发表机构
Research Ireland – Centre for Research Training in AI (CRT-AI); J.E. Cairnes School of Business & Economics; School of Computer Science; University of Galway, Ireland（爱尔兰研究机构——人工智能研究培训中心（CRT-AI）; J.E. Cairnes 商学院; 计算机科学学院; 爱尔兰Galway大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文系统综述深度学习中利普希茨连续性，涵盖理论基础、估计方法、正则化方法及可验证鲁棒性，为研究者和从业者深入理解其在深度学习中的意义提供全面参考。
AI 中文摘要
利普希茨连续性是神经网络的基本属性，表征其对输入扰动的敏感性，在深度学习中对鲁棒性、泛化和优化动态起关键作用。但相关研究分散。本文对深度学习中的利普希茨连续性进行系统综述，探究其理论基础、估计方法、正则化方法及可验证鲁棒性，为相关研究者和从业者提供全面参考。
英文摘要
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.
CommentsPublished in Transactions on Machine Learning Research (TMLR)
