automatic differentiation libraries

Automatic differentiation libraries are tools that efficiently compute derivatives—rates of change—of functions used in machine learning and scientific computing. Unlike manual calculations or symbolic methods, these libraries automatically track computations step-by-step to produce accurate derivatives quickly. They are essential for training models where gradients guide adjustments. Think of them as intelligent tools that understand and remember every calculation a function performs, then automatically generate derivatives without human intervention, saving time and reducing errors in complex mathematical models.