log_softmax

→Tensor

log_softmax(input: Tensor, dim: _int = ..., dtype: DTypeLike | None = ...)

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Implementing kernel

Numerically stable log-softmax along a dimension.

Parameters

inputTensor

Input logits of any shape.

dimint or None

Dimension along which the log-softmax is computed.

_stacklevelint

Internal stack level for the implicit-dimension warning.

dtypeDTypeLike or None

Target floating-point dtype to cast input to before log-softmax.

Returns

Tensor

Log-probabilities of the same shape as input.

Notes

\text{log\_softmax}(x)_i = x_i - \log\!\sum_j e^{x_j} = (x_i - m) - \log\!\sum_j e^{x_j - m}, \quad m = \max_j x_j

Pairing log_softmax with nll_loss is numerically equivalent to — and more stable than — softmax followed by cross_entropy.

Examples

>>> import lucid
>>> from lucid.nn.functional import log_softmax
>>> logits = lucid.tensor([[1.0, 2.0, 3.0]])
>>> log_softmax(logits, dim=1)
tensor([[-2.408, -1.408, -0.4076]])