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arXiv · 2408.15375

Signals as submanifolds, and configurations of points

Tatyana Barron·Spencer Kelly·Colin Poulton
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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.

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Tatyana Barron, Spencer Kelly, Colin Poulton. 2025-04-14. Signals as submanifolds, and configurations of points. https://arxiv.org/abs/2408.15375

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