A sigmoid function is a mathematical function having a characteristic “S”-shaped curve or sigmoid curve. It is used in neural networks as an activation function, defining the output of a node given a set of inputs.

The Sigmoid function often refers to the special case of the logistic function shown in the first figure and defined by the formula:

The graph representing this function forms an “S” shape from **R** to ]0;1[

The sigmoid function has a first derivative that is always non-negative and forms a bell shape.

Read more on the sigmoid function on Wikipedia.

## The use of the sigmoid function in neural networks

The sigmoid function is used to program neural networks as an activation function. It is a standard function in a neural net node (a “neuron”), used to normalize the sum of data inputs after applying weights.

It ensures the output of the node is always in the interval ]0;1[, while also signifying high confidence for large positive or negative numbers.

In practice the sigmoid function used in neural nets has the following formula:

The sigmoid function derivative is used in the training period to modify weights applied to the training data, during the process of **gradient descent**.

Read more on the use of the sigmoid function in the post on programming a simple neural network or review the video on principles of neural nets.