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

arXiv: https://arxiv.org/abs/2502.09898 · HTML: https://mlsanity.com/paper/2502.09898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2025.

## Abstract (arXiv)

The injectivity of ReLU layers in neural networks, the recovery of vectors from clipped or saturated measurements, and (real) phase retrieval in ℝn 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.