On the Geometry of Deep Learning
Machine Learning
2025-01-16 v2 Artificial Intelligence
Computer Vision and Pattern Recognition
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.
Cite
@article{arxiv.2408.04809,
title = {On the Geometry of Deep Learning},
author = {Randall Balestriero and Ahmed Imtiaz Humayun and Richard Baraniuk},
journal= {arXiv preprint arXiv:2408.04809},
year = {2025}
}
Comments
Accepted for publication at 'Notices of the American Mathematical Society'