Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval
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.
Authors
- Daniel Freeman (ORCID: https://orcid.org/0000-0003-1603-3942)
- Daniel Haider (ORCID: https://orcid.org/0000-0001-8012-5521)
Institutions
- Austrian Academy of Sciences (AT)
- University of Missouri–St. Louis (US)
- Acoustics Research Institute (AT)
- Saint Louis University (US)
Publication Details
- Journal
- Applied and Computational Harmonic Analysis
- Published
- 2025-08-28
- DOI
- https://doi.org/10.1016/j.acha.2025.101801
- Primary Topic
- Advancements in Photolithography Techniques
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Österreichische Agentur für Internationale Mobilität und Kooperation in Bildung, Wissenschaft und Forschung