class

SigmoidTransform

extendsTransform

SigmoidTransform()

source

Element-wise sigmoid bijection $y = \sigma(x) = 1/(1 + e^{-x})$ .

Maps $\mathbb{R} \to (0, 1)$ element-wise. The natural unconstrained → probability transform — composed with a base distribution on $\mathbb{R}$ , the pushforward lives on the unit interval. Monotone increasing, bijective, event_dim = 0.

Notes

Forward: $y = \sigma(x) = 1/(1 + e^{-x})$ .

Inverse (logit): $x = \log\!\bigl(y/(1-y)\bigr)$ .

Log Jacobian determinant:

\log\!\left|\frac{\partial y}{\partial x}\right| = \log\bigl(\sigma(x)(1 - \sigma(x))\bigr) = \log y + \log(1 - y)

The transform is closely related to the StickBreakingTransform (which generalises to the simplex) and to TanhTransform (which targets $(-1, 1)$ ).

Examples

>>> import lucid
>>> from lucid.distributions.transforms import SigmoidTransform
>>> T = SigmoidTransform()
>>> y = T(lucid.tensor(0.0))  # σ(0) = 0.5
Tensor(0.5)

Methods (1)

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source

Log-Jacobian $\log\bigl(y\,(1-y)\bigr)$ of the sigmoid map.