∂ is for Dialectica
Résumé
Automatic Differentiation is the study of the efficient computation of differentials. While the first automatic differentiation algorithms are concomitant with the birth of computer science, the specific backpropagation algorithm has been brought to a modern light by its application to neural networks. In this work, we unveil a surprising connection between backpropagation and Gödel's Dialectica interpretation, a logical translation that realizes semi-classical axioms. This unexpected correspondence is exploited through different logical settings. It opens the way for explorations on the logical power of automatic differentiation algorithms.
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