# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 82: Sigmoid Functions

A sigmoid function is a differentiable function  $f: \mathbb{R} \rightarrow \mathbb{R}$ which has the following properties:

1. the derivative of $f$ is either positive at all points or negative at all points
2. the function is bounded by two horizontal asymptotes between which it takes its values

Applications of sigmoid functions include uses in statistics and as activation functions for artificial neurons in neural networks.

Generally, the integral of a ‘bump-shaped’ function is sigmoidal. For example, the CDF of the normal distribution is a sigmoid function.