# Tag Archives | partial derivatives ## Calculus in Action: Neural Networks

An artificial neural network is a computational model that approximates a mapping between inputs and outputs.  It is inspired by the structure of the human brain, in that it is similarly composed of a network of interconnected neurons that propagate information upon receiving sets of stimuli from neighbouring neurons. Training a neural network involves a […] ## The Chain Rule of Calculus – Even More Functions

The chain rule is an important derivative rule that allows us to work with composite functions. It is essential in understanding the workings of the backpropagation algorithm, which applies the chain rule extensively in order to calculate the error gradient of the loss function with respect to each weight of a neural network. We will […] ## The Chain Rule of Calculus for Univariate and Multivariate Functions

The chain rule allows us to find the derivative of composite functions. It is computed extensively by the backpropagation algorithm, in order to train feedforward neural networks. By applying the chain rule in an efficient manner while following a specific order of operations, the backpropagation algorithm calculates the error gradient of the loss function with […] ## A Gentle Introduction to the Jacobian

In the literature, the term Jacobian is often interchangeably used to refer to both the Jacobian matrix or its determinant.  Both the matrix and the determinant have useful and important applications: in machine learning, the Jacobian matrix aggregates the partial derivatives that are necessary for backpropagation; the determinant is useful in the process of changing […] ## A Gentle Introduction To Partial Derivatives and Gradient Vectors

Partial derivatives and gradient vectors are used very often in machine learning algorithms for finding the minimum or maximum of a function. Gradient vectors are used in the training of neural networks, logistic regression, and many other classification and regression problems. In this tutorial, you will discover partial derivatives and the gradient vector. After completing […] ## A Gentle Introduction to Multivariate Calculus

It is often desirable to study functions that depend on many variables.  Multivariate calculus provides us with the tools to do so by extending the concepts that we find in calculus, such as the computation of the rate of change, to multiple variables. It plays an essential role in the process of training a neural […]