Stable sigmoid function

Computes sigmoid(x) = 1/(1+exp(-x)) with overflow protection.

Usage

sigmoid_stable(x)

Arguments

x

A value object or numeric

Value

Sigmoid values in (0, 1)

Details

For large positive x, exp(-x) underflows to 0, giving sigmoid = 1 (correct). For large negative x, we use sigmoid(x) = exp(x)/(1+exp(x)) to avoid overflow.