Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval

Daniel Freeman; Daniel Haider

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arXiv · 2502.09898

Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval

Daniel Freeman·Daniel Haider

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Abstract

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.

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Daniel Freeman, Daniel Haider. 2025-02-14. Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval. https://arxiv.org/abs/2502.09898

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