Some Fundamental Aspects about Lipschitz Continuity of Neural Networks
This work provides foundational insights into neural network properties for researchers in machine learning theory and robustness.
The authors empirically investigated the Lipschitz continuity behavior of neural networks across various architectures, datasets, and label noise settings, revealing a remarkable fidelity of lower Lipschitz bounds, a Double Descent trend in both bounds, and effects of label noise on smoothness and generalization.
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.