5 papers
The Geometry of Cochains on Sampled Vietoris-Rips Complexes
Darrick Lee, Kelly Maggs
We study the geometry of simplicial cochains on Vietoris-Rips complexes built from i.i.d. samples of a compact embedded manifold. By integrating differential forms over affine simp…
Neural Point-Forms
Bruno Trentini, Jacob Hume, Vincenzo Antonio Isoldi +3
Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature…
Interval-sphere model structures
Kathryn Hess, Samuel Lavenir, Kelly Maggs
The bedrock of persistence theory over a single parameter is decomposition of persistence modules into intervals. In [HLM24], the authors leveraged interval decomposition to produc…
Simplicial Representation Learning with Neural -Forms
Kelly Maggs, Celia Hacker, Bastian Rieck
Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of…
Cell decompositions of persistent minimal models
Kathryn Hess, Samuel Lavenir, Kelly Maggs
In this article we generalize the main structure theorems of rational homotopy theory to the persistent setting. Our main motivation is the computation of an explicit finite, cellu…