Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909616856629248 |
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| 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 |