Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing

@article{Huot2020CorrectnessOA,
  title={Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing},
  author={Mathieu Huot and S. Staton and Matthijs V{\'a}k{\'a}r},
  journal={Foundations of Software Science and Computation Structures},
  year={2020},
  volume={12077},
  pages={319 - 338}
}
We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this… Expand
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