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[2602.15499] ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networks
Summary
The paper presents ExLipBaB, a method for exact computation of Lipschitz constants in piecewise linear neural networks, addressing limitations of existing algorithms.
Why It Matters
Understanding Lipschitz constants is crucial for ensuring the robustness and generalizability of neural networks. This research fills a gap in the exact computation methods for various activation functions, which is vital for applications requiring high reliability in sensitive data contexts.
Key Takeaways
- ExLipBaB generalizes the LipBaB algorithm for arbitrary piecewise linear neural networks.
- The method supports various activation functions beyond ReLU, enhancing its applicability.
- Exact computation of Lipschitz constants can improve robustness guarantees in neural networks.
Computer Science > Machine Learning arXiv:2602.15499 (cs) [Submitted on 17 Feb 2026] Title:ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networks Authors:Tom A. Splittgerber View a PDF of the paper titled ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networks, by Tom A. Splittgerber View PDF HTML (experimental) Abstract:It has been shown that a neural network's Lipschitz constant can be leveraged to derive robustness guarantees, to improve generalizability via regularization or even to construct invertible networks. Therefore, a number of methods varying in the tightness of their bounds and their computational cost have been developed to approximate the Lipschitz constant for different classes of networks. However, comparatively little research exists on methods for exact computation, which has been shown to be NP-hard. Nonetheless, there are applications where one might readily accept the computational cost of an exact method. These applications could include the benchmarking of new methods or the computation of robustness guarantees for small models on sensitive data. Unfortunately, existing exact algorithms restrict themselves to only ReLU-activated networks, which are known to come with severe downsides in the context of Lipschitz-constrained networks. We therefore propose a generalization of the LipBaB algorithm to compute exact Lipschitz constants for arbitrary piecewise linear neural networks and $p$-norms. W...
