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arXiv · 2505.13582

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

Leyang Zhang·Yaoyu Zhang·Tao Luo
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Abstract

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.

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Leyang Zhang, Yaoyu Zhang, Tao Luo. 2025-05-19. Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting. https://arxiv.org/abs/2505.13582

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