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.
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.
| Original language | English |
|---|---|
| Title of host publication | Interactive Theorem Proving - 8th International Conference, ITP 2017, Brasilia, Brazil, September 26-29, 2017, Proceedings |
| Publisher | Springer |
| Pages | 46-64 |
| Volume | 10499 |
| Publication status | Published - 2017 |
Publication series
| Name | LNCS |
|---|
