Differential Equations Needed for ML

In this post I want to include basic derivaties and primitive building blocks required from calculus for the model optimization. These are commonly used, but after some time I’m losing grip of these basics, so I want to keep it one place for future references.

Standard functions and its derivatives

Basic Derivatives

Sigmoid activation function

Sigmoid helps to bring the inputs between [0, 1], used most of the classification problems. eg; regression, neural network etc.

math sigmoid derivative

Tanh activation function

Speciality of tanh function is it brings the inputs into [-1, 1], some cases this range is important especially RNN, where the model want to selectively forget things.

math tanh derivative


Widely used activation function in Neural network and CNN models. This activation function helps the Deep learning jump in multiple domains. As early days getting a proper activation function was really restricting complex neural network architectures.

math relu derivative

Leaky Relu

Improved version of Relu which reduces the chance of vanishing gradient issue.

math leaky relu derivative


Used mainly as last layer in nerual network. This function helps to bring all activations from previous layer into probability values. Because of this property this function used most of the classification problems.

math softmax derivative 1
math softmax derivative 2

Cross entropy loss function

Objective function used in neural network or classification problems.

math entropy loss derivative

Partial Derviative

This concept are learned in undergrad courses. All ML problems are finally comes to numerical optimization problem. Derivatives plays a method to optimize the parameters of the function. We required partial derivatives to find derivative of multi-varite equations.

The key idea is, at every step we calculate the derivative of one-dimention or (one variable) keeping all other variables constant.

The math equetions are created using https://www.mathcha.io online editor.
Go Top