Lipschitz Thinking: Ten Years of Certifiable-by-Design Robust Neural Networks
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 certif...
| Authors | Fabio Brau, Giorgio Piras, Maura Pintor et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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