Automatic Differentiation
Automatic Differentiation (AD) is a set of techniques for efficiently and accurately computing derivatives of functions implemented in computer programs. It works by breaking down complex functions into elementary operations (like addition and multiplication) and applying the chain rule systematically, avoiding the numerical instability of finite differences and the symbolic complexity of manual differentiation. AD is fundamental in fields like machine learning for gradient-based optimization, scientific computing, and engineering simulations.
Developers should learn automatic differentiation when building or optimizing models that require gradients, such as in deep learning frameworks (e.g., for backpropagation in neural networks), physics simulations, or financial modeling. It enables precise derivative calculations without manual derivation, improving performance and reducing errors in applications like training AI models, solving differential equations, or sensitivity analysis.