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cs.PL2022
Dual-Numbers Reverse AD, Efficiently
Tom Smeding, Matthijs Vákár
Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent derivative, dual-numbers /reverse-mode/ AD attempts to achieve reverse AD us…
cs.PL2020
Reverse AD at Higher Types: Pure, Principled and Denotationally Correct
Matthijs Vákár
We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generat…
cs.PL2020
Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing
Mathieu Huot, Sam Staton, Matthijs Vákár
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 characte…