Signals as submanifolds, and configurations of points
<|reference_start|>Signals as submanifolds, and configurations of points: 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.<|reference_end|>
@article{barron2024signals,
    title={Signals as submanifolds, and configurations of points},
    author={Tatyana Barron, Spencer Kelly, Colin Poulton},
    journal={arXiv preprint arXiv:2408.15375},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.15375},
    primaryClass={cs.IT math.DG math.IT}
}