Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxations

• URL: http://arxiv.org/abs/2211.17244v3
• Date: Wed, 14 Jun 2023 15:55:34 GMT
• Title: Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxations
• Authors: Hong-Ming Chiu and Richard Y. Zhang
• Abstract summary: We propose a non certification technique for adversarial network models. Non certification makes strong certifications comparable to much more expensive SDP methods, while optimizing variables dramatically fewer comparable to LP methods. Our experiments find that the non certification almost completely closes the gap towards exact certification adversarially trained models.
• Score: 12.589519278962378
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a "convex relaxation barrier" that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

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