We present a system for the automatic differentiation (AD) of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source forward-mode AD and global optimisations such as loop transformations. In combination, gradient computation with forward-mode AD can be as efficient as reverse mode, and that the Jacobian matrices required for numerical algorithms such as Gauss-Newton and Levenberg-Marquardt can be efficiently computed.

@article{paperbot583,
  title = {Efficient differentiable programming in a functional array-processing language},
  author = {Amir Shaikhha and Andrew Fitzgibbon and Dimitrios Vytiniotis and Simon Peyton Jones},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {3},
  number = {ICFP},
  year = {2019},
  doi = {10.1145/3341701}
}