Deep Neural Networks (DNNs) need to be both efficient and robust for practical uses. Quantization and structure simplification are promising ways to adapt DNNs to mobile devices, and adversarial training is one of the most successful methods to train robust DNNs. In this work, we aim to realize both advantages by applying a convergent relaxation quantization algorithm, i.e., Binary-Relax (BR), to an adversarially trained robust model, i.e. the ResNets Ensemble via Feynman-Kac Formalism (EnResNet). We discover that high-precision quantization, such as ternary (tnn) or 4-bit, produces sparse DNNs. However, this sparsity is unstructured under adversarial training. To solve the problems that adversarial training jeopardizes DNNs’ accuracy on clean images and break the structure of sparsity, we design a trade-off loss function that helps DNNs preserve natural accuracy and improve channel sparsity. With our newly designed trade-off loss function, we achieve both goals with no reduction of resistance under weak attacks and very minor reduction of resistance under strong adversarial attacks. Together with our model and algorithm selections and loss function design, we provide an integrated approach to produce robust DNNs with high efficiency and accuracy. Furthermore, we provide a missing benchmark on robustness of quantized models.
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Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxations
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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- Award ID(s):
- 2047462
- PAR ID:
- 10488547
- Publisher / Repository:
- Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5631-5660, 2023.
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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