arxivstat.MLcs.LG2026-07-15
Lipschitz Continuity in Deep Learning: A Systematic Review of Theoretical Foundations, Estimation Methods, Regularization Approaches, and Certifiable Robustness
Róisín Luo, James McDermott, Colm O'Riordan
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 importan…