On the Geometry of Deep Learning
Randall Balestriero, Ahmed Imtiaz Humayun, Richard G. Baraniuk · Notices of the American Mathematical Society · 2025
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 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.