Boosting the Certified Robustness of L-infinity Distance Nets

Abstract

Recently, Zhang et al. (2021) developed a new neural network architecture based on ${\ell }_{\infty }$-distance functions, which naturally possesses certified ${\ell }_{\infty }$ robustness by its construction. Despite the novel design and theoretical foundation, so far the model only achieved comparable performance to conventional networks. In this paper, we make the following two contributions: $(\mathrm{i})$ We demonstrate that ${\ell }_{\infty }$-distance nets enjoy a fundamental advantage in certified robustness over conventional networks (under typical certification approaches); $(\mathrm{ii})$ With an improved training process we are able to significantly boost the certified accuracy of ${\ell }_{\infty }$-distance nets. Our training approach largely alleviates the optimization problem that arose in the previous training scheme, in particular, the unexpected large Lipschitz constant due to the use of a crucial trick called ${\ell }_p$-relaxation. The core of our training approach is a novel objective function that combines scaled cross-entropy loss and clipped hinge loss with a decaying mixing coefficient. Experiments show that using the proposed training strategy, the certified accuracy of ${\ell }_{\infty }$-distance net can be dramatically improved from 33.30% to 40.06% on CIFAR-10 ($\epsilon =8/255$), meanwhile outperforming other approaches in this area by a large margin. Our results clearly demonstrate the effectiveness and potential of ${\ell }_{\infty }$-distance net for certified robustness. Codes are available at https://github.com/zbh2047/L_inf-dist-net-v2.

arXiv commentAccepted for ICLR 2022; 21 pages

References in corpus (21)

• Theoretically Principled Trade-off between Robustness and Accuracy
• Provable defenses against adversarial examples via the convex outer adversarial polytope
• Certified Adversarial Robustness via Randomized Smoothing
• Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks
• Certified Defenses against Adversarial Examples
• Adversarial Risk and the Dangers of Evaluating Against Weak Attacks
• Efficient Neural Network Robustness Certification with General Activation Functions
• On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models
• Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers
• Spectral Norm Regularization for Improving the Generalizability of Deep Learning
• Certified Adversarial Robustness with Additive Noise
• Efficient Formal Safety Analysis of Neural Networks
• Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks
• A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks
• Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability
• MMA Training: Direct Input Space Margin Maximization through Adversarial Training
• Generalizable Adversarial Training via Spectral Normalization
• MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radius
• Provable Robustness of ReLU networks via Maximization of Linear Regions
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness
• Globally-Robust Neural Networks

Cited by in corpus (3)

• Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspective
• Multi-head Ensemble of Smoothed Classifiers for Certified Robustness
• Adversarial Defenses via Vector Quantization