c++ sigmoid

The sigmoid function, also known as the logistic function, is a mathematical function that maps any input value to a range between 0 and 1. It is commonly used in machine learning and neural networks as an activation function to introduce non-linearity into the model.

The sigmoid function is defined as:

sigmoid(x) = 1 / (1 + e^(-x))

where e is the mathematical constant known as Euler's number (approximately equal to 2.71828), and x is the input value. The output of the sigmoid function always falls between 0 and 1, with an output of 0.5 occurring when the input value is 0.

The sigmoid function is useful in machine learning because it allows the model to assign probabilities to different outcomes. For example, in a binary classification problem where the model is trying to predict whether an input belongs to class 0 or class 1, the sigmoid function can be used to calculate the probability that the input belongs to class 1. If the output of the sigmoid function is greater than 0.5, the model predicts that the input belongs to class 1, and if the output is less than 0.5, the model predicts that the input belongs to class 0.