logit

→Tensor

logit(x: Tensor, eps: float | None = ...)

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Logit function — inverse of the logistic sigmoid.

Maps a probability in $(0, 1)$ to a log-odds value in $\mathbb{R}$ . Optionally clamps the input to $[\epsilon, 1 - \epsilon]$ first to avoid divergence at the boundaries.

Parameters

xTensor

Input tensor with values in

(0, 1)

epsfloat | None

If provided, x is clamped to [eps, 1 - eps] before the log-ratio is taken, preventing infinities. Defaults to None (no clamping).

Returns

Tensor

Element-wise logit value.

Notes

Mathematical definition:

\operatorname{logit}(x) = \log\!\Bigl(\tfrac{x}{1 - x}\Bigr).

Inverse of the sigmoid: $\operatorname{logit}(\sigma(z)) = z$ . Without eps, inputs of exactly 0 or 1 produce $-\infty$ and $+\infty$ respectively.

Examples

>>> import lucid
>>> x = lucid.tensor([0.1, 0.5, 0.9])
>>> lucid.logit(x)
Tensor([-2.1972,  0.    ,  2.1972])