Improved Scalable Lipschitz Bounds for Deep Neural Networks

• URL: http://arxiv.org/abs/2503.14297v1
• Date: Tue, 18 Mar 2025 14:39:47 GMT
• Title: Improved Scalable Lipschitz Bounds for Deep Neural Networks
• Authors: Usman Syed, Bin Hu,
• Abstract summary: We develop a new family of improved scalable Lipschitz bounds that can be combined to outperform ECLipsE-Fast.<n>Specifically, we leverage more general parameterizations of feasible points of LipSDP to derive various closed-form Lipschitz bounds.<n>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.
• Score: 3.195044561824979
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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