发表机构
University of Cagliari（卡利亚里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述了Lipschitz有界神经网络十年发展，阐述其原理、约束机制及单次前向传播获得鲁棒性认证的方法，并展望其作为设计即得稳定性通用框架的未来方向。
AI 中文摘要
深度神经网络的 Lipschitz 性质提供了其对于输入扰动敏感性的直接度量，当被显式控制时，它为限制误差传播和提高鲁棒性提供了一种原则性方法。在过去十年中，Lipschitz 有界层已被纳入越来越具有表达力和高性能的深度模型中，缩小了经验鲁棒性与形式化、设计即得的稳定性保证之间的差距。本文介绍了 Lipschitz 有界神经网络背后的基本概念，解释了 Lipschitz 约束层的原理、用于强制执行其界限的机制，以及它们如何以单次前向传播为代价产生鲁棒性认证。本教程最后讨论了新兴和开放的方向，强调 Lipschitz 控制作为提供有保证的、设计即得的稳定性的通用框架。
英文摘要
The Lipschitz property of a deep neural network provides a direct measure of its sensitivity to input perturbations and, when explicitly controlled, offers a principled way to limit the propagation of errors and improve robustness. Over the past decade, Lipschitz-bounded layers have been incorporated into increasingly expressive and high-performing deep models, narrowing the gap between empirical robustness and formal, by-design guarantees of stability. This article introduces the fundamental concepts underlying Lipschitz-bounded neural networks, explaining the principles behind Lipschitz-constrained layers, the mechanisms used to enforce their bounds, and how they yield robustness certificates at the cost of a single forward pass. The tutorial concludes by discussing emerging and open directions, highlighting Lipschitz control as a general framework for offering guaranteed, by-design stability.
