The Taylor Series is a mathematical tool that approximates complex functions with polynomials, playing a crucial role in machine learning optimization. It enhances gradient descent by incorporating second-order information, leading to faster and more stable convergence. Additionally, it aids in linearizing non-linear models and informs regularization techniques. This post explores the significance of the Taylor Series in improving model training efficiency and understanding model behavior. $$\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n}$$

Simulated Annealing (SA) is a probabilistic technique used for finding an approximate solution to an optimization problem. It is particularly useful for problems where the search space is large and complex, and other methods might get stuck in local optima.

Self-teaching notes of advanced Mathematics