Generalization in Neural Networks Through the Lens of Magnitude Potential

Excerpt

arXiv:2610.01633v1 Announce Type: new Abstract: Explaining generalization and training dynamics in neural networks remains a challenge, and various approaches have been developed to study different aspects of these phenomena. In this paper, we introduce the idea of {\em magnitude potential} -- a quantity based on the theory of metric magnitude -- that reflects how well an arbitrary point is represented by a given set. We find that this basic quantity can be applied to examine various features in