Some Fundamental Aspects about Lipschitz Continuity of Neural Networks

TL;DR

This paper empirically investigates the Lipschitz continuity of neural networks across various architectures and datasets, revealing key behaviors like the double descent trend and effects of label noise on smoothness and generalisation.

Contribution

It provides a comprehensive empirical analysis of neural network Lipschitz bounds, highlighting their fidelity, trends, and the impact of label noise on model properties.

Findings

Lower Lipschitz bounds show remarkable fidelity.

Double Descent trend observed in Lipschitz bounds.

Label noise affects function smoothness and generalisation.

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.