch, only clusters for which at least one target is present are evaluated.

The idea is that the clusters which are accessed frequently (like the first one, containing most frequent labels), should also be cheap to compute – that is, contain a small number of assigned labels.

We highly recommend taking a look at the original paper for more details.

• cutoffs should be an ordered Sequence of integers sorted in the increasing order. It controls number of clusters and the partitioning of targets into clusters. For example setting cutoffs = [10, 100, 1000] means that first 10 targets will be assigned to the ‘head’ of the adaptive softmax, targets 11, 12, …, 100 will be assigned to the first cluster, and targets 101, 102, …, 1000 will be assigned to the second cluster, while targets 1001, 1002, …, n_classes - 1 will be assigned to the last, third cluster
• div_value is used to compute the size of each additional cluster, which is given as \(\left\lfloor\frac{in\_features}{div\_value^{idx}}\right\rfloor\), where \(idx\) is the cluster index (with clusters for less frequent words having larger indices, and indices starting from \(1\)).
• head_bias if set to True, adds a bias term to the ‘head’ of the adaptive softmax. See paper for details. Set to False in the official implementation.

Warning

Labels passed as inputs to this module should be sorted accoridng to their frequency. This means that the most frequent label should be represented by the index 0, and the least frequent label should be represented by the index n_classes - 1.

Note

This module returns a NamedTuple with output and loss fields. See further documentation for details.

Note

To compute log-probabilities for all classes, the log_prob method can be used.

Parameters:

• in_features (int) – Number of features in the input tensor
• n_classes (int) – Number of classes in the dataset.
• cutoffs (Sequence) – Cutoffs used to assign targets to their buckets.
• div_value (float, optional) – value used as an exponent to compute sizes of the clusters. Default: 4.0

Returns:

• output is a Tensor of size N containing computed target log probabilities for each example
• loss is a Scalar representing the computed negative log likelihood loss

Return type:

NamedTuple with output and loss fields

Shape:

• input: \((N, in\_features)\)
• target: \((N)\) where each value satisfies \(0 <= target[i] <= n\_classes\)
• output: \((N)\)
• loss: Scalar

log_prob(input)

Computes log probabilities for all \(n\_classes\)

Parameters:input (Tensor) – a minibatch of examples Returns:log-probabilities of for each class \(c\) in range \(0 <= c <= n\_classes\), where \(n\_classes\) is a parameter passed to AdaptiveLogSoftmaxWithLoss constructor.

Shape:

• Input: \((N, in\_features)\)
• Output: \((N, n\_classes)\)

predict(input)

This is equivalent to self.log_pob(input).argmax(dim=1), but is more efficient in some cases.

Parameters:input (Tensor) – a minibatch of examples Returns:a class with the highest probability for each example Return type:output (Tensor)

Shape:

• Input: \((N, in\_features)\)
• Output: \((N)\)

Normalization layers

BatchNorm1d

class torch.nn.BatchNorm1d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)

Applies Batch Normalization over a 2D or 3D input (a mini-batch of 1D inputs with optional additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

\[y = \frac{x - \mathrm{E}[x]}{\sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension over the mini-batches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.

Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, L) slices, it’s common terminology to call this Temporal Batch Normalization.

Parameters:

• num_features – \(C\) from an expected input of size \((N, C, L)\) or \(L\) from input of size \((N, L)\)
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• momentum – the value used for the running_mean and running_var computation. Can be set to None for cumulative moving average (i.e. simple average). Default: 0.1
• affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True
• track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: True

Shape:

• Input: \((N, C)\) or \((N, C, L)\)
• Output: \((N, C)\) or \((N, C, L)\) (same shape as input)

Examples:

>>> # With Learnable Parameters
>>> m = nn.BatchNorm1d(100)
>>> # Without Learnable Parameters
>>> m = nn.BatchNorm1d(100, affine=False)
>>> input = torch.randn(20, 100)
>>> output = m(input)

BatchNorm2d

class torch.nn.BatchNorm2d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)

Applies Batch Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension over the mini-batches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.

Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, H, W) slices, it’s common terminology to call this Spatial Batch Normalization.

Parameters:

• num_features – \(C\) from an expected input of size \((N, C, H, W)\)
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• momentum – the value used for the running_mean and running_var computation. Can be set to None for cumulative moving average (i.e. simple average). Default: 0.1
• affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True
• track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: True

Shape:

• Input: \((N, C, H, W)\)
• Output: \((N, C, H, W)\) (same shape as input)

Examples:

>>> # With Learnable Parameters
>>> m = nn.BatchNorm2d(100)
>>> # Without Learnable Parameters
>>> m = nn.BatchNorm2d(100, affine=False)
>>> input = torch.randn(20, 100, 35, 45)
>>> output = m(input)

BatchNorm3d

class torch.nn.BatchNorm3d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)

Applies Batch Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension over the mini-batches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.

Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, D, H, W) slices, it’s common terminology to call this Volumetric Batch Normalization or Spatio-temporal Batch Normalization.

Parameters:

• num_features – \(C\) from an expected input of size \((N, C, D, H, W)\)
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• momentum – the value used for the running_mean and running_var computation. Can be set to None for cumulative moving average (i.e. simple average). Default: 0.1
• affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True
• track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: True

Shape:

• Input: \((N, C, D, H, W)\)
• Output: \((N, C, D, H, W)\) (same shape as input)

Examples:

>>> # With Learnable Parameters
>>> m = nn.BatchNorm3d(100)
>>> # Without Learnable Parameters
>>> m = nn.BatchNorm3d(100, affine=False)
>>> input = torch.randn(20, 100, 35, 45, 10)
>>> output = m(input)

GroupNorm

class torch.nn.GroupNorm(num_groups, num_channels, eps=1e-05, affine=True)

Applies Group Normalization over a mini-batch of inputs as described in the paper Group Normalization .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta \]

The input channels are separated into num_groups groups, each containing num_channels / num_groups channels. The mean and standard-deviation are calculated separately over the each group. \(\gamma\) and \(\beta\) are learnable per-channel affine transform parameter vectorss of size num_channels if affine is True.

This layer uses statistics computed from input data in both training and evaluation modes.

Parameters:

• num_groups (int) – number of groups to separate the channels into
• num_channels (int) – number of channels expected in input
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• affine – a boolean value that when set to True, this module has learnable per-channel affine parameters initialized to ones (for weights) and zeros (for biases). Default: True.

Shape:

• Input: \((N, num\_channels, *)\)
• Output: \((N, num\_channels, *)\) (same shape as input)

Examples:

>>> input = torch.randn(20, 6, 10, 10)
>>> # Separate 6 channels into 3 groups
>>> m = nn.GroupNorm(3, 6)
>>> # Separate 6 channels into 6 groups (equivalent with InstanceNorm)
>>> m = nn.GroupNorm(6, 6)
>>> # Put all 6 channels into a single group (equivalent with LayerNorm)
>>> m = nn.GroupNorm(1, 6)
>>> # Activating the module
>>> output = m(input)

InstanceNorm1d

class torch.nn.InstanceNorm1d(num_features, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)

Applies Instance Normalization over a 2D or 3D input (a mini-batch of 1D inputs with optional additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size) if affine is True.

By default, this layer uses instance statistics computed from input data in both training and evaluation modes.

If track_running_stats is set to True, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Note

InstanceNorm1d and LayerNorm are very similar, but have some subtle differences. InstanceNorm1d is applied on each channel of channeled data like multidimensional time series, but LayerNorm is usually applied on entire sample and often in NLP tasks. Additionaly, LayerNorm applies elementwise affine transform, while InstanceNorm1d usually don’t apply affine transform.

Parameters:

• num_features – \(C\) from an expected input of size \((N, C, L)\) or \(L\) from input of size \((N, L)\)
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• momentum – the value used for the running_mean and running_var computation. Default: 0.1
• affine – a boolean value that when set to True, this module has learnable affine parameters, initialized the same way as done for batch normalization. Default: False.
• track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: False

Shape:

• Input: \((N, C, L)\)
• Output: \((N, C, L)\) (same shape as input)

Examples:

>>> # Without Learnable Parameters
>>> m = nn.InstanceNorm1d(100)
>>> # With Learnable Parameters
>>> m = nn.InstanceNorm1d(100, affine=True)
>>> input = torch.randn(20, 100, 40)
>>> output = m(input)

InstanceNorm2d

class torch.nn.InstanceNorm2d(num_features, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)

Applies Instance Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size) if affine is True.

By default, this layer uses instance statistics computed from input data in both training and evaluation modes.

If track_running_stats is set to True, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Note

InstanceNorm2d and LayerNorm are very similar, but have some subtle differences. InstanceNorm2d is applied on each channel of channeled data like RGB images, but LayerNorm is usually applied on entire sample and often in NLP tasks. Additionaly, LayerNorm applies elementwise affine transform, while InstanceNorm2d usually don’t apply affine transform.

Parameters:

• num_features – \(C\) from an expected input of size \((N, C, H, W)\)
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• momentum – the value used for the running_mean and running_var computation. Default: 0.1
• affine – a boolean value that when set to True, this module has learnable affine parameters, initialized the same way as done for batch normalization. Default: False.
• track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: False

Shape:

• Input: \((N, C, H, W)\)
• Output: \((N, C, H, W)\) (same shape as input)

Examples:

>>> # Without Learnable Parameters
>>> m = nn.InstanceNorm2d(100)
>>> # With Learnable Parameters
>>> m = nn.InstanceNorm2d(100, affine=True)
>>> input = torch.randn(20, 100, 35, 45)
>>> output = m(input)

InstanceNorm3d

class torch.nn.InstanceNorm3d(num_features, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)

Applies Instance Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size) if affine is True.

By default, this layer uses instance statistics computed from input data in both training and evaluation modes.

If track_running_stats is set to True, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Note

InstanceNorm3d and LayerNorm are very similar, but have some subtle differences. InstanceNorm3d is applied on each channel of channeled data like 3D models with RGB color, but LayerNorm is usually applied on entire sample and often in NLP tasks. Additionaly, LayerNorm applies elementwise affine transform, while InstanceNorm3d usually don’t apply affine transform.

Parameters:

• num_features – \(C\) from an expected input of size \((N, C, D, H, W)\)
• eps – a value added to the denominator for numerical stability. Default: 1e-5
• momentum – the value used for the running_mean and running_var computation. Default: 0.1
• affine – a boolean value that when set to True, this module has learnable affine parameters, initialized the same way as done for batch normalization. Default: False.
• track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: False

Shape:

• Input: \((N, C, D, H, W)\)
• Output: \((N, C, D, H, W)\) (same shape as input)

Examples:

>>> # Without Learnable Parameters
>>> m = nn.InstanceNorm3d(100)
>>> # With Learnable Parameters
>>> m = nn.InstanceNorm3d(100, affine=True)
>>> input = torch.randn(20, 100, 35, 45, 10)
>>> output = m(input)

LayerNorm

class torch.nn.LayerNorm(normalized_shape, eps=1e-05, elementwise_affine=True)

Applies Layer Normalization over a mini-batch of inputs as described in the paper Layer Normalization .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta \]

The mean and standard-deviation are calculated separately over the last certain number dimensions which have to be of the shape specified by normalized_shape. \(\gamma\) and \(\beta\) are learnable affine transform parameters of normalized_shape if elementwise_affine is True.

Note

Unlike Batch Normalization and Instance Normalization, which applies scalar scale and bias for each entire channel/plane with the affine option, Layer Normalization applies per-element scale and bias with elementwise_affine.

This layer uses statistics computed from input data in both training and evaluation modes.

Parameters:

• normalized_shape (int or list or torch.Size) –

  input shape from an expected input of size

  \[[* \times \text{normalized\_shape}[0] \times \text{normalized\_shape}[1] \times \ldots \times \text{normalized\_shape}[-1]] \]

  If a single integer is used, it is treated as a singleton list, and this module will normalize over the last dimension which is expected to be of that specific size.

• eps – a value added to the denominator for numerical stability. Default: 1e-5
• elementwise_affine – a boolean value that when set to True, this module has learnable per-element affine parameters initialized to ones (for weights) and zeros (for biases). Default: True.

Shape:

• Input: \((N, *)\)
• Output: \((N, *)\) (same shape as input)

Examples:

>>> input = torch.randn(20, 5, 10, 10)
>>> # With Learnable Parameters
>>> m = nn.LayerNorm(input.size()[1:])
>>> # Without Learnable Parameters
>>> m = nn.LayerNorm(input.size()[1:], elementwise_affine=False)
>>> # Normalize over last two dimensions
>>> m = nn.LayerNorm([10, 10])
>>> # Normalize over last dimension of size 10
>>> m = nn.LayerNorm(10)
>>> # Activating the module
>>> output = m(input)

LocalResponseNorm

class torch.nn.LocalResponseNorm(size, alpha=0.0001, beta=0.75, k=1.0)

Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.

\[b_{c} = a_{c}\left(k + \frac{\alpha}{n} \sum_{c'=\max(0, c-n/2)}^{\min(N-1,c+n/2)}a_{c'}^2\right)^{-\beta} \]

Parameters:

• size – amount of neighbouring channels used for normalization
• alpha – multiplicative factor. Default: 0.0001
• beta – exponent. Default: 0.75
• k – additive factor. Default: 1

Shape:

• Input: \((N, C, ...)\)
• Output: \((N, C, ...)\) (same shape as input)

Examples:

>>> lrn = nn.LocalResponseNorm(2)
>>> signal_2d = torch.randn(32, 5, 24, 24)
>>> signal_4d = torch.randn(16, 5, 7, 7, 7, 7)
>>> output_2d = lrn(signal_2d)
>>> output_4d = lrn(signal_4d)

Recurrent layers

RNN

class torch.nn.RNN(*args, **kwargs)

Applies a multi-layer Elman RNN with \(tanh\) or \(ReLU\) non-linearity to an input sequence.

For each element in the input sequence, each layer computes the following function:

\[h_t = \text{tanh}(w_{ih} x_t + b_{ih} + w_{hh} h_{(t-1)} + b_{hh}) \]

where \(h_t\) is the hidden state at time t, \(x_t\) is the input at time t, and \(h_{(t-1)}\) is the hidden state of the previous layer at time t-1 or the initial hidden state at time 0. If nonlinearity is ‘relu’, then ReLU is used instead of tanh.

Parameters:

• input_size – The number of expected features in the input x
• hidden_size – The number of features in the hidden state h
• num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two RNNs together to form a stacked RNN, with the second RNN taking in outputs of the first RNN and computing the final results. Default: 1
• nonlinearity – The non-linearity to use. Can be either ‘tanh’ or ‘relu’. Default: ‘tanh’
• bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True
• batch_first – If True, then the input and output tensors are provided as (batch, seq, feature). Default: False
• dropout – If non-zero, introduces a Dropout layer on the outputs of each RNN layer except the last layer, with dropout probability equal to dropout. Default: 0
• bidirectional – If True, becomes a bidirectional RNN. Default: False

Inputs: input, h_0

• input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See torch.nn.utils.rnn.pack_padded_sequence() or torch.nn.utils.rnn.pack_sequence() for details.
• h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

Outputs: output, h_n

• output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features (h_k) from the last layer of the RNN, for each k. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence.

  For the unpacked case, the directions can be separated using output.view(seq_len, batch, num_directions, hidden_size), with forward and backward being direction 0 and 1 respectively. Similarly, the directions can be separated in the packed case.

• h_n (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for k = seq_len.

  Like output, the layers can be separated using h_n.view(num_layers, num_directions, batch, hidden_size).

Variables:

• weight_ih_l[k] – the learnable input-hidden weights of the k-th layer, of shape (hidden_size * input_size) for k = 0. Otherwise, the shape is (hidden_size * hidden_size)
• weight_hh_l[k] – the learnable hidden-hidden weights of the k-th layer, of shape (hidden_size * hidden_size)
• bias_ih_l[k] – the learnable input-hidden bias of the k-th layer, of shape (hidden_size)
• bias_hh_l[k] – the learnable hidden-hidden bias of the k-th layer, of shape (hidden_size)

Note

All the weights and biases are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype torch.float16 4) V100 GPU is used, 5) input data is not in PackedSequence format persistent algorithm can be selected to improve performance.

Examples:

>>> rnn = nn.RNN(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> output, hn = rnn(input, h0)

LSTM

class torch.nn.LSTM(*args, **kwargs)

Applies a multi-layer long short-term memory (LSTM) RNN to an input sequence.

For each element in the input sequence, each layer computes the following function:

\[\begin{array}{ll} \\ i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{(t-1)} + b_{hg}) \\ o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t c_{(t-1)} + i_t g_t \\ h_t = o_t \tanh(c_t) \\ \end{array} \]

where \(h_t\) is the hidden state at time t, \(c_t\) is the cell state at time t, \(x_t\) is the input at time t, \(h_{(t-1)}\) is the hidden state of the layer at time t-1 or the initial hidden state at time 0, and \(i_t\), \(f_t\), \(g_t\), \(o_t\) are the input, forget, cell, and output gates, respectively. \(\sigma\) is the sigmoid function.

In a multilayer LSTM, the input \(i^{(l)}_t\) of the \(l\) -th layer (\(l >= 2\)) is the hidden state \(h^{(l-1)}_t\) of the previous layer multiplied by dropout \(\delta^{(l-1)}_t\) where each \(\delta^{(l-1)_t}\) is a Bernoulli random variable which is \(0\) with probability dropout.

Parameters:

• input_size – The number of expected features in the input x
• hidden_size – The number of features in the hidden state h
• num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two LSTMs together to form a stacked LSTM, with the second LSTM taking in outputs of the first LSTM and computing the final results. Default: 1
• bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True
• batch_first – If True, then the input and output tensors are provided as (batch, seq, feature). Default: False
• dropout – If non-zero, introduces a Dropout layer on the outputs of each LSTM layer except the last layer, with dropout probability equal to dropout. Default: 0
• bidirectional – If True, becomes a bidirectional LSTM. Default: False

Inputs: input, (h_0, c_0)

• input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See torch.nn.utils.rnn.pack_padded_sequence() or torch.nn.utils.rnn.pack_sequence() for details.

• h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

• c_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial cell state for each element in the batch.

  If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.

Outputs: output, (h_n, c_n)

• output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features (h_t) from the last layer of the LSTM, for each t. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence.

  For the unpacked case, the directions can be separated using output.view(seq_len, batch, num_directions, hidden_size), with forward and backward being direction 0 and 1 respectively. Similarly, the directions can be separated in the packed case.

• h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len.

  Like output, the layers can be separated using h_n.view(num_layers, num_directions, batch, hidden_size) and similarly for c_n.

• c_n (num_layers * num_directions, batch, hidden_size): tensor containing the cell state for t = seq_len

Variables:

• weight_ih_l[k] – the learnable input-hidden weights of the \(\text{k}^{th}\) layer (W_ii|W_if|W_ig|W_io), of shape (4*hidden_size x input_size)
• weight_hh_l[k] – the learnable hidden-hidden weights of the \(\text{k}^{th}\) layer (W_hi|W_hf|W_hg|W_ho), of shape (4*hidden_size x hidden_size)
• bias_ih_l[k] – the learnable input-hidden bias of the \(\text{k}^{th}\) layer (b_ii|b_if|b_ig|b_io), of shape (4*hidden_size)
• bias_hh_l[k] – the learnable hidden-hidden bias of the \(\text{k}^{th}\) layer (b_hi|b_hf|b_hg|b_ho), of shape (4*hidden_size)

Note

All the weights and biases are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype torch.float16 4) V100 GPU is used, 5) input data is not in PackedSequence format persistent algorithm can be selected to improve performance.

Examples:

>>> rnn = nn.LSTM(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> c0 = torch.randn(2, 3, 20)
>>> output, (hn, cn) = rnn(input, (h0, c0))

GRU

class torch.nn.GRU(*args, **kwargs)

Applies a multi-layer gated recurrent unit (GRU) RNN to an input sequence.

For each element in the input sequence, each layer computes the following function:

\[\begin{array}{ll} r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) n_t + z_t h_{(t-1)} \end{array} \]

where \(h_t\) is the hidden state at time t, \(x_t\) is the input at time t, \(h_{(t-1)}\) is the hidden state of the layer at time t-1 or the initial hidden state at time 0, and \(r_t\), \(z_t\), \(n_t\) are the reset, update, and new gates, respectively. \(\sigma\) is the sigmoid function.

In a multilayer GRU, the input \(i^{(l)}_t\) of the \(l\) -th layer (\(l >= 2\)) is the hidden state \(h^{(l-1)}_t\) of the previous layer multiplied by dropout \(\delta^{(l-1)}_t\) where each \(\delta^{(l-1)_t}\) is a Bernoulli random variable which is \(0\) with probability dropout.

Parameters:

• input_size – The number of expected features in the input x
• hidden_size – The number of features in the hidden state h
• num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two GRUs together to form a stacked GRU, with the second GRU taking in outputs of the first GRU and computing the final results. Default: 1
• bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True
• batch_first – If True, then the input and output tensors are provided as (batch, seq, feature). Default: False
• dropout – If non-zero, introduces a Dropout layer on the outputs of each GRU layer except the last layer, with dropout probability equal to dropout. Default: 0
• bidirectional – If True, becomes a bidirectional GRU. Default: False

Inputs: input, h_0

• input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See torch.nn.utils.rnn.pack_padded_sequence() for details.
• h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

Outputs: output, h_n

• output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features h_t from the last layer of the GRU, for each t. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence. For the unpacked case, the directions can be separated using output.view(seq_len, batch, num_directions, hidden_size), with forward and backward being direction 0 and 1 respectively.

  Similarly, the directions can be separated in the packed case.

• h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len

  Like output, the layers can be separated using h_n.view(num_layers, num_directions, batch, hidden_size).

Variables:

• weight_ih_l[k] – the learnable input-hidden weights of the \(\text{k}^{th}\) layer (W_ir|W_iz|W_in), of shape (3*hidden_size x input_size)
• weight_hh_l[k] – the learnable hidden-hidden weights of the \(\text{k}^{th}\) layer (W_hr|W_hz|W_hn), of shape (3*hidden_size x hidden_size)
• bias_ih_l[k] – the learnable input-hidden bias of the \(\text{k}^{th}\) layer (b_ir|b_iz|b_in), of shape (3*hidden_size)
• bias_hh_l[k] – the learnable hidden-hidden bias of the \(\text{k}^{th}\) layer (b_hr|b_hz|b_hn), of shape (3*hidden_size)

Note

All the weights and biases are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype torch.float16 4) V100 GPU is used, 5) input data is not in PackedSequence format persistent algorithm can be selected to improve performance.

Examples:

>>> rnn = nn.GRU(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> output, hn = rnn(input, h0)

RNNCell

class torch.nn.RNNCell(input_size, hidden_size, bias=True, nonlinearity='tanh')

An Elman RNN cell with tanh or ReLU non-linearity.

\[h' = \tanh(w_{ih} x + b_{ih} + w_{hh} h + b_{hh})\]

If nonlinearity is ‘relu’, then ReLU is used in place of tanh.

Parameters:

• input_size – The number of expected features in the input x
• hidden_size – The number of features in the hidden state h
• bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True
• nonlinearity – The non-linearity to use. Can be either ‘tanh’ or ‘relu’. Default: ‘tanh’

Inputs: input, hidden

• input of shape (batch, input_size): tensor containing input features
• hidden of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.

Outputs: h’

• h’ of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch

Variables:

• weight_ih – the learnable input-hidden weights, of shape (hidden_size x input_size)
• weight_hh – the learnable hidden-hidden weights, of shape (hidden_size x hidden_size)
• bias_ih – the learnable input-hidden bias, of shape (hidden_size)
• bias_hh – the learnable hidden-hidden bias, of shape (hidden_size)

Note

All the weights and biases are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)

Examples:

>>> rnn = nn.RNNCell(10, 20)
>>> input = torch.randn(6, 3, 10)
>>> hx = torch.randn(3, 20)
>>> output = []
>>> for i in range(6):
        hx = rnn(input[i], hx)
        output.append(hx)

LSTMCell

class torch.nn.LSTMCell(input_size, hidden_size, bias=True)

A long short-term memory (LSTM) cell.

\[\begin{array}{ll} i = \sigma(W_{ii} x + b_{ii} + W_{hi} h + b_{hi}) \\ f = \sigma(W_{if} x + b_{if} + W_{hf} h + b_{hf}) \\ g = \tanh(W_{ig} x + b_{ig} + W_{hg} h + b_{hg}) \\ o = \sigma(W_{io} x + b_{io} + W_{ho} h + b_{ho}) \\ c' = f * c + i * g \\ h' = o \tanh(c') \\ \end{array}\]

where \(\sigma\) is the sigmoid function.

Parameters:

• input_size – The number of expected features in the input x
• hidden_size – The number of features in the hidden state h
• bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True

Inputs: input, (h_0, c_0)

• input of shape (batch, input_size): tensor containing input features

• h_0 of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch.

• c_0 of shape (batch, hidden_size): tensor containing the initial cell state for each element in the batch.

  If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.

Outputs: h_1, c_1

• h_1 of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
• c_1 of shape (batch, hidden_size): tensor containing the next cell state for each element in the batch

Variables:

• weight_ih – the learnable input-hidden weights, of shape (4*hidden_size x input_size)
• weight_hh – the learnable hidden-hidden weights, of shape (4*hidden_size x hidden_size)
• bias_ih – the learnable input-hidden bias, of shape (4*hidden_size)
• bias_hh – the learnable hidden-hidden bias, of shape (4*hidden_size)

Note

All the weights and biases are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)

Examples:

>>> rnn = nn.LSTMCell(10, 20)
>>> input = torch.randn(6, 3, 10)
>>> hx = torch.randn(3, 20)
>>> cx = torch.randn(3, 20)
>>> output = []
>>> for i in range(6):
        hx, cx = rnn(input[i], (hx, cx))
        output.append(hx)

GRUCell

class torch.nn.GRUCell(input_size, hidden_size, bias=True)

A gated recurrent unit (GRU) cell

\[\begin{array}{ll} r = \sigma(W_{ir} x + b_{ir} + W_{hr} h + b_{hr}) \\ z = \sigma(W_{iz} x + b_{iz} + W_{hz} h + b_{hz}) \\ n = \tanh(W_{in} x + b_{in} + r * (W_{hn} h + b_{hn})) \\ h' = (1 - z) * n + z * h \end{array}\]

where \(\sigma\) is the sigmoid function.

Parameters:

• input_size – The number of expected features in the input x
• hidden_size – The number of features in the hidden state h
• bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True

Inputs: input, hidden

• input of shape (batch, input_size): tensor containing input features
• hidden of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.

Outputs: h’

• h’ of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch

Variables:

• weight_ih – the learnable input-hidden weights, of shape (3*hidden_size x input_size)
• weight_hh – the learnable hidden-hidden weights, of shape (3*hidden_size x hidden_size)
• bias_ih – the learnable input-hidden bias, of shape (3*hidden_size)
• bias_hh – the learnable hidden-hidden bias, of shape (3*hidden_size)

Note

All the weights and biases are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)

Examples:

>>> rnn = nn.GRUCell(10, 20)
>>> input = torch.randn(6, 3, 10)
>>> hx = torch.randn(3, 20)
>>> output = []
>>> for i in range(6):
        hx = rnn(input[i], hx)
        output.append(hx)

Linear layers

Linear

class torch.nn.Linear(in_features, out_features, bias=True)

Applies a linear transformation to the incoming data: \(y = xA^T + b\)

Parameters:

• in_features – size of each input sample
• out_features – size of each output sample
• bias – If set to False, the layer will not learn an additive bias. Default: True

Shape:

• Input: \((N, *, \text{in\_features})\) where \(*\) means any number of additional dimensions
• Output: \((N, *, \text{out\_features})\) where all but the last dimension are the same shape as the input.

Variables:

• weight – the learnable weights of the module of shape \((\text{out\_features}, \text{in\_features})\). The values are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\), where \(k = \frac{1}{\text{in\_features}}\)
• bias – the learnable bias of the module of shape \((\text{out\_features})\). If bias is True, the values are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{in\_features}}\)

Examples:

>>> m = nn.Linear(20, 30)
>>> input = torch.randn(128, 20)
>>> output = m(input)
>>> print(output.size())
torch.Size([128, 30])

Bilinear

class torch.nn.Bilinear(in1_features, in2_features, out_features, bias=True)

Applies a bilinear transformation to the incoming data: \(y = x_1 A x_2 + b\)

Parameters:

• in1_features – size of each first input sample
• in2_features – size of each second input sample
• out_features – size of each output sample
• bias – If set to False, the layer will not learn an additive bias. Default: True

Shape:

• Input: \((N, *, \text{in1\_features})\), \((N, *, \text{in2\_features})\) where \(*\) means any number of additional dimensions. All but the last dimension of the inputs should be the same.
• Output: \((N, *, \text{out\_features})\) where all but the last dimension are the same shape as the input.

Variables:

• weight – the learnable weights of the module of shape \((\text{out\_features} x \text{in1\_features} x \text{in2\_features})\). The values are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\), where \(k = \frac{1}{\text{in1\_features}}\)
• bias – the learnable bias of the module of shape \((\text{out\_features})\) If bias is True, the values are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\), where \(k = \frac{1}{\text{in1\_features}}\)

Examples:

>>> m = nn.Bilinear(20, 30, 40)
>>> input1 = torch.randn(128, 20)
>>> input2 = torch.randn(128, 30)
>>> output = m(input1, input2)
>>> print(output.size())
torch.Size([128, 40])

Dropout layers

Dropout

class torch.nn.Dropout(p=0.5, inplace=False)

During training, randomly zeroes some of the elements of the input tensor with probability p using samples from a Bernoulli distribution. Each channel will be zeroed out independently on every forward call.

This has proven to be an effective technique for regularization and preventing the co-adaptation of neurons as described in the paper Improving neural networks by preventing co-adaptation of feature detectors .

Furthermore, the outputs are scaled by a factor of \(\frac{1}{1-p}\) during training. This means that during evaluation the module simply computes an identity function.

Parameters:

• p – probability of an element to be zeroed. Default: 0.5
• inplace – If set to True, will do this operation in-place. Default: False

Shape:

• Input: Any. Input can be of any shape
• Output: Same. Output is of the same shape as input

Examples:

>>> m = nn.Dropout(p=0.2)
>>> input = torch.randn(20, 16)
>>> output = m(input)

Dropout2d

class torch.nn.Dropout2d(p=0.5, inplace=False)

Randomly zero out entire channels (a channel is a 2D feature map, e.g., the \(j\)-th channel of the \(i\)-th sample in the batched input is a 2D tensor \(\text{input}[i, j]\)) of the input tensor). Each channel will be zeroed out independently on every forward call. with probability p using samples from a Bernoulli distribution.

Usually the input comes from nn.Conv2d modules.

As described in the paper Efficient Object Localization Using Convolutional Networks , if adjacent pixels within feature maps are strongly correlated (as is normally the case in early convolution layers) then i.i.d. dropout will not regularize the activations and will otherwise just result in an effective learning rate decrease.

In this case, nn.Dropout2d() will help promote independence between feature maps and should be used instead.

Parameters:

• p (float, optional) – probability of an element to be zero-ed.
• inplace (bool, optional) – If set to True, will do this operation in-place

Shape:

• Input: \((N, C, H, W)\)
• Output: \((N, C, H, W)\) (same shape as input)

Examples:

>>> m = nn.Dropout2d(p=0.2)
>>> input = torch.randn(20, 16, 32, 32)
>>> output = m(input)

Dropout3d

class torch.nn.Dropout3d(p=0.5, inplace=False)

Randomly zero out entire channels (a channel is a 3D feature map, e.g., the \(j\)-th channel of the \(i\)-th sample in the batched input is a 3D tensor \(\text{input}[i, j]\)) of the input tensor). Each channel will be zeroed out independently on every forward call. with probability p using samples from a Bernoulli distribution.

Usually the input comes from nn.Conv3d modules.

As described in the paper Efficient Object Localization Using Convolutional Networks , if adjacent pixels within feature maps are strongly correlated (as is normally the case in early convolution layers) then i.i.d. dropout will not regularize the activations and will otherwise just result in an effective learning rate decrease.

In this case, nn.Dropout3d() will help promote independence between feature maps and should be used instead.

Parameters:

• p (float, optional) – probability of an element to be zeroed.
• inplace (bool, optional) – If set to True, will do this operation in-place

Shape:

• Input: \((N, C, D, H, W)\)
• Output: \((N, C, D, H, W)\) (same shape as input)

Examples:

>>> m = nn.Dropout3d(p=0.2)
>>> input = torch.randn(20, 16, 4, 32, 32)
>>> output = m(input)

AlphaDropout

class torch.nn.AlphaDropout(p=0.5, inplace=False)

Applies Alpha Dropout over the input.

Alpha Dropout is a type of Dropout that maintains the self-normalizing property. For an input with zero mean and unit standard deviation, the output of Alpha Dropout maintains the original mean and standard deviation of the input. Alpha Dropout goes hand-in-hand with SELU activation function, which ensures that the outputs have zero mean and unit standard deviation.

During training, it randomly masks some of the elements of the input tensor with probability p using samples from a bernoulli distribution. The elements to masked are randomized on every forward call, and scaled and shifted to maintain zero mean and unit standard deviation.

During evaluation the module simply computes an identity function.

More details can be found in the paper Self-Normalizing Neural Networks .

Parameters:

• p (float) – probability of an element to be dropped. Default: 0.5
• inplace (bool, optional) – If set to True, will do this operation in-place

Shape:

• Input: Any. Input can be of any shape
• Output: Same. Output is of the same shape as input

Examples:

>>> m = nn.AlphaDropout(p=0.2)
>>> input = torch.randn(20, 16)
>>> output = m(input)

Sparse layers

Embedding

class torch.nn.Embedding(num_embeddings, embedding_dim, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False, _weight=None)

A simple lookup table that stores embeddings of a fixed dictionary and size.

This module is often used to store word embeddings and retrieve them using indices. The input to the module is a list of indices, and the output is the corresponding word embeddings.

Parameters:

• num_embeddings (int) – size of the dictionary of embeddings
• embedding_dim (int) – the size of each embedding vector
• padding_idx (int, optional) – If given, pads the output with the embedding vector at padding_idx (initialized to zeros) whenever it encounters the index.
• max_norm (float, optional) – If given, each embedding vector with norm larger than max_norm is renormalized to have norm max_norm.
• norm_type (float, optional) – The p of the p-norm to compute for the max_norm option. Default 2.
• scale_grad_by_freq (boolean, optional) – If given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default False.
• sparse (bool, optional) – If True, gradient w.r.t. weight matrix will be a sparse tensor. See Notes for more details regarding sparse gradients.

Variables:

weight (Tensor) – the learnable weights of the module of shape (num_embeddings, embedding_dim) initialized from \(\mathcal{N}(0, 1)\)

Shape:

• Input: LongTensor of arbitrary shape containing the indices to extract
• Output: (*, embedding_dim), where * is the input shape

Note

Keep in mind that only a limited number of optimizers support sparse gradients: currently it’s optim.SGD (CUDA and CPU), optim.SparseAdam (CUDA and CPU) and optim.Adagrad (CPU)

Note

With padding_idx set, the embedding vector at padding_idx is initialized to all zeros. However, note that this vector can be modified afterwards, e.g., using a customized initialization method, and thus changing the vector used to pad the output. The gradient for this vector from Embedding is always zero.

Examples:

>>> # an Embedding module containing 10 tensors of size 3
>>> embedding = nn.Embedding(10, 3)
>>> # a batch of 2 samples of 4 indices each
>>> input = torch.LongTensor([[1,2,4,5],[4,3,2,9]])
>>> embedding(input)
tensor([[[-0.0251, -1.6902,  0.7172],
         [-0.6431,  0.0748,  0.6969],
         [ 1.4970,  1.3448, -0.9685],
         [-0.3677, -2.7265, -0.1685]],

        [[ 1.4970,  1.3448, -0.9685],
         [ 0.4362, -0.4004,  0.9400],
         [-0.6431,  0.0748,  0.6969],
         [ 0.9124, -2.3616,  1.1151]]])


>>> # example with padding_idx
>>> embedding = nn.Embedding(10, 3, padding_idx=0)
>>> input = torch.LongTensor([[0,2,0,5]])
>>> embedding(input)
tensor([[[ 0.0000,  0.0000,  0.0000],
         [ 0.1535, -2.0309,  0.9315],
         [ 0.0000,  0.0000,  0.0000],
         [-0.1655,  0.9897,  0.0635]]])

classmethod from_pretrained(embeddings, freeze=True, sparse=False)

Creates Embedding instance from given 2-dimensional FloatTensor.

Parameters:

• embeddings (Tensor) – FloatTensor containing weights for the Embedding. First dimension is being passed to Embedding as ‘num_embeddings’, second as ‘embedding_dim’.
• freeze (boolean, optional) – If True, the tensor does not get updated in the learning process. Equivalent to embedding.weight.requires_grad = False. Default: True
• sparse (bool, optional) – if True, gradient w.r.t. weight matrix will be a sparse tensor. See Notes for more details regarding sparse gradients.

Examples:

>>> # FloatTensor containing pretrained weights
>>> weight = torch.FloatTensor([[1, 2.3, 3], [4, 5.1, 6.3]])
>>> embedding = nn.Embedding.from_pretrained(weight)
>>> # Get embeddings for index 1
>>> input = torch.LongTensor([1])
>>> embedding(input)
tensor([[ 4.0000,  5.1000,  6.3000]])

EmbeddingBag

class torch.nn.EmbeddingBag(num_embeddings, embedding_dim, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, mode='mean', sparse=False)

Computes sums or means of ‘bags’ of embeddings, without instantiating the intermediate embeddings.

For bags of constant length, this class

• with mode="sum" is equivalent to Embedding followed by torch.sum(dim=1),
• with mode="mean" is equivalent to Embedding followed by torch.mean(dim=1),
• with mode="max" is equivalent to Embedding followed by torch.max(dim=1).

However, EmbeddingBag is much more time and memory efficient than using a chain of these operations.

Parameters:

• num_embeddings (int) – size of the dictionary of embeddings
• embedding_dim (int) – the size of each embedding vector
• max_norm (float, optional) – If given, each embedding vector with norm larger than max_norm is renormalized to have norm max_norm.
• norm_type (float, optional) – The p of the p-norm to compute for the max_norm option. Default 2.
• scale_grad_by_freq (boolean, optional) – if given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default False. Note: this option is not supported when mode="max".
• mode (string, optional) – "sum", "mean" or "max". Specifies the way to reduce the bag. Default: "mean"
• sparse (bool, optional) – if True, gradient w.r.t. weight matrix will be a sparse tensor. See Notes for more details regarding sparse gradients. Note: this option is not supported when mode="max".

Variables:

weight (Tensor) – the learnable weights of the module of shape (num_embeddings x embedding_dim) initialized from \(\mathcal{N}(0, 1)\).

Inputs: input (LongTensor) and offsets (LongTensor, optional)

• If input is 2D of shape B x N,

  it will be treated as B bags (sequences) each of fixed length N, and this will return B values aggregated in a way depending on the mode. offsets is ignored and required to be None in this case.

• If input is 1D of shape N,

  it will be treated as a concatenation of multiple bags (sequences). offsets is required to be a 1D tensor containing the starting index positions of each bag in input. Therefore, for offsets of shape B, input will be viewed as having B bags. Empty bags (i.e., having 0-length) will have returned vectors filled by zeros.

Output shape: B x embedding_dim

Examples:

>>> # an Embedding module containing 10 tensors of size 3
>>> embedding_sum = nn.EmbeddingBag(10, 3, mode='sum')
>>> # a batch of 2 samples of 4 indices each
>>> input = torch.LongTensor([1,2,4,5,4,3,2,9])
>>> offsets = torch.LongTensor([0,4])
>>> embedding_sum(input, offsets)
tensor([[-0.8861, -5.4350, -0.0523],
        [ 1.1306, -2.5798, -1.0044]])

Distance functions

CosineSimilarity

class torch.nn.CosineSimilarity(dim=1, eps=1e-08)

Returns cosine similarity between \(x_1\) and \(x_2\), computed along dim.

\[\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)} \]

Parameters:

• dim (int, optional) – Dimension where cosine similarity is computed. Default: 1
• eps (float, optional) – Small value to avoid division by zero. Default: 1e-8

Shape:

• Input1: \((\ast_1, D, \ast_2)\) where D is at position dim
• Input2: \((\ast_1, D, \ast_2)\), same shape as the Input1
• Output: \((\ast_1, \ast_2)\)

Examples:

>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> cos = nn.CosineSimilarity(dim=1, eps=1e-6)
>>> output = cos(input1, input2)

PairwiseDistance

class torch.nn.PairwiseDistance(p=2.0, eps=1e-06, keepdim=False)

Computes the batchwise pairwise distance between vectors \(v_1\), \(v_2\) using the p-norm:

\[\Vert x \Vert _p := \left( \sum_{i=1}^n \vert x_i \vert ^ p \right) ^ {1/p} \]

Parameters:

• p (real) – the norm degree. Default: 2
• eps (float, optional) – Small value to avoid division by zero. Default: 1e-6
• keepdim (bool, optional) – Determines whether or not to keep the batch dimension. Default: False

Shape:

• Input1: \((N, D)\) where D = vector dimension
• Input2: \((N, D)\), same shape as the Input1
• Output: \((N)\). If keepdim is False, then \((N, 1)\).

Examples:

>>> pdist = nn.PairwiseDistance(p=2)
>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> output = pdist(input1, input2)

Loss functions

L1Loss

class torch.nn.L1Loss(size_average=None, reduce=None, reduction='mean')

Creates a criterion that measures the mean absolute error (MAE) between each element in the input x and target y.

The loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left| x_n - y_n \right|, \]

where \(N\) is the batch size. If reduce is True, then:

\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if size\_average} = \text{True;}\\ \operatorname{sum}(L), & \text{if size\_average} = \text{False.} \end{cases} \]

x and y are tensors of arbitrary shapes with a total of n elements each.

The sum operation still operates over all the elements, and divides by n.

The division by n can be avoided if one sets the constructor argument size_average=False.

Parameters:

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Target: \((N, *)\), same shape as the input
• Output: scalar. If reduce is False, then \((N, *)\), same shape as the input

Examples:

>>> loss = nn.L1Loss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randn(3, 5)
>>> output = loss(input, target)
>>> output.backward()

MSELoss

class torch.nn.MSELoss(size_average=None, reduce=None, reduction='mean')

Creates a criterion that measures the mean squared error (squared L2 norm) between each element in the input x and target y.

The loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left( x_n - y_n \right)^2, \]

where \(N\) is the batch size. If reduce is True, then:

\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size\_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size\_average} = \text{False}. \end{cases} \]

The sum operation still operates over all the elements, and divides by n.

The division by n can be avoided if one sets size_average to False.

To get a batch of losses, a loss per batch element, set reduce to False. These losses are not averaged and are not affected by size_average.

Parameters:

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Target: \((N, *)\), same shape as the input

Examples:

>>> loss = nn.MSELoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randn(3, 5)
>>> output = loss(input, target)
>>> output.backward()

CrossEntropyLoss

class torch.nn.CrossEntropyLoss(weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')

This criterion combines nn.LogSoftmax() and nn.NLLLoss() in one single class.

It is useful when training a classification problem with C classes. If provided, the optional argument weight should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.

The input is expected to contain scores for each class.

input has to be a Tensor of size either \((minibatch, C)\) or \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 2\) for the K-dimensional case (described later).

This criterion expects a class index (0 to C-1) as the target for each value of a 1D tensor of size minibatch

The loss can be described as:

\[\text{loss}(x, class) = -\log\left(\frac{\exp(x[class])}{\sum_j \exp(x[j])}\right) = -x[class] + \log\left(\sum_j \exp(x[j])\right) \]

or in the case of the weight argument being specified:

\[\text{loss}(x, class) = weight[class] \left(-x[class] + \log\left(\sum_j \exp(x[j])\right)\right) \]

The losses are averaged across observations for each minibatch.

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 2\), where \(K\) is the number of dimensions, and a target of appropriate shape (see below).

Parameters:

• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets.
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, C)\) where C = number of classes, or \((N, C, d_1, d_2, ..., d_K)\) with \(K \geq 2\) in the case of K-dimensional loss.
• Target: \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C-1\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 2\) in the case of K-dimensional loss.
• Output: scalar. If reduce is False, then the same size as the target: \((N)\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 2\) in the case of K-dimensional loss.

Examples:

>>> loss = nn.CrossEntropyLoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.empty(3, dtype=torch.long).random_(5)
>>> output = loss(input, target)
>>> output.backward()

CTCLoss

class torch.nn.CTCLoss(blank=0, reduction='mean')

The Connectionist Temporal Classification loss.

Parameters:

• blank (int, optional) – blank label. Default \(0\).
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the output losses will be divided by the target lengths and then the mean over the batch is taken. Default: ‘mean’

Inputs:

log_probs: Tensor of size \((T, N, C)\) where C = number of characters in alphabet including blank,

T = input length, and N = batch size. The logarithmized probabilities of the outputs (e.g. obtained with torch.nn.functional.log_softmax()).

targets: Tensor of size \((N, S)\) or (sum(target_lengths)).

Targets (cannot be blank). In the second form, the targets are assumed to be concatenated.

input_lengths: Tuple or tensor of size \((N)\).

Lengths of the inputs (must each be \(\leq T\))

target_lengths: Tuple or tensor of size \((N)\).

Lengths of the targets

Example:

>>> ctc_loss = nn.CTCLoss()
>>> log_probs = torch.randn(50, 16, 20).log_softmax(2).detach().requires_grad_()
>>> targets = torch.randint(1, 20, (16, 30), dtype=torch.long)
>>> input_lengths = torch.full((16,), 50, dtype=torch.long)
>>> target_lengths = torch.randint(10,30,(16,), dtype=torch.long)
>>> loss = ctc_loss(log_probs, targets, input_lengths, target_lengths)
>>> loss.backward()

Reference:

A. Graves et al.: Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks: https://www.cs.toronto.edu/~graves/icml_2006.pdf

Note

In order to use CuDNN, the following must be satisfied: targets must be in concatenated format, all input_lengths must be T. \(blank=0\), target_lengths \(\leq 256\), the integer arguments must be of dtype torch.int32.

The regular implementation uses the (more common in PyTorch) torch.long dtype.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

NLLLoss

class torch.nn.NLLLoss(weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')

The negative log likelihood loss. It is useful to train a classification problem with C classes.

If provided, the optional argument weight should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.

The input given through a forward call is expected to contain log-probabilities of each class. input has to be a Tensor of size either \((minibatch, C)\) or \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 2\) for the K-dimensional case (described later).

Obtaining log-probabilities in a neural network is easily achieved by adding a LogSoftmax layer in the last layer of your network. You may use CrossEntropyLoss instead, if you prefer not to add an extra layer.

The target that this loss expects is a class index (0 to C-1, where C = number of classes)

If reduce is False, the loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_{y_n} x_{n,y_n}, \quad w_{c} = \text{weight}[c] \cdot \mathbb{1}\{c \not= \text{ignore\_index}\}, \]

where \(N\) is the batch size. If reduce is True (default), then

\[\ell(x, y) = \begin{cases} \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n}} l_n, & \text{if}\; \text{size\_average} = \text{True},\\ \sum_{n=1}^N l_n, & \text{if}\; \text{size\_average} = \text{False}. \end{cases} \]

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 2\), where \(K\) is the number of dimensions, and a target of appropriate shape (see below). In the case of images, it computes NLL loss per-pixel.

Parameters:

• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets.
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, C)\) where C = number of classes, or \((N, C, d_1, d_2, ..., d_K)\) with \(K \geq 2\) in the case of K-dimensional loss.
• Target: \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C-1\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 2\) in the case of K-dimensional loss.
• Output: scalar. If reduce is False, then the same size as the target: \((N)\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 2\) in the case of K-dimensional loss.

Examples:

>>> m = nn.LogSoftmax()
>>> loss = nn.NLLLoss()
>>> # input is of size N x C = 3 x 5
>>> input = torch.randn(3, 5, requires_grad=True)
>>> # each element in target has to have 0 <= value < C
>>> target = torch.tensor([1, 0, 4])
>>> output = loss(m(input), target)
>>> output.backward()
>>>
>>>
>>> # 2D loss example (used, for example, with image inputs)
>>> N, C = 5, 4
>>> loss = nn.NLLLoss()
>>> # input is of size N x C x height x width
>>> data = torch.randn(N, 16, 10, 10)
>>> conv = nn.Conv2d(16, C, (3, 3))
>>> m = nn.LogSoftmax()
>>> # each element in target has to have 0 <= value < C
>>> target = torch.empty(N, 8, 8, dtype=torch.long).random_(0, C)
>>> output = loss(m(conv(data)), target)
>>> output.backward()

PoissonNLLLoss

class torch.nn.PoissonNLLLoss(log_input=True, full=False, size_average=None, eps=1e-08, reduce=None, reduction='mean')

Negative log likelihood loss with Poisson distribution of target.

The loss can be described as:

\[\text{target} \sim \mathrm{Poisson}(\text{input}) \text{loss}(\text{input}, \text{target}) = \text{input} - \text{target} * \log(\text{input}) + \log(\text{target!})\]

The last term can be omitted or approximated with Stirling formula. The approximation is used for target values more than 1. For targets less or equal to 1 zeros are added to the loss.

Parameters:

• log_input (bool, optional) – if True the loss is computed as \(\exp(\text{input}) - \text{target}*\text{input}\), if False the loss is \(\text{input} - \text{target}*\log(\text{input}+\text{eps})\).
• full (bool, optional) –

  whether to compute full loss, i. e. to add the Stirling approximation term

  \[\text{target}*\log(\text{target}) - \text{target} + 0.5 * \log(2\pi\text{target}). \]
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• eps (float, optional) – Small value to avoid evaluation of \(\log(0)\) when log_input == False. Default: 1e-8
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Examples:

>>> loss = nn.PoissonNLLLoss()
>>> log_input = torch.randn(5, 2, requires_grad=True)
>>> target = torch.randn(5, 2)
>>> output = loss(log_input, target)
>>> output.backward()

KLDivLoss

class torch.nn.KLDivLoss(size_average=None, reduce=None, reduction='mean')

The Kullback-Leibler divergence Loss

KL divergence is a useful distance measure for continuous distributions and is often useful when performing direct regression over the space of (discretely sampled) continuous output distributions.

As with NLLLoss, the input given is expected to contain log-probabilities. However, unlike NLLLoss, input is not restricted to a 2D Tensor. The targets are given as probabilities (i.e. without taking the logarithm).

This criterion expects a target Tensor of the same size as the input Tensor.

The unreduced (i.e. with reduce set to False) loss can be described as:

\[l(x,y) = L := \{ l_1,\dots,l_N \}, \quad l_n = y_n \cdot \left( \log y_n - x_n \right) \]

where the index \(N\) spans all dimensions of input and \(L\) has the same shape as input. If reduce is True (the default), then:

\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size\_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size\_average} = \text{False}. \end{cases} \]

In default reduction mode ‘mean’, the losses are averaged for each minibatch over observations as well as over dimensions. ‘batchmean’ mode gives the correct KL divergence where losses are averaged over batch dimension only. ‘mean’ mode’s behavior will be changed to the same as ‘batchmean’ in the next major release.

Parameters:

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘batchmean’ | ‘sum’ | ‘mean’. ‘none’: no reduction will be applied. ‘batchmean’: the sum of the output will be divided by batchsize. ‘sum’: the output will be summed. ‘mean’: the output will be divided by the number of elements in the output. Default: ‘mean’

:param .. note:: size_average and reduce are in the process of being deprecated,: and in the meantime, specifying either of those two args will override reduction. :param .. note:: reduction=’mean’ doesn’t return the true kl divergence value, please use: reduction=’batchmean’ which aligns with KL math definition.

In the next major release, ‘mean’ will be changed to be the same as ‘batchmean’.

Shape:

• input: \((N, *)\) where * means, any number of additional dimensions
• target: \((N, *)\), same shape as the input
• output: scalar by default. If reduce is False, then \((N, *)\), the same shape as the input

BCELoss

class torch.nn.BCELoss(weight=None, size_average=None, reduce=None, reduction='mean')

Creates a criterion that measures the Binary Cross Entropy between the target and the output:

The loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ y_n \cdot \log x_n + (1 - y_n) \cdot \log (1 - x_n) \right], \]

where \(N\) is the batch size. If reduce is True, then

\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size\_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size\_average} = \text{False}. \end{cases} \]

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the targets y should be numbers between 0 and 1.

Parameters:

• weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size “nbatch”.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Target: \((N, *)\), same shape as the input
• Output: scalar. If reduce is False, then \((N, *)\), same shape as input.

Examples:

>>> m = nn.Sigmoid()
>>> loss = nn.BCELoss()
>>> input = torch.randn(3, requires_grad=True)
>>> target = torch.empty(3).random_(2)
>>> output = loss(m(input), target)
>>> output.backward()

BCEWithLogitsLoss

class torch.nn.BCEWithLogitsLoss(weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)

This loss combines a Sigmoid layer and the BCELoss in one single class. This version is more numerically stable than using a plain Sigmoid followed by a BCELoss as, by combining the operations into one layer, we take advantage of the log-sum-exp trick for numerical stability.

The loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ y_n \cdot \log \sigma(x_n) + (1 - y_n) \cdot \log (1 - \sigma(x_n)) \right], \]

where \(N\) is the batch size. If reduce is True, then

\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if size\_average} = \text{True},\\ \operatorname{sum}(L), & \text{if size\_average} = \text{False}. \end{cases} \]

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the targets t[i] should be numbers between 0 and 1.

It’s possible to trade off recall and precision by adding weights to positive examples. In this case the loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ p_n y_n \cdot \log \sigma(x_n) + (1 - y_n) \cdot \log (1 - \sigma(x_n)) \right], \]

where \(p_n\) is the positive weight of class \(n\). \(p_n > 1\) increases the recall, \(p_n < 1\) increases the precision.

For example, if a dataset contains 100 positive and 300 negative examples of a single class, then pos_weight for the class should be equal to \(\frac{300}{100}=3\). The loss would act as if the dataset contains \(3\times 100=300\) positive examples.

Parameters:

• weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size “nbatch”.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’
• pos_weight – a weight of positive examples. Must be a vector with length equal to the number of classes.

MarginRankingLoss

class torch.nn.MarginRankingLoss(margin=0.0, size_average=None, reduce=None, reduction='mean')

Creates a criterion that measures the loss given inputs x1, x2, two 1D mini-batch Tensor`s, and a label 1D mini-batch tensor `y with values (1 or -1).

If y == 1 then it assumed the first input should be ranked higher (have a larger value) than the second input, and vice-versa for y == -1.

The loss function for each sample in the mini-batch is:

\[\text{loss}(x, y) = \max(0, -y * (x1 - x2) + \text{margin}) \]

Parameters:

• margin (float, optional) – Has a default value of 0.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, D)\) where N is the batch size and D is the size of a sample.
• Target: \((N)\)
• Output: scalar. If reduce is False, then \((N)\).

HingeEmbeddingLoss

class torch.nn.HingeEmbeddingLoss(margin=1.0, size_average=None, reduce=None, reduction='mean')

Measures the loss given an input tensor x and a labels tensor y containing values (1 or -1). This is usually used for measuring whether two inputs are similar or dissimilar, e.g. using the L1 pairwise distance as x, and is typically used for learning nonlinear embeddings or semi-supervised learning.

The loss function for \(n\)-th sample in the mini-batch is

\[l_n = \begin{cases} x_n, & \text{if}\; y_n = 1,\\ \max \{0, \Delta - x_n\}, & \text{if}\; y_n = -1, \end{cases} \]

and the total loss functions is

\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if size\_average} = \text{True},\\ \operatorname{sum}(L), & \text{if size\_average} = \text{False}. \end{cases} \]

where \(L = \{l_1,\dots,l_N\}^\top\).

Parameters:

• margin (float, optional) – Has a default value of 1.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: Tensor of arbitrary shape. The sum operation operates over all the elements.
• Target: Same shape as input.
• Output: scalar. If reduce is False, then same shape as the input

MultiLabelMarginLoss

class torch.nn.MultiLabelMarginLoss(size_average=None, reduce=None, reduction='mean')

Creates a criterion that optimizes a multi-class multi-classification hinge loss (margin-based loss) between input x (a 2D mini-batch Tensor) and output y (which is a 2D Tensor of target class indices). For each sample in the mini-batch:

\[\text{loss}(x, y) = \sum_{ij}\frac{\max(0, 1 - (x[y[j]] - x[i]))}{\text{x.size}(0)} \]

where \(i == 0\) to \(x.size(0)\), \(j == 0\) to \(y.size(0)\), \(y[j] \geq 0\), and \(i \neq y[j]\) for all \(i\) and \(j\).

y and x must have the same size.

The criterion only considers a contiguous block of non-negative targets that starts at the front.

This allows for different samples to have variable amounts of target classes

Parameters:

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((C)\) or \((N, C)\) where N is the batch size and C is the number of classes.
• Target: \((C)\) or \((N, C)\), same shape as the input.
• Output: scalar. If reduce is False, then \((N)\).

SmoothL1Loss

class torch.nn.SmoothL1Loss(size_average=None, reduce=None, reduction='mean')

Creates a criterion that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise. It is less sensitive to outliers than the MSELoss and in some cases prevents exploding gradients (e.g. see “Fast R-CNN” paper by Ross Girshick). Also known as the Huber loss:

\[\text{loss}(x, y) = \frac{1}{n} \sum_{i} z_{i} \]

where \(z_{i}\) is given by:

\[z_{i} = \begin{cases} 0.5 (x_i - y_i)^2, & \text{if } |x_i - y_i| < 1 \\ |x_i - y_i| - 0.5, & \text{otherwise } \end{cases} \]

x and y arbitrary shapes with a total of n elements each the sum operation still operates over all the elements, and divides by n.

The division by n can be avoided if one sets size_average to False

Parameters:

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, *)\) where * means, any number of additional dimensions
• Target: \((N, *)\), same shape as the input
• Output: scalar. If reduce is False, then \((N, *)\), same shape as the input

SoftMarginLoss

class torch.nn.SoftMarginLoss(size_average=None, reduce=None, reduction='mean')

Creates a criterion that optimizes a two-class classification logistic loss between input tensor x and target tensor y (containing 1 or -1).

\[\text{loss}(x, y) = \sum_i \frac{\log(1 + \exp(-y[i]*x[i]))}{\text{x.nelement}()} \]

Parameters:

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: Tensor of arbitrary shape.
• Target: Same shape as input.
• Output: scalar. If reduce is False, then same shape as the input

MultiLabelSoftMarginLoss

class torch.nn.MultiLabelSoftMarginLoss(weight=None, size_average=None, reduce=None, reduction='mean')

Creates a criterion that optimizes a multi-label one-versus-all loss based on max-entropy, between input x and target y of size (N, C). For each sample in the minibatch:

\[loss(x, y) = - \frac{1}{C} * \sum_i y[i] * \log((1 + \exp(-x[i]))^{-1}) + (1-y[i]) * \log\left(\frac{\exp(-x[i])}{(1 + \exp(-x[i]))}\right) \]

where i == 0 to x.nElement()-1, y[i] in {0,1}.

Parameters:

• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, C)\) where N is the batch size and C is the number of classes.
• Target: \((N, C)\), same shape as the input.
• Output: scalar. If reduce is False, then \((N)\).

CosineEmbeddingLoss

class torch.nn.CosineEmbeddingLoss(margin=0.0, size_average=None, reduce=None, reduction='mean')

Creates a criterion that measures the loss given input tensors \(x_1\), \(x_2\) and a Tensor label y with values 1 or -1. This is used for measuring whether two inputs are similar or dissimilar, using the cosine distance, and is typically used for learning nonlinear embeddings or semi-supervised learning.

The loss function for each sample is:

\[\text{loss}(x, y) = \begin{cases} 1 - \cos(x_1, x_2), & \text{if } y == 1 \\ \max(0, \cos(x_1, x_2) - \text{margin}), & \text{if } y == -1 \end{cases} \]

Parameters:

• margin (float, optional) – Should be a number from -1 to 1, 0 to 0.5 is suggested. If margin is missing, the default value is 0.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

MultiMarginLoss

class torch.nn.MultiMarginLoss(p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')

Creates a criterion that optimizes a multi-class classification hinge loss (margin-based loss) between input x (a 2D mini-batch Tensor) and output y (which is a 1D tensor of target class indices, \(0 \leq y \leq \text{x.size}(1)\)):

For each mini-batch sample, the loss in terms of the 1D input x and scalar output y is:

\[\text{loss}(x, y) = \frac{\sum_i \max(0, \text{margin} - x[y] + x[i]))^p}{\text{x.size}(0)} \]

where i == 0 to x.size(0) and \(i \neq y\).

Optionally, you can give non-equal weighting on the classes by passing a 1D weight tensor into the constructor.

The loss function then becomes:

\[\text{loss}(x, y) = \frac{\sum_i \max(0, w[y] * (\text{margin} - x[y] + x[i]))^p)}{\text{x.size}(0)} \]

Parameters:

• p (int, optional) – Has a default value of 1. 1 and 2 are the only supported values
• margin (float, optional) – Has a default value of 1.
• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

TripletMarginLoss

class torch.nn.TripletMarginLoss(margin=1.0, p=2.0, eps=1e-06, swap=False, size_average=None, reduce=None, reduction='mean')

Creates a criterion that measures the triplet loss given an input tensors x1, x2, x3 and a margin with a value greater than 0. This is used for measuring a relative similarity between samples. A triplet is composed by a, p and n: anchor, positive examples and negative example respectively. The shapes of all input tensors should be \((N, D)\).

The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al.

The loss function for each sample in the mini-batch is:

\[L(a, p, n) = \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\} \]

where

\[d(x_i, y_i) = \left\lVert {\bf x}_i - {\bf y}_i \right\rVert_p \]

Parameters:

• margin (float, optional) – Default: 1.
• p (int, optional) – The norm degree for pairwise distance. Default: 2.
• swap (float, optional) – The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al. Default: False.
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Shape:

• Input: \((N, D)\) where D is the vector dimension.
• Output: scalar. If reduce is False, then \((N)\).

>>> triplet_loss = nn.TripletMarginLoss(margin=1.0, p=2)
>>> input1 = torch.randn(100, 128, requires_grad=True)
>>> input2 = torch.randn(100, 128, requires_grad=True)
>>> input3 = torch.randn(100, 128, requires_grad=True)
>>> output = triplet_loss(input1, input2, input3)
>>> output.backward()

Vision layers

PixelShuffle

class torch.nn.PixelShuffle(upscale_factor)

Rearranges elements in a tensor of shape \((*, C \times r^2, H, W)\) to a tensor of shape \((C, H \times r, W \times r)\).

This is useful for implementing efficient sub-pixel convolution with a stride of \(1/r\).

Look at the paper: Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network by Shi et. al (2016) for more details.

Parameters:upscale_factor (int) – factor to increase spatial resolution by

Shape:

• Input: \((N, C \times \text{upscale_factor}^2, H, W)\)
• Output: \((N, C, H \times \text{upscale_factor}, W \times \text{upscale_factor})\)

Examples:

>>> pixel_shuffle = nn.PixelShuffle(3)
>>> input = torch.randn(1, 9, 4, 4)
>>> output = pixel_shuffle(input)
>>> print(output.size())
torch.Size([1, 1, 12, 12])

Upsample

class torch.nn.Upsample(size=None, scale_factor=None, mode='nearest', align_corners=None)

Upsamples a given multi-channel 1D (temporal), 2D (spatial) or 3D (volumetric) data.

The input data is assumed to be of the form minibatch x channels x [optional depth] x [optional height] x width. Hence, for spatial inputs, we expect a 4D Tensor and for volumetric inputs, we expect a 5D Tensor.

The algorithms available for upsampling are nearest neighbor and linear, bilinear and trilinear for 3D, 4D and 5D input Tensor, respectively.

One can either give a scale_factor or the target output size to calculate the output size. (You cannot give both, as it is ambiguous)

Parameters:

• size (tuple, optional) – a tuple of ints ([optional D_out], [optional H_out], W_out) output sizes
• scale_factor (int / tuple of python:ints, optional) – the multiplier for the image height / width / depth
• mode (string, optional) – the upsampling algorithm: one of nearest, linear, bilinear and trilinear. Default: nearest
• align_corners (bool, optional) – if True, the corner pixels of the input and output tensors are aligned, and thus preserving the values at those pixels. This only has effect when mode is linear, bilinear, or trilinear. Default: False

Shape:

• Input: \((N, C, W_{in})\), \((N, C, H_{in}, W_{in})\) or \((N, C, D_{in}, H_{in}, W_{in})\)
• Output: \((N, C, W_{out})\), \((N, C, H_{out}, W_{out})\) or \((N, C, D_{out}, H_{out}, W_{out})\), where

\[D_{out} = \left\lfloor D_{in} \times \text{scale\_factor} \right\rfloor \text{ or size}[-3] \]

\[H_{out} = \left\lfloor H_{in} \times \text{scale\_factor} \right\rfloor \text{ or size}[-2] \]

\[W_{out} = \left\lfloor W_{in} \times \text{scale\_factor} \right\rfloor \text{ or size}[-1] \]

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See below for concrete examples on how this affects the outputs.

Note

If you want downsampling/general resizing, you should use interpolate().

Examples:

>>> input = torch.arange(1, 5).view(1, 1, 2, 2).float()
>>> input
tensor([[[[ 1.,  2.],
          [ 3.,  4.]]]])

>>> m = nn.Upsample(scale_factor=2, mode='nearest')
>>> m(input)
tensor([[[[ 1.,  1.,  2.,  2.],
          [ 1.,  1.,  2.,  2.],
          [ 3.,  3.,  4.,  4.],
          [ 3.,  3.,  4.,  4.]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear')  # align_corners=False
>>> m(input)
tensor([[[[ 1.0000,  1.2500,  1.7500,  2.0000],
          [ 1.5000,  1.7500,  2.2500,  2.5000],
          [ 2.5000,  2.7500,  3.2500,  3.5000],
          [ 3.0000,  3.2500,  3.7500,  4.0000]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear', align_corners=True)
>>> m(input)
tensor([[[[ 1.0000,  1.3333,  1.6667,  2.0000],
          [ 1.6667,  2.0000,  2.3333,  2.6667],
          [ 2.3333,  2.6667,  3.0000,  3.3333],
          [ 3.0000,  3.3333,  3.6667,  4.0000]]]])

>>> # Try scaling the same data in a larger tensor
>>>
>>> input_3x3 = torch.zeros(3, 3).view(1, 1, 3, 3)
>>> input_3x3[:, :, :2, :2].copy_(input)
tensor([[[[ 1.,  2.],
          [ 3.,  4.]]]])
>>> input_3x3
tensor([[[[ 1.,  2.,  0.],
          [ 3.,  4.,  0.],
          [ 0.,  0.,  0.]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear')  # align_corners=False
>>> # Notice that values in top left corner are the same with the small input (except at boundary)
>>> m(input_3x3)
tensor([[[[ 1.0000,  1.2500,  1.7500,  1.5000,  0.5000,  0.0000],
          [ 1.5000,  1.7500,  2.2500,  1.8750,  0.6250,  0.0000],
          [ 2.5000,  2.7500,  3.2500,  2.6250,  0.8750,  0.0000],
          [ 2.2500,  2.4375,  2.8125,  2.2500,  0.7500,  0.0000],
          [ 0.7500,  0.8125,  0.9375,  0.7500,  0.2500,  0.0000],
          [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear', align_corners=True)
>>> # Notice that values in top left corner are now changed
>>> m(input_3x3)
tensor([[[[ 1.0000,  1.4000,  1.8000,  1.6000,  0.8000,  0.0000],
          [ 1.8000,  2.2000,  2.6000,  2.2400,  1.1200,  0.0000],
          [ 2.6000,  3.0000,  3.4000,  2.8800,  1.4400,  0.0000],
          [ 2.4000,  2.7200,  3.0400,  2.5600,  1.2800,  0.0000],
          [ 1.2000,  1.3600,  1.5200,  1.2800,  0.6400,  0.0000],
          [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000]]]])

UpsamplingNearest2d

class torch.nn.UpsamplingNearest2d(size=None, scale_factor=None)

Applies a 2D nearest neighbor upsampling to an input signal composed of several input channels.

To specify the scale, it takes either the size or the scale_factor as it’s constructor argument.

When size is given, it is the output size of the image (h, w).

Parameters:

• size (tuple, optional) – a tuple of ints (H_out, W_out) output sizes
• scale_factor (int, optional) – the multiplier for the image height or width

Warning

This class is deprecated in favor of interpolate().

Shape:

• Input: \((N, C, H_{in}, W_{in})\)
• Output: \((N, C, H_{out}, W_{out})\) where

\[H_{out} = \left\lfloor H_{in} \times \text{scale\_factor} \right\rfloor \]

\[W_{out} = \left\lfloor W_{in} \times \text{scale\_factor} \right\rfloor \]

Examples:

>>> input = torch.arange(1, 5).view(1, 1, 2, 2)
>>> input
tensor([[[[ 1.,  2.],
          [ 3.,  4.]]]])

>>> m = nn.UpsamplingNearest2d(scale_factor=2)
>>> m(input)
tensor([[[[ 1.,  1.,  2.,  2.],
          [ 1.,  1.,  2.,  2.],
          [ 3.,  3.,  4.,  4.],
          [ 3.,  3.,  4.,  4.]]]])

UpsamplingBilinear2d

class torch.nn.UpsamplingBilinear2d(size=None, scale_factor=None)

Applies a 2D bilinear upsampling to an input signal composed of several input channels.

To specify the scale, it takes either the size or the scale_factor as it’s constructor argument.

When size is given, it is the output size of the image (h, w).

Parameters:

• size (tuple, optional) – a tuple of ints (H_out, W_out) output sizes
• scale_factor (int, optional) – the multiplier for the image height or width

Warning

This class is deprecated in favor of interpolate(). It is equivalent to nn.functional.interpolate(..., mode='bilinear', align_corners=True).

Shape:

• Input: \((N, C, H_{in}, W_{in})\)
• Output: \((N, C, H_{out}, W_{out})\) where

\[H_{out} = \left\lfloor H_{in} \times \text{scale\_factor} \right\rfloor \]

\[W_{out} = \left\lfloor W_{in} \times \text{scale\_factor} \right\rfloor \]

Examples:

>>> input = torch.arange(1, 5).view(1, 1, 2, 2)
>>> input
tensor([[[[ 1.,  2.],
          [ 3.,  4.]]]])

>>> m = nn.UpsamplingBilinear2d(scale_factor=2)
>>> m(input)
tensor([[[[ 1.0000,  1.3333,  1.6667,  2.0000],
          [ 1.6667,  2.0000,  2.3333,  2.6667],
          [ 2.3333,  2.6667,  3.0000,  3.3333],
          [ 3.0000,  3.3333,  3.6667,  4.0000]]]])

DataParallel layers (multi-GPU, distributed)

DataParallel

class torch.nn.DataParallel(module, device_ids=None, output_device=None, dim=0)

Implements data parallelism at the module level.

This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension (other objects will be copied once per device). In the forward pass, the module is replicated on each device, and each replica handles a portion of the input. During the backwards pass, gradients from each replica are summed into the original module.

The batch size should be larger than the number of GPUs used.

See also: Use nn.DataParallel instead of multiprocessing

Arbitrary positional and keyword inputs are allowed to be passed into DataParallel EXCEPT Tensors. All tensors will be scattered on dim specified (default 0). Primitive types will be broadcasted, but all other types will be a shallow copy and can be corrupted if written to in the model’s forward pass.

The parallelized module must have its parameters and buffers on device_ids[0] before running this DataParallel module.

Warning

In each forward, module is replicated on each device, so any updates to the runing module in forward will be lost. For example, if module has a counter attribute that is incremented in each forward, it will always stay at the initial value becasue the update is done on the replicas which are destroyed after forward. However, DataParallel guarantees that the replica on device[0] will have its parameters and buffers sharing storage with the base parallelized module. So in-place updates to the parameters or buffers on device[0] will be recorded. E.g., BatchNorm2d and spectral_norm() rely on this behavior to update the buffers.

Warning

Forward and backward hooks defined on module and its submodules will be invoked len(device_ids) times, each with inputs located on a particular device. Particularly, the hooks are only guaranteed to be executed in correct order with respect to operations on corresponding devices. For example, it is not guaranteed that hooks set via register_forward_pre_hook() be executed before all len(device_ids) forward() calls, but that each such hook be executed before the corresponding forward() call of that device.

Warning

When module returns a scalar (i.e., 0-dimensional tensor) in forward(), this wrapper will return a vector of length equal to number of devices used in data parallelism, containing the result from each device.

Note

There is a subtlety in using the pack sequence -> recurrent network -> unpack sequence pattern in a Module wrapped in DataParallel. See My recurrent network doesn’t work with data parallelism section in FAQ for details.

Parameters:

• module (Module) – module to be parallelized
• device_ids (list of python:int or torch.device) – CUDA devices (default: all devices)
• output_device (int or torch.device) – device location of output (default: device_ids[0])

Variables:

module (Module) – the module to be parallelized

Example:

>>> net = torch.nn.DataParallel(model, device_ids=[0, 1, 2])
>>> output = net(input_var)

DistributedDataParallel

class torch.nn.parallel.DistributedDataParallel(module, device_ids=None, output_device=None, dim=0, broadcast_buffers=True, process_group=None, bucket_cap_mb=25, check_reduction=False)

Implements distributed data parallelism that is based on torch.distributed package at the module level.

This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension. The module is replicated on each machine and each device, and each such replica handles a portion of the input. During the backwards pass, gradients from each node are averaged.

The batch size should be larger than the number of GPUs used locally. It should also be an integer multiple of the number of GPUs so that each chunk is the same size (so that each GPU processes the same number of samples).

See also: Basics and Use nn.DataParallel instead of multiprocessing. The same constraints on input as in torch.nn.DataParallel apply.

Creation of this class requires that torch.distributed to be already initialized, by calling torch.distributed.init_process_group()

DistributedDataParallel can be used in the following two ways:

1. Single-Process Multi-GPU

In this case, a single process will be spawned on each host/node and each process will operate on all the GPUs of the node where it’s running. To use DistributedDataParallel in this way, you can simply construct the model as the following:

>>> torch.distributed.init_process_group(backend="nccl")
>>> model = DistributedDataParallel(model) # device_ids will include all GPU devices be default

2. Multi-Process Single-GPU

This is the highly recommended way to use DistributedDataParallel, with multiple processes, each of which operates on a single GPU. This is currently the fastest approach to do data parallel training using PyTorch and applies to both single-node(multi-GPU) and multi-node data parallel training. It is proven to be significantly faster than torch.nn.DataParallel for single-node multi-GPU data parallel training.

Here is how to use it: on each host with N GPUs, you should spawn up N processes, while ensuring that each process invidually works on a single GPU from 0 to N-1. Therefore, it is your job to ensure that your training script operates on a single given GPU by calling:

>>> torch.cuda.set_device(i)

where i is from 0 to N-1. In each process, you should refer the following to construct this module:

>>> torch.distributed.init_process_group(backend='nccl', world_size=4, init_method='...')
>>> model = DistributedDataParallel(model, device_ids=[i], output_device=i)

In order to spawn up multiple processes per node, you can use either torch.distributed.launch or torch.multiprocessing.spawn

Note

nccl backend is currently the fastest and highly recommended backend to be used with Multi-Process Single-GPU distributed training and this applies to both single-node and multi-node distributed training

Warning

This module works only with the gloo and nccl backends.

Warning

Constructor, forward method, and differentiation of the output (or a function of the output of this module) is a distributed synchronization point. Take that into account in case different processes might be executing different code.

Warning

This module assumes all parameters are registered in the model by the time it is created. No parameters should be added nor removed later. Same applies to buffers.

Warning

This module assumes all parameters are registered in the model of each distributed processes are in the same order. The module itself will conduct gradient all-reduction following the reverse order of the registered parameters of the model. In other wise, it is users’ responsibility to ensure that each distributed process has the exact same model and thus the exact parameter registeration order.

Warning

This module assumes all buffers and gradients are dense.

Warning

This module doesn’t work with torch.autograd.grad() (i.e. it will only work if gradients are to be accumulated in .grad attributes of parameters).

Warning

If you plan on using this module with a nccl backend or a gloo backend (that uses Infiniband), together with a DataLoader that uses multiple workers, please change the multiprocessing start method to forkserver (Python 3 only) or spawn. Unfortunately Gloo (that uses Infiniband) and NCCL2 are not fork safe, and you will likely experience deadlocks if you don’t change this setting.

Warning

Forward and backward hooks defined on module and its submodules won’t be invoked anymore, unless the hooks are initialized in the forward() method.

Warning

You should never try to change your model’s parameters after wrapping up your model with DistributedDataParallel. In other words, when wrapping up your model with DistributedDataParallel, the constructor of DistributedDataParallel will register the additional gradient reduction functions on all the parameters of the model itself at the time of construction. If you change the model’s parameters after the DistributedDataParallel construction, this is not supported and unexpected behaviors can happen, since some parameters’ gradient reduction functions might not get called.

Note

Parameters are never broadcast between processes. The module performs an all-reduce step on gradients and assumes that they will be modified by the optimizer in all processes in the same way. Buffers (e.g. BatchNorm stats) are broadcast from the module in process of rank 0, to all other replicas in the system in every iteration.

Parameters:

• module (Module) – module to be parallelized
• device_ids (list of python:int or torch.device) – CUDA devices (default: all devices)
• output_device (int or torch.device) – device location of output (default: device_ids[0])
• broadcast_buffers (bool) – flag that enables syncing (broadcasting) buffers of the module at beginning of the forward function. (default: True)
• process_group – the process group to be used for distributed data all-reduction. If None, the default process group, which is created by `torch.distributed.init_process_group`, will be used. (default: None)
• bucket_cap_mb – DistributedDataParallel will bucket parameters into multiple buckets so that gradient reduction of each bucket can potentially overlap with backward computation. bucket_cap_mb controls the bucket size in MegaBytes (MB) (default: 25)
• check_reduction – when setting to True, it enables DistributedDataParallel to automatically check if the previous iteration’s backward reductions were successfully issued at the beginning of every iteration’s forward function. You normally don’t need this option enabled unless you are observing weird behaviors such as different ranks are getting different gradients, which should not happen if DistributedDataParallel is corrected used. (default: False)

Variables:

module (Module) – the module to be parallelized

Example::

>>> torch.distributed.init_process_group(backend='nccl', world_size=4, init_method='...')
>>> net = torch.nn.DistributedDataParallel(model, pg)

DistributedDataParallelCPU

class torch.nn.parallel.DistributedDataParallelCPU(module)

Implements distributed data parallelism for CPU at the module level.

This module supports the mpi and gloo backends.

This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension. The module is replicated on each machine, and each such replica handles a portion of the input. During the backwards pass, gradients from each node are averaged.

This module could be used in conjunction with the DistributedSampler, (see :class torch.utils.data.distributed.DistributedSampler) which will load a subset of the original datset for each node with the same batch size. So strong scaling should be configured like this:

n = 1, batch size = 12

n = 2, batch size = 64

n = 4, batch size = 32

n = 8, batch size = 16

Creation of this class requires the distributed package to be already initialized in the process group mode (see torch.distributed.init_process_group()).

Warning

Constructor, forward method, and differentiation of the output (or a function of the output of this module) is a distributed synchronization point. Take that into account in case different node might be executing different code.

Warning

This module assumes all parameters are registered in the model by the time it is created. No parameters should be added nor removed later.

Warning

This module assumes all gradients are dense.

Warning

This module doesn’t work with torch.autograd.grad() (i.e. it will only work if gradients are to be accumulated in .grad attributes of parameters).

Warning

Forward and backward hooks defined on module and its submodules won’t be invoked anymore, unless the hooks are initialized in the forward() method.

Note

Parameters are broadcast between nodes in the __init__() function. The module performs an all-reduce step on gradients and assumes that they will be modified by the optimizer in all nodes in the same way.

Parameters:module – module to be parallelized

Example:

>>> torch.distributed.init_process_group(world_size=4, init_method='...')
>>> net = torch.nn.DistributedDataParallelCPU(model)

Utilities

clip_grad_norm_

torch.nn.utils.clip_grad_norm_(parameters, max_norm, norm_type=2)

Clips gradient norm of an iterable of parameters.

The norm is computed over all gradients together, as if they were concatenated into a single vector. Gradients are modified in-place.

Parameters:

• parameters (Iterable[Tensor] or Tensor) – an iterable of Tensors or a single Tensor that will have gradients normalized
• max_norm (float or int) – max norm of the gradients
• norm_type (float or int) – type of the used p-norm. Can be 'inf' for infinity norm.

Returns:

Total norm of the parameters (viewed as a single vector).

clip_grad_value_

torch.nn.utils.clip_grad_value_(parameters, clip_value)

Clips gradient of an iterable of parameters at specified value.

Gradients are modified in-place.

Parameters:

• parameters (Iterable[Tensor] or Tensor) – an iterable of Tensors or a single Tensor that will have gradients normalized
• clip_value (float or int) – maximum allowed value of the gradients The gradients are clipped in the range [-clip_value, clip_value]

parameters_to_vector

torch.nn.utils.parameters_to_vector(parameters)

Convert parameters to one vector

Parameters:parameters (Iterable[Tensor]) – an iterator of Tensors that are the parameters of a model. Returns:The parameters represented by a single vector

vector_to_parameters

torch.nn.utils.vector_to_parameters(vec, parameters)

Convert one vector to the parameters

Parameters:

• vec (Tensor) – a single vector represents the parameters of a model.
• parameters (Iterable[Tensor]) – an iterator of Tensors that are the parameters of a model.

weight_norm

torch.nn.utils.weight_norm(module, name='weight', dim=0)

Applies weight normalization to a parameter in the given module.

\[\mathbf{w} = g \dfrac{\mathbf{v}}{\|\mathbf{v}\|} \]

Weight normalization is a reparameterization that decouples the magnitude of a weight tensor from its direction. This replaces the parameter specified by name (e.g. “weight”) with two parameters: one specifying the magnitude (e.g. “weight_g”) and one specifying the direction (e.g. “weight_v”). Weight normalization is implemented via a hook that recomputes the weight tensor from the magnitude and direction before every forward() call.

By default, with dim=0, the norm is computed independently per output channel/plane. To compute a norm over the entire weight tensor, use dim=None.

See https://arxiv.org/abs/1602.07868

Parameters:

• module (nn.Module) – containing module
• name (str, optional) – name of weight parameter
• dim (int, optional) – dimension over which to compute the norm

Returns:

The original module with the weight norm hook

Example:

>>> m = weight_norm(nn.Linear(20, 40), name='weight')
Linear (20 -> 40)
>>> m.weight_g.size()
torch.Size([40, 1])
>>> m.weight_v.size()
torch.Size([40, 20])

remove_weight_norm

torch.nn.utils.remove_weight_norm(module, name='weight')

Removes the weight normalization reparameterization from a module.

Parameters:

• module (nn.Module) – containing module
• name (str, optional) – name of weight parameter

Example

>>> m = weight_norm(nn.Linear(20, 40))
>>> remove_weight_norm(m)

spectral_norm

torch.nn.utils.spectral_norm(module, name='weight', n_power_iterations=1, eps=1e-12, dim=None)

Applies spectral normalization to a parameter in the given module.

\[\mathbf{W} = \dfrac{\mathbf{W}}{\sigma(\mathbf{W})} \\ \sigma(\mathbf{W}) = \max_{\mathbf{h}: \mathbf{h} \ne 0} \dfrac{\|\mathbf{W} \mathbf{h}\|_2}{\|\mathbf{h}\|_2} \]

Spectral normalization stabilizes the training of discriminators (critics) in Generaive Adversarial Networks (GANs) by rescaling the weight tensor with spectral norm \(\sigma\) of the weight matrix calculated using power iteration method. If the dimension of the weight tensor is greater than 2, it is reshaped to 2D in power iteration method to get spectral norm. This is implemented via a hook that calculates spectral norm and rescales weight before every forward() call.

See Spectral Normalization for Generative Adversarial Networks .

Parameters:

• module (nn.Module) – containing module
• name (str, optional) – name of weight parameter
• n_power_iterations (int, optional) – number of power iterations to calculate spectal norm
• eps (float, optional) – epsilon for numerical stability in calculating norms
• dim (int, optional) – dimension corresponding to number of outputs, the default is 0, except for modules that are instances of ConvTranspose1/2/3d, when it is 1

Returns:

The original module with the spectal norm hook

Example:

>>> m = spectral_norm(nn.Linear(20, 40))
Linear (20 -> 40)
>>> m.weight_u.size()
torch.Size([20])

remove_spectral_norm

torch.nn.utils.remove_spectral_norm(module, name='weight')

Removes the spectral normalization reparameterization from a module.

Parameters:

• module (nn.Module) – containing module
• name (str, optional) – name of weight parameter

Example

>>> m = spectral_norm(nn.Linear(40, 10))
>>> remove_spectral_norm(m)

PackedSequence

torch.nn.utils.rnn.PackedSequence(data, batch_sizes=None)

Holds the data and list of batch_sizes of a packed sequence.

All RNN modules accept packed sequences as inputs.

Note

Instances of this class should never be created manually. They are meant to be instantiated by functions like pack_padded_sequence().

Batch sizes represent the number elements at each sequence step in the batch, not the varying sequence lengths passed to pack_padded_sequence(). For instance, given data abc and x the PackedSequence would contain data axbc with batch_sizes=[2,1,1].

Variables:

• data (Tensor) – Tensor containing packed sequence
• batch_sizes (Tensor) – Tensor of integers holding information about the batch size at each sequence step

pack_padded_sequence

torch.nn.utils.rnn.pack_padded_sequence(input, lengths, batch_first=False)

Packs a Tensor containing padded sequences of variable length.

Input can be of size T x B x * where T is the length of the longest sequence (equal to lengths[0]), B is the batch size, and * is any number of dimensions (including 0). If batch_first is True B x T x * inputs are expected.

The sequences should be sorted by length in a decreasing order, i.e. input[:,0] should be the longest sequence, and input[:,B-1] the shortest one.

Note

This function accepts any input that has at least two dimensions. You can apply it to pack the labels, and use the output of the RNN with them to compute the loss directly. A Tensor can be retrieved from a PackedSequence object by accessing its .data attribute.

Parameters:

• input (Tensor) – padded batch of variable length sequences.
• lengths (Tensor) – list of sequences lengths of each batch element.
• batch_first (bool, optional) – if True, the input is expected in B x T x * format.

Returns:

a PackedSequence object

pad_packed_sequence

torch.nn.utils.rnn.pad_packed_sequence(sequence, batch_first=False, padding_value=0.0, total_length=None)

Pads a packed batch of variable length sequences.

It is an inverse operation to pack_padded_sequence().

The returned Tensor’s data will be of size T x B x *, where T is the length of the longest sequence and B is the batch size. If batch_first is True, the data will be transposed into B x T x * format.

Batch elements will be ordered decreasingly by their length.

Note

total_length is useful to implement the pack sequence -> recurrent network -> unpack sequence pattern in a Module wrapped in DataParallel. See this FAQ section for details.

Parameters:

• sequence (PackedSequence) – batch to pad
• batch_first (bool, optional) – if True, the output will be in B x T x * format.
• padding_value (float, optional) – values for padded elements.
• total_length (int, optional) – if not None, the output will be padded to have length total_length. This method will throw ValueError if total_length is less than the max sequence length in sequence.

Returns:

Tuple of Tensor containing the padded sequence, and a Tensor containing the list of lengths of each sequence in the batch.

pad_sequence

torch.nn.utils.rnn.pad_sequence(sequences, batch_first=False, padding_value=0)

Pad a list of variable length Tensors with zero

pad_sequence stacks a list of Tensors along a new dimension, and pads them to equal length. For example, if the input is list of sequences with size L x * and if batch_first is False, and T x B x * otherwise.

B is batch size. It is equal to the number of elements in sequences. T is length of the longest sequence. L is length of the sequence. * is any number of trailing dimensions, including none.

Example

>>> from torch.nn.utils.rnn import pad_sequence
>>> a = torch.ones(25, 300)
>>> b = torch.ones(22, 300)
>>> c = torch.ones(15, 300)
>>> pad_sequence([a, b, c]).size()
torch.Size([25, 3, 300])

Note

This function returns a Tensor of size T x B x * or B x T x * where T is the length of the longest sequence. This function assumes trailing dimensions and type of all the Tensors in sequences are same.

Parameters:

• sequences (list[Tensor]) – list of variable length sequences.
• batch_first (bool, optional) – output will be in B x T x * if True, or in T x B x * otherwise
• padding_value (float, optional) – value for padded elements. Default: 0.

Returns:

Tensor of size T x B x * if batch_first is False. Tensor of size B x T x * otherwise

pack_sequence

torch.nn.utils.rnn.pack_sequence(sequences)

Packs a list of variable length Tensors

sequences should be a list of Tensors of size L x *, where L is the length of a sequence and * is any number of trailing dimensions, including zero. They should be sorted in the order of decreasing length.

Example

>>> from torch.nn.utils.rnn import pack_sequence
>>> a = torch.tensor([1,2,3])
>>> b = torch.tensor([4,5])
>>> c = torch.tensor([6])
>>> pack_sequence([a, b, c])
PackedSequence(data=tensor([ 1,  4,  6,  2,  5,  3]), batch_sizes=tensor([ 3,  2,  1]))

Parameters:sequences (list[Tensor]) – A list of sequences of decreasing length. Returns:a PackedSequence object

torch.nn.functional

Convolution functions

conv1d

torch.nn.functional.conv1d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 1D convolution over an input signal composed of several input planes.

See Conv1d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iW)\)
• weight – filters of shape \((\text{out\_channels} \times \frac{\text{in\_channels}}{\text{groups}} \times kW)\)
• bias – optional bias of shape \((\text{out\_channels})\). Default: None
• stride – the stride of the convolving kernel. Can be a single number or a one-element tuple (sW,). Default: 1
• padding – implicit zero paddings on both sides of the input. Can be a single number or a one-element tuple (padW,). Default: 0
• dilation – the spacing between kernel elements. Can be a single number or a one-element tuple (dW,). Default: 1
• groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1

Examples:

>>> filters = torch.randn(33, 16, 3)
>>> inputs = torch.randn(20, 16, 50)
>>> F.conv1d(inputs, filters)

conv2d

torch.nn.functional.conv2d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 2D convolution over an input image composed of several input planes.

See Conv2d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iH \times iW)\)
• weight – filters of shape \((\text{out\_channels} \times \frac{\text{in\_channels}}{\text{groups}} \times kH \times kW)\)
• bias – optional bias tensor of shape \((\text{out\_channels})\). Default: None
• stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1
• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0
• dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1
• groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1

Examples:

>>> # With square kernels and equal stride
>>> filters = torch.randn(8,4,3,3)
>>> inputs = torch.randn(1,4,5,5)
>>> F.conv2d(inputs, filters, padding=1)

conv3d

torch.nn.functional.conv3d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 3D convolution over an input image composed of several input planes.

See Conv3d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iT \times iH \times iW)\)
• weight – filters of shape \((\text{out\_channels} \times \frac{\text{in\_channels}}{\text{groups}} \times kT \times kH \times kW)\)
• bias – optional bias tensor of shape \((\text{out\_channels})\). Default: None
• stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1
• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW). Default: 0
• dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1
• groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1

Examples:

>>> filters = torch.randn(33, 16, 3, 3, 3)
>>> inputs = torch.randn(20, 16, 50, 10, 20)
>>> F.conv3d(inputs, filters)

conv_transpose1d

torch.nn.functional.conv_transpose1d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 1D transposed convolution operator over an input signal composed of several input planes, sometimes also called “deconvolution”.

See ConvTranspose1d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iW)\)
• weight – filters of shape \((\text{in\_channels} \times \frac{\text{out\_channels}}{\text{groups}} \times kW)\)
• bias – optional bias of shape \((\text{out\_channels})\). Default: None
• stride – the stride of the convolving kernel. Can be a single number or a tuple (sW,). Default: 1
• padding – kernel_size - 1 - padding zero-padding will be added to both sides of each dimension in the input. Can be a single number or a tuple (padW,). Default: 0
• output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple (out_padW). Default: 0
• groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
• dilation – the spacing between kernel elements. Can be a single number or a tuple (dW,). Default: 1

Examples:

>>> inputs = torch.randn(20, 16, 50)
>>> weights = torch.randn(16, 33, 5)
>>> F.conv_transpose1d(inputs, weights)

conv_transpose2d

torch.nn.functional.conv_transpose2d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 2D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”.

See ConvTranspose2d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iH \times iW)\)
• weight – filters of shape \((\text{in\_channels} \times \frac{\text{out\_channels}}{\text{groups}} \times kH \times kW)\)
• bias – optional bias of shape \((\text{out\_channels})\). Default: None
• stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1
• padding – kernel_size - 1 - padding zero-padding will be added to both sides of each dimension in the input. Can be a single number or a tuple (padH, padW). Default: 0
• output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple (out_padH, out_padW). Default: 0
• groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
• dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1

Examples:

>>> # With square kernels and equal stride
>>> inputs = torch.randn(1, 4, 5, 5)
>>> weights = torch.randn(4, 8, 3, 3)
>>> F.conv_transpose2d(inputs, weights, padding=1)

conv_transpose3d

torch.nn.functional.conv_transpose3d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 3D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”

See ConvTranspose3d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iT \times iH \times iW)\)
• weight – filters of shape \((\text{in\_channels} \times \frac{\text{out\_channels}}{\text{groups}} \times kT \times kH \times kW)\)
• bias – optional bias of shape \((\text{out\_channels})\). Default: None
• stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1
• padding – kernel_size - 1 - padding zero-padding will be added to both sides of each dimension in the input. Can be a single number or a tuple (padT, padH, padW). Default: 0
• output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple (out_padT, out_padH, out_padW). Default: 0
• groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
• dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1

Examples:

>>> inputs = torch.randn(20, 16, 50, 10, 20)
>>> weights = torch.randn(16, 33, 3, 3, 3)
>>> F.conv_transpose3d(inputs, weights)

unfold

torch.nn.functional.unfold(input, kernel_size, dilation=1, padding=0, stride=1)

Extracts sliding local blocks from an batched input tensor.

Warning

Currently, only 4-D input tensors (batched image-like tensors) are supported.

See torch.nn.Unfold for details

fold

torch.nn.functional.fold(input, output_size, kernel_size, dilation=1, padding=0, stride=1)

Combines an array of sliding local blocks into a large containing tensor.

Warning

Currently, only 4-D output tensors (batched image-like tensors) are supported.

See torch.nn.Fold for details

Pooling functions

avg_pool1d

torch.nn.functional.avg_pool1d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor

Applies a 1D average pooling over an input signal composed of several input planes.

See AvgPool1d for details and output shape.

Parameters:

• input – input tensor of shape \((\text{minibatch} \times \text{in\_channels} \times iW)\)
• kernel_size – the size of the window. Can be a single number or a tuple \((kW,)\)
• stride – the stride of the window. Can be a single number or a tuple (sW,). Default: kernel_size
• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padW,). Default: 0
• ceil_mode – when True, will use ceil instead of floor to compute the output shape. Default: False
• count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: True

Examples::

>>> # pool of square window of size=3, stride=2
>>> input = torch.tensor([[[1,2,3,4,5,6,7]]])
>>> F.avg_pool1d(input, kernel_size=3, stride=2)
tensor([[[ 2.,  4.,  6.]]])

avg_pool2d

torch.nn.functional.avg_pool2d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor

Applies 2D average-pooling operation in \(kH \times kW\) regions by step size \(sH \times sW\) steps. The number of output features is equal to the number of input planes.

See AvgPool2d for details and output shape.

Parameters:

• input – input tensor \((\text{minibatch} \times \text{in\_channels} \times iH \times iW)\)
• kernel_size – size of the pooling region. Can be a single number or a tuple \((kH \times kW)\)
• stride – stride of the pooling operation. Can be a single number or a tuple (sH, sW). Default: kernel_size
• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0
• ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape. Default: False
• count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: True

avg_pool3d

torch.nn.functional.avg_pool3d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor

Applies 3D average-pooling operation in \(kT \times kH \times kW\) regions by step size \(sT \times sH \times sW\) steps. The number of output features is equal to \(\lfloor\frac{\text{input planes}}{sT}\rfloor\).

See AvgPool3d for details and output shape.

Parameters:

• input – input tensor \((\text{minibatch} \times \text{in\_channels} \times iT \times iH \times iW)\)
• kernel_size – size of the pooling region. Can be a single number or a tuple \((kT \times kH \times kW)\)
• stride – stride of the pooling operation. Can be a single number or a tuple (sT, sH, sW). Default: kernel_size
• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW), Default: 0
• ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape
• count_include_pad – when True, will include the zero-padding in the averaging calculation

max_pool1d

torch.nn.functional.max_pool1d(*args, **kwargs)

Applies a 1D max pooling over an input signal composed of several input planes.

See MaxPool1d for details.

max_pool2d

torch.nn.functional.max_pool2d(*args, **kwargs)

Applies a 2D max pooling over an input signal composed of several input planes.

See MaxPool2d for details.

max_pool3d

torch.nn.functional.max_pool3d(*args, **kwargs)

Applies a 3D max pooling over an input signal composed of several input planes.

See MaxPool3d for details.

max_unpool1d

torch.nn.functional.max_unpool1d(input, indices, kernel_size, stride=None, padding=0, output_size=None)

Computes a partial inverse of MaxPool1d.

See MaxUnpool1d for details.

max_unpool2d

torch.nn.functional.max_unpool2d(input, indices, kernel_size, stride=None, padding=0, output_size=None)

Computes a partial inverse of MaxPool2d.

See MaxUnpool2d for details.

max_unpool3d

torch.nn.functional.max_unpool3d(input, indices, kernel_size, stride=None, padding=0, output_size=None)

Computes a partial inverse of MaxPool3d.

See MaxUnpool3d for details.

lp_pool1d

torch.nn.functional.lp_pool1d(input, norm_type, kernel_size, stride=None, ceil_mode=False)

Applies a 1D power-average pooling over an input signal composed of several input planes. If the sum of all inputs to the power of p is zero, the gradient is set to zero as well.

See LPPool1d for details.

lp_pool2d

torch.nn.functional.lp_pool2d(input, norm_type, kernel_size, stride=None, ceil_mode=False)

Applies a 2D power-average pooling over an input signal composed of several input planes. If the sum of all inputs to the power of p is zero, the gradient is set to zero as well.

See LPPool2d for details.

adaptive_max_pool1d

torch.nn.functional.adaptive_max_pool1d(*args, **kwargs)

Applies a 1D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool1d for details and output shape.

Parameters:

• output_size – the target output size (single integer)
• return_indices – whether to return pooling indices. Default: False

adaptive_max_pool2d

torch.nn.functional.adaptive_max_pool2d(*args, **kwargs)

Applies a 2D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool2d for details and output shape.

Parameters:

• output_size – the target output size (single integer or double-integer tuple)
• return_indices – whether to return pooling indices. Default: False

adaptive_max_pool3d

torch.nn.functional.adaptive_max_pool3d(*args, **kwargs)

Applies a 3D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool3d for details and output shape.

Parameters:

• output_size – the target output size (single integer or triple-integer tuple)
• return_indices – whether to return pooling indices. Default: False

adaptive_avg_pool1d

torch.nn.functional.adaptive_avg_pool1d(input, output_size) → Tensor

Applies a 1D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool1d for details and output shape.

Parameters:output_size – the target output size (single integer)

adaptive_avg_pool2d

torch.nn.functional.adaptive_avg_pool2d(input, output_size)

Applies a 2D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool2d for details and output shape.

Parameters:output_size – the target output size (single integer or double-integer tuple)

adaptive_avg_pool3d

torch.nn.functional.adaptive_avg_pool3d(input, output_size)

Applies a 3D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool3d for details and output shape.

Parameters:output_size – the target output size (single integer or triple-integer tuple)

Non-linear activation functions

threshold

torch.nn.functional.threshold(input, threshold, value, inplace=False)

Thresholds each element of the input Tensor.

See Threshold for more details.

torch.nn.functional.threshold_(input, threshold, value) → Tensor

In-place version of threshold().

relu

torch.nn.functional.relu(input, inplace=False) → Tensor

Applies the rectified linear unit function element-wise. See ReLU for more details.

torch.nn.functional.relu_(input) → Tensor

In-place version of relu().

hardtanh

torch.nn.functional.hardtanh(input, min_val=-1., max_val=1., inplace=False) → Tensor

Applies the HardTanh function element-wise. See Hardtanh for more details.

torch.nn.functional.hardtanh_(input, min_val=-1., max_val=1.) → Tensor

In-place version of hardtanh().

relu6

torch.nn.functional.relu6(input, inplace=False) → Tensor

Applies the element-wise function \(\text{ReLU6}(x) = \min(\max(0,x), 6)\).

See ReLU6 for more details.

elu

torch.nn.functional.elu(input, alpha=1.0, inplace=False)

Applies element-wise, \(\text{ELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x) - 1))\).

See ELU for more details.

torch.nn.functional.elu_(input, alpha=1.) → Tensor

In-place version of elu().

selu

torch.nn.functional.selu(input, inplace=False) → Tensor

Applies element-wise, \(\text{SELU}(x) = scale * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1)))\), with \(\alpha=1.6732632423543772848170429916717\) and \(scale=1.0507009873554804934193349852946\).

See SELU for more details.

celu

torch.nn.functional.celu(input, alpha=1., inplace=False) → Tensor

Applies element-wise, \(\text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x/\alpha) - 1))\).

See CELU for more details.

leaky_relu

torch.nn.functional.leaky_relu(input, negative_slope=0.01, inplace=False) → Tensor

Applies element-wise, \(\text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x)\)

See LeakyReLU for more details.

torch.nn.functional.leaky_relu_(input, negative_slope=0.01) → Tensor

In-place version of leaky_relu().

prelu

torch.nn.functional.prelu(input, weight) → Tensor

Applies element-wise the function \(\text{PReLU}(x) = \max(0,x) + \text{weight} * \min(0,x)\) where weight is a learnable parameter.

See PReLU for more details.

rrelu

torch.nn.functional.rrelu(input, lower=1./8, upper=1./3, training=False, inplace=False) → Tensor

Randomized leaky ReLU.

See RReLU for more details.

torch.nn.functional.rrelu_(input, lower=1./8, upper=1./3, training=False) → Tensor

In-place version of rrelu().

glu

torch.nn.functional.glu(input, dim=-1) → Tensor

The gated linear unit. Computes:

\[H = A \times \sigma(B)\]

where input is split in half along dim to form A and B.

See Language Modeling with Gated Convolutional Networks.

Parameters:

• input (Tensor) – input tensor
• dim (int) – dimension on which to split the input

logsigmoid

torch.nn.functional.logsigmoid(input) → Tensor

Applies element-wise \(\text{LogSigmoid}(x) = \log \left(\frac{1}{1 + \exp(-x_i)}\right)\)

See LogSigmoid for more details.

hardshrink

torch.nn.functional.hardshrink(input, lambd=0.5) → Tensor

Applies the hard shrinkage function element-wise

See Hardshrink for more details.

tanhshrink

torch.nn.functional.tanhshrink(input) → Tensor

Applies element-wise, \(\text{Tanhshrink}(x) = x - \text{Tanh}(x)\)

See Tanhshrink for more details.

softsign

torch.nn.functional.softsign(input) → Tensor

Applies element-wise, the function \(\text{SoftSign}(x) = \frac{x}{1 + |x|}\)

See Softsign for more details.

softplus

torch.nn.functional.softplus(input, beta=1, threshold=20) → Tensor

softmin

torch.nn.functional.softmin(input, dim=None, _stacklevel=3, dtype=None)

Applies a softmin function.

Note that \(\text{Softmin}(x) = \text{Softmax}(-x)\). See softmax definition for mathematical formula.

See Softmin for more details.

Parameters:

• input (Tensor) – input
• dim (int) – A dimension along which softmin will be computed (so every slice along dim will sum to 1).
• dtype (torch.dtype, optional) – the desired data type of returned tensor.

:param If specified, the input tensor is casted to dtype before the operation: :param is performed. This is useful for preventing data type overflows. Default: None.

softmax

torch.nn.functional.softmax(input, dim=None, _stacklevel=3, dtype=None)

Applies a softmax function.

Softmax is defined as:

\(\text{Softmax}(x_{i}) = \frac{exp(x_i)}{\sum_j exp(x_j)}\)

It is applied to all slices along dim, and will re-scale them so that the elements lie in the range (0, 1) and sum to 1.

See Softmax for more details.

Parameters:

• input (Tensor) – input
• dim (int) – A dimension along which softmax will be computed.
• dtype (torch.dtype, optional) – the desired data type of returned tensor.

:param If specified, the input tensor is casted to dtype before the operation: :param is performed. This is useful for preventing data type overflows. Default: None.

Note

This function doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use log_softmax instead (it’s faster and has better numerical properties).

softshrink

torch.nn.functional.softshrink(input, lambd=0.5) → Tensor

Applies the soft shrinkage function elementwise

See Softshrink for more details.

gumbel_softmax

torch.nn.functional.gumbel_softmax(logits, tau=1.0, hard=False, eps=1e-10)

Sample from the Gumbel-Softmax distribution and optionally discretize.

Parameters:

• logits – [batch_size, num_features] unnormalized log probabilities
• tau – non-negative scalar temperature
• hard – if True, the returned samples will be discretized as one-hot vectors, but will be differentiated as if it is the soft sample in autograd

Returns:

Sampled tensor of shape batch_size x num_features from the Gumbel-Softmax distribution. If hard=True, the returned samples will be one-hot, otherwise they will be probability distributions that sum to 1 across features

Constraints:

• Currently only work on 2D input logits tensor of shape batch_size x num_features

Based on https://github.com/ericjang/gumbel-softmax/blob/3c8584924603869e90ca74ac20a6a03d99a91ef9/Categorical%20VAE.ipynb , (MIT license)

log_softmax

torch.nn.functional.log_softmax(input, dim=None, _stacklevel=3, dtype=None)

Applies a softmax followed by a logarithm.

While mathematically equivalent to log(softmax(x)), doing these two operations separately is slower, and numerically unstable. This function uses an alternative formulation to compute the output and gradient correctly.

See LogSoftmax for more details.

Parameters:

• input (Tensor) – input
• dim (int) – A dimension along which log_softmax will be computed.
• dtype (torch.dtype, optional) – the desired data type of returned tensor.

:param If specified, the input tensor is casted to dtype before the operation: :param is performed. This is useful for preventing data type overflows. Default: None.

tanh

torch.nn.functional.tanh(input) → Tensor

Applies element-wise, \(\text{Tanh}(x) = \tanh(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)}\)

See Tanh for more details.

sigmoid

torch.nn.functional.sigmoid(input) → Tensor

Applies the element-wise function \(\text{Sigmoid}(x) = \frac{1}{1 + \exp(-x)}\)

See Sigmoid for more details.

Normalization functions

batch_norm

torch.nn.functional.batch_norm(input, running_mean, running_var, weight=None, bias=None, training=False, momentum=0.1, eps=1e-05)

Applies Batch Normalization for each channel across a batch of data.

See BatchNorm1d, BatchNorm2d, BatchNorm3d for details.

instance_norm

torch.nn.functional.instance_norm(input, running_mean=None, running_var=None, weight=None, bias=None, use_input_stats=True, momentum=0.1, eps=1e-05)

Applies Instance Normalization for each channel in each data sample in a batch.

See InstanceNorm1d, InstanceNorm2d, InstanceNorm3d for details.

layer_norm

torch.nn.functional.layer_norm(input, normalized_shape, weight=None, bias=None, eps=1e-05)

Applies Layer Normalization for last certain number of dimensions.

See LayerNorm for details.

local_response_norm

torch.nn.functional.local_response_norm(input, size, alpha=0.0001, beta=0.75, k=1.0)

Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.

See LocalResponseNorm for details.

normalize

torch.nn.functional.normalize(input, p=2, dim=1, eps=1e-12, out=None)

Performs \(L_p\) normalization of inputs over specified dimension.

For a tensor input of sizes \((n_0, ..., n_{dim}, ..., n_k)\), each \(n_{dim}\) -element vector \(v\) along dimension dim is transformed as

\[v = \frac{v}{\max(\lVert v \rVert_p, \epsilon)}. \]

With the default arguments it uses the Euclidean norm over vectors along dimension \(1\) for normalization.

Parameters:

• input – input tensor of any shape
• p (float) – the exponent value in the norm formulation. Default: 2
• dim (int) – the dimension to reduce. Default: 1
• eps (float) – small value to avoid division by zero. Default: 1e-12
• out (Tensor, optional) – the output tensor. If out is used, this operation won’t be differentiable.

Linear functions

linear

torch.nn.functional.linear(input, weight, bias=None)

Applies a linear transformation to the incoming data: \(y = xA^T + b\).

Shape:

• Input: \((N, *, in\_features)\) where * means any number of additional dimensions
• Weight: \((out\_features, in\_features)\)
• Bias: \((out\_features)\)
• Output: \((N, *, out\_features)\)

bilinear

torch.nn.functional.bilinear(input1, input2, weight, bias=None)

Dropout functions

dropout

torch.nn.functional.dropout(input, p=0.5, training=True, inplace=False)

During training, randomly zeroes some of the elements of the input tensor with probability p using samples from a Bernoulli distribution.

See Dropout for details.

Parameters:

• p – probability of an element to be zeroed. Default: 0.5
• training – apply dropout if is True. Defualt: True
• inplace – If set to True, will do this operation in-place. Default: False

alpha_dropout

torch.nn.functional.alpha_dropout(input, p=0.5, training=False, inplace=False)

Applies alpha dropout to the input.

See AlphaDropout for details.

dropout2d

torch.nn.functional.dropout2d(input, p=0.5, training=True, inplace=False)

Randomly zero out entire channels (a channel is a 2D feature map, e.g., the \(j\)-th channel of the \(i\)-th sample in the batched input is a 2D tensor \(\text{input}[i, j]\)) of the input tensor). Each channel will be zeroed out independently on every forward call. with probability p using samples from a Bernoulli distribution.

See Dropout2d for details.

Parameters:

• p – probability of a channel to be zeroed. Default: 0.5
• training – apply dropout if is True. Defualt: True
• inplace – If set to True, will do this operation in-place. Default: False

dropout3d

torch.nn.functional.dropout3d(input, p=0.5, training=True, inplace=False)

Randomly zero out entire channels (a channel is a 3D feature map, e.g., the \(j\)-th channel of the \(i\)-th sample in the batched input is a 3D tensor \(\text{input}[i, j]\)) of the input tensor). Each channel will be zeroed out independently on every forward call. with probability p using samples from a Bernoulli distribution.

See Dropout3d for details.

Parameters:

• p – probability of a channel to be zeroed. Default: 0.5
• training – apply dropout if is True. Defualt: True
• inplace – If set to True, will do this operation in-place. Default: False

Sparse functions

embedding

torch.nn.functional.embedding(input, weight, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False)

A simple lookup table that looks up embeddings in a fixed dictionary and size.

This module is often used to retrieve word embeddings using indices. The input to the module is a list of indices, and the embedding matrix, and the output is the corresponding word embeddings.

See torch.nn.Embedding for more details.

Parameters:

• input (LongTensor) – Tensor containing indices into the embedding matrix
• weight (Tensor) – The embedding matrix with number of rows equal to the maximum possible index + 1, and number of columns equal to the embedding size
• padding_idx (int, optional) – If given, pads the output with the embedding vector at padding_idx (initialized to zeros) whenever it encounters the index.
• max_norm (float, optional) – If given, each embedding vector with norm larger than max_norm is renormalized to have norm max_norm. Note: this will modify weight in-place.
• norm_type (float, optional) – The p of the p-norm to compute for the max_norm option. Default 2.
• scale_grad_by_freq (boolean, optional) – If given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default False.
• sparse (bool, optional) – If True, gradient w.r.t. weight will be a sparse tensor. See Notes under torch.nn.Embedding for more details regarding sparse gradients.

Shape:

• Input: LongTensor of arbitrary shape containing the indices to extract

• Weight: Embedding matrix of floating point type with shape (V, embedding_dim),

  where V = maximum index + 1 and embedding_dim = the embedding size

• Output: (*, embedding_dim), where * is the input shape

Examples:

>>> # a batch of 2 samples of 4 indices each
>>> input = torch.tensor([[1,2,4,5],[4,3,2,9]])
>>> # an embedding matrix containing 10 tensors of size 3
>>> embedding_matrix = torch.rand(10, 3)
>>> F.embedding(input, embedding_matrix)
tensor([[[ 0.8490,  0.9625,  0.6753],
         [ 0.9666,  0.7761,  0.6108],
         [ 0.6246,  0.9751,  0.3618],
         [ 0.4161,  0.2419,  0.7383]],

        [[ 0.6246,  0.9751,  0.3618],
         [ 0.0237,  0.7794,  0.0528],
         [ 0.9666,  0.7761,  0.6108],
         [ 0.3385,  0.8612,  0.1867]]])

>>> # example with padding_idx
>>> weights = torch.rand(10, 3)
>>> weights[0, :].zero_()
>>> embedding_matrix = weights
>>> input = torch.tensor([[0,2,0,5]])
>>> F.embedding(input, embedding_matrix, padding_idx=0)
tensor([[[ 0.0000,  0.0000,  0.0000],
         [ 0.5609,  0.5384,  0.8720],
         [ 0.0000,  0.0000,  0.0000],
         [ 0.6262,  0.2438,  0.7471]]])

embedding_bag

torch.nn.functional.embedding_bag(input, weight, offsets=None, max_norm=None, norm_type=2, scale_grad_by_freq=False, mode='mean', sparse=False)

Computes sums, means or maxes of ‘bags’ of embeddings, without instantiating the intermediate embeddings.

See torch.nn.EmbeddingBag for more details. .. include:: cuda_deterministic_backward.rst

Parameters:

• input (LongTensor) – Tensor containing bags of indices into the embedding matrix
• weight (Tensor) – The embedding matrix with number of rows equal to the maximum possible index + 1, and number of columns equal to the embedding size
• offsets (LongTensor, optional) – Only used when input is 1D. offsets determines the starting index position of each bag (sequence) in input.
• max_norm (float, optional) – If given, each embedding vector with norm larger than max_norm is renormalized to have norm max_norm. Note: this will modify weight in-place.
• norm_type (float, optional) – The p in the p-norm to compute for the max_norm option. Default 2.
• scale_grad_by_freq (boolean, optional) – if given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default False. Note: this option is not supported when mode="max".
• mode (string, optional) – "sum", "mean" or "max". Specifies the way to reduce the bag. Default: "mean"
• sparse (bool, optional) – if True, gradient w.r.t. weight will be a sparse tensor. See Notes under torch.nn.Embedding for more details regarding sparse gradients. Note: this option is not supported when mode="max".

Shape:

• input (LongTensor) and offsets (LongTensor, optional)

  • If input is 2D of shape B x N,

    it will be treated as B bags (sequences) each of fixed length N, and this will return B values aggregated in a way depending on the mode. offsets is ignored and required to be None in this case.

  • If input is 1D of shape N,

    it will be treated as a concatenation of multiple bags (sequences). offsets is required to be a 1D tensor containing the starting index positions of each bag in input. Therefore, for offsets of shape B, input will be viewed as having B bags. Empty bags (i.e., having 0-length) will have returned vectors filled by zeros.

• weight (Tensor): the learnable weights of the module of shape (num_embeddings x embedding_dim)

• output: aggregated embedding values of shape B x embedding_dim

Examples:

>>> # an Embedding module containing 10 tensors of size 3
>>> embedding_matrix = torch.rand(10, 3)
>>> # a batch of 2 samples of 4 indices each
>>> input = torch.tensor([1,2,4,5,4,3,2,9])
>>> offsets = torch.tensor([0,4])
>>> F.embedding_bag(embedding_matrix, input, offsets)
tensor([[ 0.3397,  0.3552,  0.5545],
        [ 0.5893,  0.4386,  0.5882]])

Distance functions

pairwise_distance

torch.nn.functional.pairwise_distance(x1, x2, p=2.0, eps=1e-06, keepdim=False)

See torch.nn.PairwiseDistance for details

cosine_similarity

torch.nn.functional.cosine_similarity(x1, x2, dim=1, eps=1e-8) → Tensor

Returns cosine similarity between x1 and x2, computed along dim.

\[\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)} \]

Parameters:

• x1 (Tensor) – First input.
• x2 (Tensor) – Second input (of size matching x1).
• dim (int, optional) – Dimension of vectors. Default: 1
• eps (float, optional) – Small value to avoid division by zero. Default: 1e-8

Shape:

• Input: \((\ast_1, D, \ast_2)\) where D is at position dim.
• Output: \((\ast_1, \ast_2)\) where 1 is at position dim.

Example:

>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> output = F.cosine_similarity(input1, input2)
>>> print(output)

pdist

torch.nn.functional.pdist(input, p=2) → Tensor

Computes the p-norm distance between every pair of row vectors in the input. This is identical to the upper triangular portion, excluding the diagonal, of torch.norm(input[:, None] - input, dim=2, p=p). This function will be faster if the rows are contiguous.

If input has shape \(N \times M\) then the output will have shape \(\frac{1}{2} N (N - 1)\).

This function is equivalent to scipy.spatial.distance.pdist(input, ‘minkowski’, p=p) if \(p \in (0, \infty)\). When \(p = 0\) it is equivalent to scipy.spatial.distance.pdist(input, ‘hamming’) * M. When \(p = \infty\), the closest scipy function is scipy.spatial.distance.pdist(xn, lambda x, y: np.abs(x - y).max()).

Parameters:

• input – input tensor of shape \(N \times M\).
• p – p value for the p-norm distance to calculate between each vector pair \(\in [0, \infty]\).

Loss functions

binary_cross_entropy

torch.nn.functional.binary_cross_entropy(input, target, weight=None, size_average=None, reduce=None, reduction='mean')

Function that measures the Binary Cross Entropy between the target and the output.

See BCELoss for details.

Parameters:

• input – Tensor of arbitrary shape
• target – Tensor of the same shape as input
• weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Examples:

>>> input = torch.randn((3, 2), requires_grad=True)
>>> target = torch.rand((3, 2), requires_grad=False)
>>> loss = F.binary_cross_entropy(F.sigmoid(input), target)
>>> loss.backward()

binary_cross_entropy_with_logits

torch.nn.functional.binary_cross_entropy_with_logits(input, target, weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)

Function that measures Binary Cross Entropy between target and output logits.

See BCEWithLogitsLoss for details.

Parameters:

• input – Tensor of arbitrary shape
• target – Tensor of the same shape as input
• weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’
• pos_weight (Tensor, optional) – a weight of positive examples. Must be a vector with length equal to the number of classes.

Examples:

>>> input = torch.randn(3, requires_grad=True)
>>> target = torch.empty(3).random_(2)
>>> loss = F.binary_cross_entropy_with_logits(input, target)
>>> loss.backward()

poisson_nll_loss

torch.nn.functional.poisson_nll_loss(input, target, log_input=True, full=False, size_average=None, eps=1e-08, reduce=None, reduction='mean')

Poisson negative log likelihood loss.

See PoissonNLLLoss for details.

Parameters:

• input – expectation of underlying Poisson distribution.
• target – random sample \(target \sim \text{Poisson}(input)\).
• log_input – if True the loss is computed as \(\exp(\text{input}) - \text{target} * \text{input}\), if False then loss is \(\text{input} - \text{target} * \log(\text{input}+\text{eps})\). Default: True
• full – whether to compute full loss, i. e. to add the Stirling approximation term. Default: False \(\text{target} * \log(\text{target}) - \text{target} + 0.5 * \log(2 * \pi * \text{target})\).
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• eps (float, optional) – Small value to avoid evaluation of \(\log(0)\) when log_input`=``False`. Default: 1e-8
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

cosine_embedding_loss

torch.nn.functional.cosine_embedding_loss(input1, input2, target, margin=0, size_average=None, reduce=None, reduction='mean') → Tensor

See CosineEmbeddingLoss for details.

cross_entropy

torch.nn.functional.cross_entropy(input, target, weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')

This criterion combines log_softmax and nll_loss in a single function.

See CrossEntropyLoss for details.

Parameters:

• input (Tensor) – \((N, C)\) where C = number of classes or \((N, C, H, W)\) in case of 2D Loss, or \((N, C, d_1, d_2, ..., d_K)\) where \(K > 1\) in the case of K-dimensional loss.
• target (Tensor) – \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C-1\), or \((N, d_1, d_2, ..., d_K)\) where \(K \geq 1\) for K-dimensional loss.
• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. Default: -100
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Examples:

>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randint(5, (3,), dtype=torch.int64)
>>> loss = F.cross_entropy(input, target)
>>> loss.backward()

ctc_loss

torch.nn.functional.ctc_loss(log_probs, targets, input_lengths, target_lengths, blank=0, reduction='mean')

The Connectionist Temporal Classification loss.

See CTCLoss for details.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters:

• log_probs – \((T, N, C)\) where C = number of characters in alphabet including blank, T = input length, and N = batch size. The logarithmized probabilities of the outputs (e.g. obtained with torch.nn.functional.log_softmax()).
• targets – \((N, S)\) or (sum(target_lengths)). Targets (cannot be blank). In the second form, the targets are assumed to be concatenated.
• input_lengths – \((N)\). Lengths of the inputs (must each be \(\leq T\))
• target_lengths – \((N)\). Lengths of the targets
• blank (int, optional) – Blank label. Default \(0\).
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the output losses will be divided by the target lengths and then the mean over the batch is taken. Default: ‘mean’

Example:

>>> log_probs = torch.randn(50, 16, 20).log_softmax(2).detach().requires_grad_()
>>> targets = torch.randint(1, 20, (16, 30), dtype=torch.long)
>>> input_lengths = torch.full((16,), 50, dtype=torch.long)
>>> target_lengths = torch.randint(10,30,(16,), dtype=torch.long)
>>> loss = F.ctc_loss(log_probs, targets, input_lengths, target_lengths)
>>> loss.backward()

hinge_embedding_loss

torch.nn.functional.hinge_embedding_loss(input, target, margin=1.0, size_average=None, reduce=None, reduction='mean') → Tensor

See HingeEmbeddingLoss for details.

kl_div

torch.nn.functional.kl_div(input, target, size_average=None, reduce=None, reduction='mean')

The Kullback-Leibler divergence Loss.

See KLDivLoss for details.

Parameters:

• input – Tensor of arbitrary shape
• target – Tensor of the same shape as input
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘batchmean’ | ‘sum’ | ‘mean’. ‘none’: no reduction will be applied ‘batchmean’: the sum of the output will be divided by the batchsize ‘sum’: the output will be summed ‘mean’: the output will be divided by the number of elements in the output Default: ‘mean’

:param .. note:: size_average and reduce are in the process of being deprecated,: and in the meantime, specifying either of those two args will override reduction. :param .. note:: reduction=’mean’ doesn’t return the true kl divergence value, please use: reduction=’batchmean’ which aligns with KL math definition.

In the next major release, ‘mean’ will be changed to be the same as ‘batchmean’.

l1_loss

torch.nn.functional.l1_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor

Function that takes the mean element-wise absolute value difference.

See L1Loss for details.

mse_loss

torch.nn.functional.mse_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor

Measures the element-wise mean squared error.

See MSELoss for details.

margin_ranking_loss

torch.nn.functional.margin_ranking_loss(input1, input2, target, margin=0, size_average=None, reduce=None, reduction='mean') → Tensor

See MarginRankingLoss for details.

multilabel_margin_loss

torch.nn.functional.multilabel_margin_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor

See MultiLabelMarginLoss for details.

multilabel_soft_margin_loss

torch.nn.functional.multilabel_soft_margin_loss(input, target, weight=None, size_average=None) → Tensor

See MultiLabelSoftMarginLoss for details.

multi_margin_loss

torch.nn.functional.multi_margin_loss(input, target, p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')

multi_margin_loss(input, target, p=1, margin=1, weight=None, size_average=None,

reduce=None, reduction=’mean’) -> Tensor

See MultiMarginLoss for details.

nll_loss

torch.nn.functional.nll_loss(input, target, weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')

The negative log likelihood loss.

See NLLLoss for details.

Parameters:

• input – \((N, C)\) where C = number of classes or \((N, C, H, W)\) in case of 2D Loss, or \((N, C, d_1, d_2, ..., d_K)\) where \(K > 1\) in the case of K-dimensional loss.
• target – \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C-1\), or \((N, d_1, d_2, ..., d_K)\) where \(K \geq 1\) for K-dimensional loss.
• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C
• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True
• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. Default: -100
• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
• reduction (string, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: ‘mean’

Example:

>>> # input is of size N x C = 3 x 5
>>> input = torch.randn(3, 5, requires_grad=True)
>>> # each element in target has to have 0 <= value < C
>>> target = torch.tensor([1, 0, 4])
>>> output = F.nll_loss(F.log_softmax(input), target)
>>> output.backward()

smooth_l1_loss

torch.nn.functional.smooth_l1_loss(input, target, size_average=None, reduce=None, reduction='mean')

Function that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise.

See SmoothL1Loss for details.

soft_margin_loss

torch.nn.functional.soft_margin_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor

See SoftMarginLoss for details.

triplet_margin_loss

torch.nn.functional.triplet_margin_loss(anchor, positive, negative, margin=1.0, p=2, eps=1e-06, swap=False, size_average=None, reduce=None, reduction='mean')

See TripletMarginLoss for details

Vision functions

pixel_shuffle

torch.nn.functional.pixel_shuffle()

Rearranges elements in a tensor of shape \((*, C \times r^2, H, W)\) to a tensor of shape \((C, H \times r, W \times r)\).

See PixelShuffle for details.

Parameters:

• input (Tensor) – the input tensor
• upscale_factor (int) – factor to increase spatial resolution by

Examples:

>>> input = torch.randn(1, 9, 4, 4)
>>> output = torch.nn.functional.pixel_shuffle(input, 3)
>>> print(output.size())
torch.Size([1, 1, 12, 12])

pad

torch.nn.functional.pad(input, pad, mode='constant', value=0)

Pads tensor.

Pading size:

The number of dimensions to pad is \(\left\lfloor\frac{\text{len(pad)}}{2}\right\rfloor\) and the dimensions that get padded begins with the last dimension and moves forward. For example, to pad the last dimension of the input tensor, then pad has form (padLeft, padRight); to pad the last 2 dimensions of the input tensor, then use (padLeft, padRight, padTop, padBottom); to pad the last 3 dimensions, use (padLeft, padRight, padTop, padBottom, padFront, padBack).

Padding mode:

See torch.nn.ConstantPad2d, torch.nn.ReflectionPad2d, and torch.nn.ReplicationPad2d for concrete examples on how each of the padding modes works. Constant padding is implemented for arbitrary dimensions. Replicate padding is implemented for padding the last 3 dimensions of 5D input tensor, or the last 2 dimensions of 4D input tensor, or the last dimension of 3D input tensor. Reflect padding is only implemented for padding the last 2 dimensions of 4D input tensor, or the last dimension of 3D input tensor.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters:

• input (Tensor) – Nd tensor
• pad (tuple) – m-elem tuple, where \(\frac{m}{2} \leq\) input dimensions and \(m\) is even.
• mode – ‘constant’, ‘reflect’ or ‘replicate’. Default: ‘constant’
• value – fill value for ‘constant’ padding. Default: 0

Examples:

>>> t4d = torch.empty(3, 3, 4, 2)
>>> p1d = (1, 1) # pad last dim by 1 on each side
>>> out = F.pad(t4d, p1d, "constant", 0)  # effectively zero padding
>>> print(out.data.size())
torch.Size([3, 3, 4, 4])
>>> p2d = (1, 1, 2, 2) # pad last dim by (1, 1) and 2nd to last by (2, 2)
>>> out = F.pad(t4d, p2d, "constant", 0)
>>> print(out.data.size())
torch.Size([3, 3, 8, 4])
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p3d = (0, 1, 2, 1, 3, 3) # pad by (0, 1), (2, 1), and (3, 3)
>>> out = F.pad(t4d, p3d, "constant", 0)
>>> print(out.data.size())
torch.Size([3, 9, 7, 3])

interpolate

torch.nn.functional.interpolate(input, size=None, scale_factor=None, mode='nearest', align_corners=None)

Down/up samples the input to either the given size or the given scale_factor

The algorithm used for interpolation is determined by mode.

Currently temporal, spatial and volumetric sampling are supported, i.e. expected inputs are 3-D, 4-D or 5-D in shape.

The input dimensions are interpreted in the form: mini-batch x channels x [optional depth] x [optional height] x width.

The modes available for resizing are: nearest, linear (3D-only), bilinear (4D-only), trilinear (5D-only), area

Parameters:

• input (Tensor) – the input tensor
• size (int or Tuple[int] or Tuple[int, int] or Tuple[int, int, int]) – output spatial size.
• scale_factor (float or Tuple[float]) – multiplier for spatial size. Has to match input size if it is a tuple.
• mode (string) – algorithm used for upsampling: ‘nearest’ | ‘linear’ | ‘bilinear’ | ‘trilinear’ | ‘area’. Default: ‘nearest’
• align_corners (bool, optional) – if True, the corner pixels of the input and output tensors are aligned, and thus preserving the values at those pixels. This only has effect when mode is linear, bilinear, or trilinear. Default: False

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See Upsample for concrete examples on how this affects the outputs.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

upsample

torch.nn.functional.upsample(input, size=None, scale_factor=None, mode='nearest', align_corners=None)

Upsamples the input to either the given size or the given scale_factor

Warning

This function is deprecated in favor of torch.nn.functional.interpolate(). This is equivalent with nn.functional.interpolate(...).

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

The algorithm used for upsampling is determined by mode.

Currently temporal, spatial and volumetric upsampling are supported, i.e. expected inputs are 3-D, 4-D or 5-D in shape.

The input dimensions are interpreted in the form: mini-batch x channels x [optional depth] x [optional height] x width.

The modes available for upsampling are: nearest, linear (3D-only), bilinear (4D-only), trilinear (5D-only)

Parameters:

• input (Tensor) – the input tensor
• size (int or Tuple[int] or Tuple[int, int] or Tuple[int, int, int]) – output spatial size.
• scale_factor (int) – multiplier for spatial size. Has to be an integer.
• mode (string) – algorithm used for upsampling: ‘nearest’ | ‘linear’ | ‘bilinear’ | ‘trilinear’. Default: ‘nearest’
• align_corners (bool, optional) – if True, the corner pixels of the input and output tensors are aligned, and thus preserving the values at those pixels. This only has effect when mode is linear, bilinear, or trilinear. Default: False

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See Upsample for concrete examples on how this affects the outputs.

upsample_nearest

torch.nn.functional.upsample_nearest(input, size=None, scale_factor=None)

Upsamples the input, using nearest neighbours’ pixel values.

Warning

This function is deprecated in favor of torch.nn.functional.interpolate(). This is equivalent with nn.functional.interpolate(..., mode='nearest').

Currently spatial and volumetric upsampling are supported (i.e. expected inputs are 4 or 5 dimensional).

Parameters:

• input (Tensor) – input
• size (int or Tuple[int, int] or Tuple[int, int, int]) – output spatia size.
• scale_factor (int) – multiplier for spatial size. Has to be an integer.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

upsample_bilinear

torch.nn.functional.upsample_bilinear(input, size=None, scale_factor=None)

Upsamples the input, using bilinear upsampling.

Warning

This function is deprecated in favor of torch.nn.functional.interpolate(). This is equivalent with nn.functional.interpolate(..., mode='bilinear', align_corners=True).

Expected inputs are spatial (4 dimensional). Use upsample_trilinear fo volumetric (5 dimensional) inputs.

Parameters:

• input (Tensor) – input
• size (int or Tuple[int, int]) – output spatial size.
• scale_factor (int or Tuple[int, int]) – multiplier for spatial size

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

grid_sample

torch.nn.functional.grid_sample(input, grid, mode='bilinear', padding_mode='zeros')

Given an input and a flow-field grid, computes the output using input values and pixel locations from grid.

Currently, only spatial (4-D) and volumetric (5-D) input are supported.

In the spatial (4-D) case, for input with shape \((N, C, H_\text{in}, W_\text{in})\) and grid with shape \((N, H_\text{out}, W_\text{out}, 2)\), the output will have shape \((N, C, H_\text{out}, W_\text{out})\).

For each output location output[n, :, h, w], the size-2 vector grid[n, h, w] specifies input pixel locations x and y, which are used to interpolate the output value output[n, :, h, w]. In the case of 5D inputs, grid[n, d, h, w] specifies the x, y, z pixel locations for interpolating output[n, :, d, h, w]. mode argument specifies nearest or bilinear interpolation method to sample the input pixels.

grid should have most values in the range of [-1, 1]. This is because the pixel locations are normalized by the input spatial dimensions. For example, values x = -1, y = -1 is the left-top pixel of input, and values x = 1, y = 1 is the right-bottom pixel of input.

If grid has values outside the range of [-1, 1], those locations are handled as defined by padding_mode. Options are

• padding_mode="zeros": use 0 for out-of-bound values,
• padding_mode="border": use border values for out-of-bound values,
• padding_mode="reflection": use values at locations reflected by the border for out-of-bound values. For location far away from the border, it will keep being reflected until becoming in bound, e.g., (normalized) pixel location x = -3.5 reflects by -1 and becomes x' = 2.5, then reflects by border 1 and becomes x'' = -0.5.

Note

This function is often used in building Spatial Transformer Networks.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters:

• input (Tensor) – input of shape \((N, C, H_\text{in}, W_\text{in})\) (4-D case) or \((N, C, D_\text{in}, H_\text{in}, W_\text{in})\) (5-D case)
• grid (Tensor) – flow-field of shape \((N, H_\text{out}, W_\text{out}, 2)\) (4-D case) or \((N, D_\text{out}, H_\text{out}, W_\text{out}, 3)\) (5-D case)
• mode (str) – interpolation mode to calculate output values ‘bilinear’ | ‘nearest’. Default: ‘bilinear’
• padding_mode (str) – padding mode for outside grid values ‘zeros’ | ‘border’ | ‘reflection’. Default: ‘zeros’

Returns:

output Tensor

Return type:

output (Tensor)

affine_grid

torch.nn.functional.affine_grid(theta, size)

Generates a 2d flow field, given a batch of affine matrices theta Generally used in conjunction with grid_sample() to implement Spatial Transformer Networks.

Parameters:

• theta (Tensor) – input batch of affine matrices (\(N \times 2 \times 3\))
• size (torch.Size) – the target output image size (\(N \times C \times H \times W\)) Example: torch.Size((32, 3, 24, 24))

Returns:

output Tensor of size (\(N \times H \times W \times 2\))

Return type:

output (Tensor)

DataParallel functions (multi-GPU, distributed)

data_parallel

torch.nn.parallel.data_parallel(module, inputs, device_ids=None, output_device=None, dim=0, module_kwargs=None)

Evaluates module(input) in parallel across the GPUs given in device_ids.

This is the functional version of the DataParallel module.

Parameters:

• module (Module) – the module to evaluate in parallel
• inputs (tensor) – inputs to the module
• device_ids (list of python:int or torch.device) – GPU ids on which to replicate module
• output_device (list of python:int or torch.device) – GPU location of the output Use -1 to indicate the CPU. (default: device_ids[0])

Returns:

a Tensor containing the result of module(input) located on output_device

torch.nn.init

torch.nn.init.calculate_gain(nonlinearity, param=None)

Return the recommended gain value for the given nonlinearity function. The values are as follows:

nonlinearity	gain
Linear / Identity	\(1\)
Conv{1,2,3}D	\(1\)
Sigmoid	\(1\)
Tanh	\(\frac{5}{3}\)
ReLU	\(\sqrt{2}\)
Leaky Relu	\(\sqrt{\frac{2}{1 + \text{negative\_slope}^2}}\)

Parameters:

• nonlinearity – the non-linear function (nn.functional name)
• param – optional parameter for the non-linear function

Examples

>>> gain = nn.init.calculate_gain('leaky_relu')

torch.nn.init.uniform_(tensor, a=0, b=1)

Fills the input Tensor with values drawn from the uniform distribution \(\mathcal{U}(a, b)\).

Parameters:

• tensor – an n-dimensional torch.Tensor
• a – the lower bound of the uniform distribution
• b – the upper bound of the uniform distribution

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.uniform_(w)

torch.nn.init.normal_(tensor, mean=0, std=1)

Fills the input Tensor with values drawn from the normal distribution \(\mathcal{N}(\text{mean}, \text{std})\).

Parameters:

• tensor – an n-dimensional torch.Tensor
• mean – the mean of the normal distribution
• std – the standard deviation of the normal distribution

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.normal_(w)

torch.nn.init.constant_(tensor, val)

Fills the input Tensor with the value \(\text{val}\).

Parameters:

• tensor – an n-dimensional torch.Tensor
• val – the value to fill the tensor with

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.constant_(w, 0.3)

torch.nn.init.eye_(tensor)

Fills the 2-dimensional input Tensor with the identity matrix. Preserves the identity of the inputs in Linear layers, where as many inputs are preserved as possible.

Parameters:tensor – a 2-dimensional torch.Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.eye_(w)

torch.nn.init.dirac_(tensor)

Fills the {3, 4, 5}-dimensional input Tensor with the Dirac delta function. Preserves the identity of the inputs in Convolutional layers, where as many input channels are preserved as possible.

Parameters:tensor – a {3, 4, 5}-dimensional torch.Tensor

Examples

>>> w = torch.empty(3, 16, 5, 5)
>>> nn.init.dirac_(w)

torch.nn.init.xavier_uniform_(tensor, gain=1)

Fills the input Tensor with values according to the method described in “Understanding the difficulty of training deep feedforward neural networks” - Glorot, X. & Bengio, Y. (2010), using a uniform distribution. The resulting tensor will have values sampled from \(\mathcal{U}(-a, a)\) where

\[a = \text{gain} \times \sqrt{\frac{6}{\text{fan\_in} + \text{fan\_out}}} \]

Also known as Glorot initialization.

Parameters:

• tensor – an n-dimensional torch.Tensor
• gain – an optional scaling factor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.xavier_uniform_(w, gain=nn.init.calculate_gain('relu'))

torch.nn.init.xavier_normal_(tensor, gain=1)

Fills the input Tensor with values according to the method described in “Understanding the difficulty of training deep feedforward neural networks” - Glorot, X. & Bengio, Y. (2010), using a normal distribution. The resulting tensor will have values sampled from \(\mathcal{N}(0, \text{std})\) where

\[\text{std} = \text{gain} \times \sqrt{\frac{2}{\text{fan\_in} + \text{fan\_out}}} \]

Also known as Glorot initialization.

Parameters:

• tensor – an n-dimensional torch.Tensor
• gain – an optional scaling factor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.xavier_normal_(w)

torch.nn.init.kaiming_uniform_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu')

Fills the input Tensor with values according to the method described in “Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification” - He, K. et al. (2015), using a uniform distribution. The resulting tensor will have values sampled from \(\mathcal{U}(-\text{bound}, \text{bound})\) where

\[\text{bound} = \sqrt{\frac{6}{(1 + a^2) \times \text{fan\_in}}} \]

Also known as He initialization.

Parameters:

• tensor – an n-dimensional torch.Tensor
• a – the negative slope of the rectifier used after this layer (0 for ReLU by default)
• mode – either ‘fan_in’ (default) or ‘fan_out’. Choosing fan_in preserves the magnitude of the variance of the weights in the forward pass. Choosing fan_out preserves the magnitudes in the backwards pass.
• nonlinearity – the non-linear function (nn.functional name), recommended to use only with ‘relu’ or ‘leaky_relu’ (default).

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.kaiming_uniform_(w, mode='fan_in', nonlinearity='relu')

torch.nn.init.kaiming_normal_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu')

Fills the input Tensor with values according to the method described in “Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification” - He, K. et al. (2015), using a normal distribution. The resulting tensor will have values sampled from \(\mathcal{N}(0, \text{std})\) where

\[\text{std} = \sqrt{\frac{2}{(1 + a^2) \times \text{fan\_in}}} \]

Also known as He initialization.

Parameters:

• tensor – an n-dimensional torch.Tensor
• a – the negative slope of the rectifier used after this layer (0 for ReLU by default)
• mode – either ‘fan_in’ (default) or ‘fan_out’. Choosing fan_in preserves the magnitude of the variance of the weights in the forward pass. Choosing fan_out preserves the magnitudes in the backwards pass.
• nonlinearity – the non-linear function (nn.functional name), recommended to use only with ‘relu’ or ‘leaky_relu’ (default).

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.kaiming_normal_(w, mode='fan_out', nonlinearity='relu')

torch.nn.init.orthogonal_(tensor, gain=1)

Fills the input Tensor with a (semi) orthogonal matrix, as described in “Exact solutions to the nonlinear dynamics of learning in deep linear neural networks” - Saxe, A. et al. (2013). The input tensor must have at least 2 dimensions, and for tensors with more than 2 dimensions the trailing dimensions are flattened.

Parameters:

• tensor – an n-dimensional torch.Tensor, where \(n \geq 2\)
• gain – optional scaling factor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.orthogonal_(w)

torch.nn.init.sparse_(tensor, sparsity, std=0.01)

Fills the 2D input Tensor as a sparse matrix, where the non-zero elements will be drawn from the normal distribution \(\mathcal{N}(0, 0.01)\), as described in “Deep learning via Hessian-free optimization” - Martens, J. (2010).

Parameters:

• tensor – an n-dimensional torch.Tensor
• sparsity – The fraction of elements in each column to be set to zero
• std – the standard deviation of the normal distribution used to generate the non-zero values

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.sparse_(w, sparsity=0.1)