系统梳理深度学习中Lipschitz连续性的理论与应用。
Lipschitz Continuity in Deep Learning: A Systematic Review of Theoretical Foundations, Estimation Methods, Regularization Approaches, and Certifiable Robustness
- 从理论、估计、正则化到可证鲁棒性全面综述
- 揭示Lipschitz连续性对模型鲁棒性与泛化的关键作用
- 适合关注模型安全性与理论分析的研究者
Lipschitz连续性是神经网络对输入扰动敏感度的核心属性，在深度学习中对鲁棒性、泛化能力及优化动态起关键作用。尽管其重要性显著，相关研究分散于多个领域，缺乏统一视角。本文系统综述了深度学习中的Lipschitz连续性，涵盖其理论基础、估计方法、正则化策略及可证鲁棒性。通过整合现有研究，本综述为希望深入理解该性质及其在深度学习中影响的研究人员和实践者提供全面参考。
原文摘要 · Abstract (English)
Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations. It plays a pivotal role in deep learning, governing \textbf{robustness}, \textbf{generalization} and \textbf{optimization dynamics}. Despite its importance, research on Lipschitz continuity is scattered across various domains, lacking a unified perspective. This paper addresses this gap by providing a systematic review of Lipschitz continuity in deep learning. We explore its \textbf{theoretical foundations}, \textbf{estimation methods}, \textbf{regularization approaches}, and \textbf{certifiable robustness}. By reviewing existing research through the lens of Lipschitz continuity, this survey serves as a comprehensive reference for researchers and practitioners seeking a deeper understanding of Lipschitz continuity and its implications in deep learning.
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