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A Formal Proof of the Expressiveness of Deep Learning

Abstract : Deep learning has had a profound impact on computer science in recent years, with applications to image recognition, language processing, bioinformatics, and more. Recently , Cohen et al. provided theoretical evidence for the superiority of deep learning over shallow learning. We formalized their mathematical proof using Isabelle/HOL. The Isabelle development simplifies and generalizes the original proof, while working around the limitations of the HOL type system. To support the formalization, we developed reusable libraries of formalized mathematics, including results about the matrix rank, the Borel measure, and multivariate polynomials as well as a library for tensor analysis.
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Contributor : Jasmin Blanchette <>
Submitted on : Tuesday, September 24, 2019 - 4:54:10 PM
Last modification on : Wednesday, September 25, 2019 - 1:19:18 AM
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Alexander Bentkamp, Jasmin Blanchette, Dietrich Klakow. A Formal Proof of the Expressiveness of Deep Learning. Journal of Automated Reasoning, Springer Verlag, 2019, 63 (2), pp.347-368. ⟨10.1007/s10817-018-9481-5⟩. ⟨hal-02296014⟩