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Communication Dans Un Congrès Année : 2024

$\partial$ 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. This work unveils 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. In particular, we show that the computational interpretation of Dialectica translates to the differential λ-calculus and that Differential Linear Logic subsumes the logical interpretation of Dialectica.
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Dates et versions

hal-04583978 , version 1 (22-05-2024)

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  • HAL Id : hal-04583978 , version 1

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Marie Kerjean, Pierre-Marie Pédrot. $\partial$ is for Dialectica. LICS 2024 - 39th Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2024, Tallinn, Estonia. pp.1-13. ⟨hal-04583978⟩
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