Some Fundamental Aspects about Lipschitz Continuity of Neural Networks

2023/02/21 by Grigory Khromov, Khromov, Grigory, Sidak Pal Singh +1 · 5 citations
Computer Science · #Adversarial Robustness in Machine Learning #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification

paper · pdf · doi:10.48550/arxiv.2302.10886

openalex publication_date 2023/02/21 · openalex created_date 2023/02/24 · openalex updated_date 2026/07/28

Abstract

Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and developing different practical strategies to enforce certain Lipschitz properties, we aim to thoroughly examine and characterise the Lipschitz behaviour of Neural Networks. Thus, we carry out an empirical investigation in a range of different settings (namely, architectures, datasets, label noise, and more) by exhausting the limits of the simplest and the most general lower and upper bounds. As a highlight of this investigation, we showcase a remarkable fidelity of the lower Lipschitz bound, identify a striking Double Descent trend in both upper and lower bounds to the Lipschitz and explain the intriguing effects of label noise on function smoothness and generalisation.

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