A sigmoid function, also known as a logistic function, is an S-shaped mathematical function that maps any input value to an output between 0 and 1.
The most common form is:
f(x) = 1 / (1 + e^(-x))
Sigmoid Function
It's used extensively in machine learning and statistics for several important reasons:
Binary Classification: The sigmoid's output range of 0 to 1 makes it perfect for representing probabilities in binary classification problems. For example, in logistic regression, it can predict the probability that an input belongs to one of two classes.
Neural Networks: Historically, sigmoid was one of the most popular activation functions in neural networks, particularly in earlier architectures. While newer alternatives like ReLU are often preferred now, sigmoid is still used in the output layer of networks performing binary classification.
Smooth Transitions: The sigmoid provides a smooth, differentiable transition between values, which is valuable for gradient-based optimization methods. This smoothness helps during the training process of machine learning models.