From Loss to Gradient Descent: A Mathematical Introduction to Parameter Updates in Feedforward Neural Networks

This expository article gives a self-contained mathematical account of how pointwise loss functions, empirical risk, differentiation, and the chain rule lead to gradient-based parameter updates in canonical feedforward neural networks. The manuscript is pedagogical in purpose and does not claim new theoretical results. Its aim is to make explicit the assumptions, notation, and elementary derivations that are often compressed in introductory presentations of deep learning.