Work

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

Year: 2025

Type: article

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

Source: Applied and Computational Harmonic Analysis

DOI: 10.1016/j.acha.2025.101801

Authors: Daniel Freeman, Daniel Haider

Institutions: Saint Louis University, Austrian Academy of Sciences, Acoustics Research Institute

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,150

Funders: National Science Foundation, Österreichische Agentur für Internationale Mobilität und Kooperation in Bildung, Wissenschaft und Forschung