Why Momentum Really Works: A Deep Dive into Gradient Descent Acceleration

This article delves into the mechanics of momentum in optimization algorithms. By analyzing convex quadratic functions, it reveals how momentum accelerates gradient descent and explains the underlying mathematical principles. The article also explores the limitations of momentum and its combination with stochastic gradient descent, offering insights into future research directions. Using clear language and concrete examples like polynomial regression and image colorization, the article provides a comprehensive understanding of momentum's principles and applications, suitable for readers interested in optimization algorithms.