torch.logsumexp

torch.logsumexp(input, dim, keepdim=False, *, out=None)

Returns the log of summed exponentials of each row of the input tensor in the given dimension dim. The computation is numerically stabilized.

For summation index \(j\) given by dim and other indices \(i\), the result is

\[\text{logsumexp}(x)_{i} = \log \sum_j \exp(x_{ij}) \]

If keepdim is True, the output tensor is of the same size as input except in the dimension(s) dim where it is of size 1. Otherwise, dim is squeezed (see torch.squeeze()), resulting in the output tensor having 1 (or len(dim)) fewer dimension(s).

Parameters:

• input (Tensor) – the input tensor.

• dim (int or tuple of ints, optional) – the dimension or dimensions to reduce. If None, all dimensions are reduced.

• keepdim (bool) – whether the output tensor has dim retained or not.

Keyword Arguments:

out (Tensor, optional) – the output tensor.

Example:

>>> a = torch.randn(3, 3)
>>> torch.logsumexp(a, 1)
tensor([1.4907, 1.0593, 1.5696])
>>> torch.dist(torch.logsumexp(a, 1), torch.log(torch.sum(torch.exp(a), 1)))
tensor(1.6859e-07)