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Invited Talk
Workshop: Advances in Programming Languages and Neurosymbolic Systems (AIPLANS)

When Gödel discovered Automatic Differentiation - Marie Kerjean - Centre national de la recherche scientifique



I will explore the boundaries between differentiable programming and logic, through the prism of the Curry-Howard correspondence. I will recall the latter and explain how automatic differentiation fits into each of its three facets: functions, proofs and programs. In particular, I will explain how backpropagation is identified with Gödel's Dialectica translation, a transformation of logical formulas historically used to prove consistency theorems and widely used in proof theory since then.