Signals as submanifolds, and configurations of points
Information Theory
2025-04-15 v2 Differential Geometry
math.IT
Abstract
For the purposes of abstract theory of signal propagation, a signal is a submanifold of a Riemannian manifold. We obtain energy inequalities, or upper bounds, lower bounds on energy in a number of specific cases, including parameter spaces of Gaussians and spaces of configurations of points. We discuss the role of time as well as graph embeddings.
Keywords
Cite
@article{arxiv.2408.15375,
title = {Signals as submanifolds, and configurations of points},
author = {Tatyana Barron and Spencer Kelly and Colin Poulton},
journal= {arXiv preprint arXiv:2408.15375},
year = {2025}
}
Comments
To appear in Quarterly Applied Math