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Expressiveness of Deep Learning

Deep learning has had a profound impact on computer science in recent years, with applications to search engines, image recognition and language processing, bioinformatics, and more. Recently, Cohen et al. [2] provided theoretical evidence for the superiority of deep learning over shallow learning. For my master’s thesis [1], I formalized their mathematical proof using Isabelle/HOL. This formalization simplifies and generalizes the original proof, while working around the limitations of the Isabelle type system. To support the formalization, I developed reusable libraries of formalized mathematics, including results about the matrix rank, the Lebesgue measure, and multivariate polynomials, as well as a library for tensor analysis.