Differentiable programming

Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation. This allows for gradient based optimization of parameters in the program, often via gradient descent. Differentiable programming has found use in a wide variety of areas, particularly scientific computing and artificial intelligence.
Approaches.
Most differentiable programming frameworks work by constructing a graph containing the control flow and data structures in the program. Earlier attempts generally fall into two groups:
Both of these early approaches are only able to differentiate code written in a suitable manner for the framework, limiting their interoperability with other programs.
A more recent package for the Julia programming language Zygote resolves the issues that earlier attempts faced by treating the language's syntax as the graph. The intermediate representation of arbitrary code can then be differentiated directly, optimized, and compiled.
A programming language "currently under development and is not yet ready for use" called Myia allows defining a model using a subset of Python, which is compiled to Myia.
Applications.
Differentiable programming has been applied in areas such as combining deep learning with physics engines in robotics, solving electronic structure problems with differentiable density functional theory, differentiable ray tracing, image processing, and probabilistic programming.