sigmoid

→Tensor

sigmoid(x: Tensor)

source

Logistic sigmoid activation.

Squashes any real-valued input into the open interval $(0, 1)$ . Historically the canonical activation for binary classification heads and the gating function in LSTM / GRU cells.

Parameters

xTensor

Input tensor of any shape; activation is element-wise.

Returns

Tensor

Activated tensor with the same shape as x, values in $(0, 1)$ .

Notes

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

Derivative $\sigma'(x) = \sigma(x)(1 - \sigma(x)) \le 0.25$ . The bounded derivative is the classical cause of the vanishing gradient problem in deep feed-forward stacks, so for hidden layers prefer ReLU / GELU / SiLU. For binary classification logits, use logsigmoid to compute $\log\sigma(x)$ in a numerically stable way.

Examples

>>> import lucid
>>> from lucid.nn.functional import sigmoid
>>> x = lucid.tensor([-2.0, 0.0, 2.0])
>>> sigmoid(x)
Tensor([0.1192, 0.5000, 0.8808])