Understanding Sigmoid Functions in Machine Learning

Sigmoid is a mathematical function that maps any real-valued number to a value between 0 and 1. It is often used in machine learning models, particularly in the context of logistic regression, where it is used to model the probability of an event occurring given some input features. The function is defined as:

sigmoid(x) = 1 / (1 + exp(-x))

where exp is the exponential function. The sigmoid function has an S-shaped curve, where the output starts at 0, increases slowly at first, then more quickly as the input increases, before leveling off at 1. This S-shaped curve allows the sigmoid to model binary outcomes, such as 0 and 1, yes and no, etc.

Sigmoidally simply means something that is related to or uses the sigmoid function. In the context of machine learning, a model that uses the sigmoid function to predict a binary outcome is said to be sigmoidally trained.