A Formal Proof of the Expressiveness of Deep Learning

  • Alexander Bentkamp
  • Jasmin Christian Blanchette
  • Dietrich Klakow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10499)


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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alexander Bentkamp
    • 1
    • 2
  • Jasmin Christian Blanchette
    • 1
    • 3
  • Dietrich Klakow
    • 2
  1. 1.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany

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