What is it?
Used for Deep Learning mainly as an activation function of an Artificial Neural Network, the sigmoid function, also called logistic function, maps any real-valued number to a value between 0 and 1, which makes it naturally useful for binary classification problems.
It ensures smooth continuous outputs, which is the base of gradient-based optimization and models with complex data, due to the introduction of non-linearity. Due to the steep gradient in , the function is sensitive to small changes in this range, which can cause a significant change in the output.
Mathematical definition
Given as an input value, and as the Euler number(≈2.718) , the sigmoid function can be mathematically defined as:
Due to it being differenciable, it’s very useful for calculations of gradient optimizations.