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title: Sigmoid Functions
---
# Sigmoid Functions

![[sigmoid-function-example.excalidraw]]

$f'(x)$ is a **sigmoid** function.

A sigmoid function compresses a function with infinite range to (0,1)

This is preferable to a floor-ceiling piece-wise function
since it remains differentiable.

## Formula

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