Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915152182378496 |
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| author | Freeman, Daniel Haider, Daniel |
| author_facet | Freeman, Daniel Haider, Daniel |
| contents | The injectivity of ReLU layers in neural networks, the recovery of vectors from clipped or saturated measurements, and (real) phase retrieval in $\mathbb{R}^n$ allow for a similar problem formulation and characterization using frame theory. In this paper, we revisit all three problems with a unified perspective and derive lower Lipschitz bounds for ReLU layers and clipping which are analogous to the previously known result for phase retrieval and are optimal up to a constant factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval Freeman, Daniel Haider, Daniel Machine Learning Numerical Analysis Functional Analysis The injectivity of ReLU layers in neural networks, the recovery of vectors from clipped or saturated measurements, and (real) phase retrieval in $\mathbb{R}^n$ allow for a similar problem formulation and characterization using frame theory. In this paper, we revisit all three problems with a unified perspective and derive lower Lipschitz bounds for ReLU layers and clipping which are analogous to the previously known result for phase retrieval and are optimal up to a constant factor. |
| title | Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval |
| topic | Machine Learning Numerical Analysis Functional Analysis |
| url | https://arxiv.org/abs/2502.09898 |