最优下Lipschitz边界的ReLU层，饱和度和相位检索

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2025-08-28 DOI:10.1016/j.acha.2025.101801

Daniel Freeman , Daniel Haider

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引用次数: 0

摘要

神经网络中ReLU层的注入性，从裁剪或饱和测量中恢复向量，以及Rn中的（真实）相位检索允许使用框架理论进行类似的问题表述和表征。在本文中，我们以统一的视角重新审视了这三个问题，并推导了ReLU层和裁剪的下Lipschitz界，这类似于先前已知的相位检索结果，并且在常量因子下是最优的。

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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.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.