统一视角下推导出ReLU层的最优下界，解决饱和与相位恢复问题
Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval
- 用框架理论统一分析ReLU、截断与相位恢复问题
- 首次获得ReLU层下 Lipschitz 界，精度达常数因子最优
- 适合研究神经网络稳定性与信号恢复的学者参考
ReLU层的单射性、从截断或饱和测量中恢复向量，以及实数域ℝⁿ中的相位恢复问题，均可通过框架理论进行统一建模与分析。本文以统一视角重新审视这三个问题，推导出ReLU层和截断操作的下Lipschitz界，其形式与此前相位恢复的已知结果类似，且在常数因子意义下为最优。
原文摘要 · Abstract (English)
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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