Deep learning is a hot area, but many of the results are empirical and short-lived. Experts in the area have asked for contributions from mathematics to bring some rigour to the area. In this talk I will describe three problems where a mathematical approach has made a contribution. The problems are: (i) deep model uncertainty, (ii) certified robust models, and (iii) neural ODEs. The math approaches are: statistical calibration, variational losses for Gaussian convolution, and regularization using Optimal Transportation, respectively. The talk will be geared to a broad audience: I’ll explain the problems in context, and present the ideas at a high level. Details can be found in the papers.
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