3 papers
cs.LG2026
Finsler Geometry, Graph Neural Networks, and You
T. Mitchell Roddenberry, Richard G. Baraniuk
Graph neural network architectures based on the graph Laplacian approximate the Laplace-Beltrami operator, thus limiting their application to isotropic operators. As a nonlinear al…
cs.LG2026
The Geometric Structure of Models Learning Sparse Data
Thomas Walker, T. Mitchell Roddenberry, Ahmed Imtiaz Humayun +2
The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the trainin…
cs.LG2025
Rates and architectures for learning geometrically non-trivial operators
T. Mitchell Roddenberry, Leo Tzou, Ivan DokmaniÄ +2
Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from v…