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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.23977 |
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| _version_ | 1866915365571788800 |
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| author | Abdeen, Zain ul Kekatos, Vassilis Jin, Ming |
| author_facet | Abdeen, Zain ul Kekatos, Vassilis Jin, Ming |
| contents | Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However, accurate methods for Lipschitz-constrained training often suffer from non-convex formulations and poor scalability due to reliance on global semidefinite programs (SDPs). In this letter, we propose a convex training framework that enforces global Lipschitz constraints via semidefinite relaxation. By reparameterizing the NN using loop transformation, we derive a convex admissibility condition that enables tractable and certifiable training. While the resulting formulation guarantees robustness, its scalability is limited by the size of global SDP. To overcome this, we develop a randomized subspace linear matrix inequalities (RS-LMI) approach that decomposes the global constraints into sketched layerwise constraints projected onto low-dimensional subspaces, yielding a smooth and memory-efficient training objective. Empirical results on MNIST, CIFAR-10, and ImageNet demonstrate that the proposed framework achieves competitive accuracy with significantly improved Lipschitz bounds and runtime performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Scalable Approach for Safe and Robust Learning via Lipschitz-Constrained Networks Abdeen, Zain ul Kekatos, Vassilis Jin, Ming Machine Learning Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However, accurate methods for Lipschitz-constrained training often suffer from non-convex formulations and poor scalability due to reliance on global semidefinite programs (SDPs). In this letter, we propose a convex training framework that enforces global Lipschitz constraints via semidefinite relaxation. By reparameterizing the NN using loop transformation, we derive a convex admissibility condition that enables tractable and certifiable training. While the resulting formulation guarantees robustness, its scalability is limited by the size of global SDP. To overcome this, we develop a randomized subspace linear matrix inequalities (RS-LMI) approach that decomposes the global constraints into sketched layerwise constraints projected onto low-dimensional subspaces, yielding a smooth and memory-efficient training objective. Empirical results on MNIST, CIFAR-10, and ImageNet demonstrate that the proposed framework achieves competitive accuracy with significantly improved Lipschitz bounds and runtime performance. |
| title | A Scalable Approach for Safe and Robust Learning via Lipschitz-Constrained Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.23977 |