expit

→Tensor

expit(x: Tensor)

source

Logistic sigmoid (expit) function $\sigma(x)$ .

Convenience alias for lucid.sigmoid. Maps the real line onto the open interval $(0, 1)$ and is the inverse of lucid.logit.

Parameters

xTensor

Input tensor; any floating-point dtype.

Returns

Tensor

$\sigma(x) = 1 / (1 + e^{-x})$ element-wise, same shape and dtype as x.

Notes

Definition:

\sigma(x) = \frac{1}{1 + e^{-x}} = \frac{e^x}{1 + e^x}.

Symmetry: $\sigma(-x) = 1 - \sigma(x)$ . Derivative: $\sigma'(x) = \sigma(x)\,(1 - \sigma(x))$ . Frequently used as the probabilistic-output activation of binary classifiers.

Examples

>>> import lucid
>>> from lucid.special import expit
>>> expit(lucid.tensor([-2.0, 0.0, 2.0]))
Tensor([0.1192, 0.5000, 0.8808])