What is Automatic Differentiation?

Explains the need for derivatives in machine learning and introduces the concept of automatic differentiation as a set of techniques to compute derivatives efficiently.

Contrasts automatic differentiation with numerical differentiation, highlighting issues like truncation error and the need for multiple evaluations in numerical differentiation.

Discusses symbolic differentiation as an automated version of manual differentiation, highlighting exact computation of derivatives but pointing out the challenges like expression swell.

Compares automatic differentiation with symbolic differentiation in terms of efficiency, accuracy, and handling complex functions.

Explains that differentiable functions are composed of primitive operations whose derivatives are known and the chain rule is used to compute derivatives efficiently.

Details the concept of forward mode autodiff, involving augmenting intermediate variables with their derivatives during evaluation and computing partial derivatives efficiently.

Discusses the efficiency of reverse mode autodiff in handling scenarios with numerous parameters, such as in machine learning, and explains the process of propagating derivatives backwards for gradient computations.

Compares forward and reverse mode autodiff in terms of computational efficiency, memory usage, and suitability for different scenarios, such as computing Jacobians and gradients in optimization settings.

Explains the hybrid approach in automatic differentiation for second-order optimization settings and the ability to compute higher-order derivatives by composing multiple executions of autodiff.