Abstract Mathematical Explanation with Examples for Neural Networks
In this article, I will explain the core ideas of neural networks from an abstract mathematical perspective. By "abstract", I mean that I will try to explain the "why" of mathematical concepts without covering all mathematical details. To simplify the mathematical concepts of neural networks, I will use some analogies from real life situations, with visualisations and examples. I will start by explaining why we need neural networks, and then discuss the role of optimisation and backpropagation algorithms. Why Do We Need Neural Networks Neural networks are tools that allow us to approximate complex multivariate functions representing the relationships between dataset inputs and outputs. Typically, it is not feasible to define one explicit equation that can reproduce these multivariate functions. The role of training is thus to approximate them. Indeed, most neural networks architectures are based on a mathematical theorem called Universal Approximation Theorem. Th...