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math.DG2026
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…
cs.LG2026
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…