Automatique Différentiation (AD) is a computational technique used to evaluate the derivative of a function specified by a computer program. Unlike numerical differentiation, which approximates derivatives using finite differences, and symbolic differentiation, which manipulates mathematical expressions, automatic differentiation provides exact derivatives using the règle de la chaîne of calculus. This makes it particularly valuable in fields like apprentissage automatique, where optimization Les problèmes dépendent souvent du calcul précis des gradients.
AD fonctionne en décomposant complex functions into simpler components, allowing derivatives to be computed in a systematic way. There are two primary modes of automatic differentiation: mode direct (forward mode) and mode inverse (reverse mode). In forward mode, the derivatives are propagated alongside the function evaluation, which is efficient for functions with fewer inputs than outputs. Conversely, reverse mode is more suited for functions with many inputs and fewer outputs, as it computes derivatives in a single passage en arrière après que la fonction a été évaluée.
Cette technique est largement utilisée dans diverses applications, y compris les algorithmes d'optimisation like gradient descent, where knowing the gradient is essential for updating model parameters. It is also a fundamental component of many machine learning frameworks, enabling efficient training of neural networks. By providing a robust and accurate means of computing derivatives, automatic differentiation plays a crucial role in modern computational science and artificial intelligence.