chainer.functions.cross_covariance

chainer.functions.cross_covariance(y, z, reduce='half_squared_sum')[source]

Computes the sum-squared cross-covariance penalty between y and z

The output is a variable whose value depends on the value of the option reduce. If it is 'no', it holds the covariant matrix that has as many rows (resp. columns) as the dimension of y (resp.z). If it is 'half_squared_sum', it holds the half of the Frobenius norm (i.e. L2 norm of a matrix flattened to a vector) of the covarianct matrix.

Parameters

  • y (Variable or N-dimensional array) – Variable holding a matrix where the first dimension corresponds to the batches.

  • z (Variable or N-dimensional array) – Variable holding a matrix where the first dimension corresponds to the batches.

  • reduce (str) – Reduction option. Its value must be either 'half_squared_sum' or 'no'. Otherwise, ValueError is raised.

Returns

A variable holding the cross covariance loss. If reduce is 'no', the output variable holds 2-dimensional array matrix of shape (M, N) where M (resp. N) is the number of columns of y (resp. z). If it is 'half_squared_sum', the output variable holds a scalar value.

Return type

Variable

Note

This cost can be used to disentangle variables. See https://arxiv.org/abs/1412.6583v3 for details.