Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting

Fuente: arXiv
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Main Authors: Zhang, Leyang, Zhang, Yaoyu, Luo, Tao
Format: Preprint
Published: 2025
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_version_ 1866909616856629248
author Zhang, Leyang
Zhang, Yaoyu
Luo, Tao
author_facet Zhang, Leyang
Zhang, Yaoyu
Luo, Tao
contents This paper investigates the sample dependence of critical points for neural networks. We introduce a sample-independent critical lifting operator that associates a parameter of one network with a set of parameters of another, thus defining sample-dependent and sample-independent lifted critical points. We then show by example that previously studied critical embeddings do not capture all sample-independent lifted critical points. Finally, we demonstrate the existence of sample-dependent lifted critical points for sufficiently large sample sizes and prove that saddles appear among them.
format Preprint
id arxiv_https___arxiv_org_abs_2505_13582
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting
Zhang, Leyang
Zhang, Yaoyu
Luo, Tao
Machine Learning
This paper investigates the sample dependence of critical points for neural networks. We introduce a sample-independent critical lifting operator that associates a parameter of one network with a set of parameters of another, thus defining sample-dependent and sample-independent lifted critical points. We then show by example that previously studied critical embeddings do not capture all sample-independent lifted critical points. Finally, we demonstrate the existence of sample-dependent lifted critical points for sufficiently large sample sizes and prove that saddles appear among them.
title Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting
topic Machine Learning
url https://arxiv.org/abs/2505.13582