On the Geometry of Deep Learning

[Submitted on 9 Aug 2024]

View a PDF of the paper titled On the Geometry of Deep Learning, by Randall Balestriero and 2 other authors

Abstract:In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in multiple dimensions). In particular, we will overview work over the past decade on understanding certain geometrical properties of a deep network’s affine spline mapping, in particular how it tessellates its input space. As we will see, the affine spline connection and geometrical viewpoint provide a powerful portal through which to view, analyze, and improve the inner workings of a deep network.