Improved Scalable Lipschitz Bounds for Deep Neural Networks
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Abstract (arXiv)
Computing tight Lipschitz bounds for deep neural networks is crucial for analyzing their robustness and stability, but existing approaches either produce relatively conservative estimates or rely on semidefinite programming (SDP) formulations (namely the LipSDP condition) that face scalability issues. Building upon ECLipsE-Fast, the state-of-the-art Lipschitz bound method that avoids SDP formulations, we derive a new family of improved scalable Lipschitz bounds that can be combined to outperform ECLipsE-Fast. Specifically, we leverage more general parameterizations of feasible points of LipSDP to derive various closed-form Lipschitz bounds, avoiding the use of SDP solvers. In addition, we show that our technique encompasses ECLipsE-Fast as a special case and leads to a much larger class of scalable Lipschitz bounds for deep neural networks. Our empirical study shows that our bounds improve ECLipsE-Fast, further advancing the scalability and precision of Lipschitz estimation for large neural networks.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 18 of its 23 references that are in the map. First posted on arXiv 18 Mar 2025.
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18 of 23 references.
References · 18
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6 more
- 2021Reliably-stabilizing piecewise-affine neural network controllerscited by 13
- 2022Lipschitz constant estimation for 1D convolutional neural networkscited by 13
- 2024Lipschitz constant estimation for general neural network architectures using control toolscited by 8
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- 2024On Robust Reinforcement Learning with Lipschitz-Bounded Policy Networkscited by 4
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.