logsigmoid

→Tensor

logsigmoid(x: Tensor)

source

Numerically stable $\log \sigma(x)$ .

Direct evaluation of $\log(1 / (1 + e^{-x}))$ underflows once $\sigma(x)$ is below machine epsilon (around $x \lesssim -37$ for float32). Rewriting as $-\operatorname{softplus}(-x)$ matches the same value while staying finite for arbitrarily negative inputs.

Parameters

xTensor

Input logits.

Returns

Tensor

$\log \sigma(x)$ with the same shape as x, values in $(-\infty, 0]$ .

Notes

\log\sigma(x) = -\log(1 + e^{-x}) = -\operatorname{softplus}(-x)

Frequently the building block of binary cross-entropy with logits (BCE-with-logits) and of importance-weighting computations in RL.

Examples

>>> import lucid
>>> from lucid.nn.functional import logsigmoid
>>> x = lucid.tensor([-10.0, 0.0, 10.0])
>>> logsigmoid(x)
Tensor([-10.0000,  -0.6931,  -0.0000])