A Closer Look at the Adversarial Robustness of Deep Equilibrium Models

Deep equilibrium models (DEQs) refrain from the traditional layer-stacking paradigm and turn to find the fixed point of a single layer. DEQs have achieved promising performance on different applications with featured memory efficiency. At the same time, the adversarial vulnerability of DEQs raises concerns. Several works propose to certify robustness for monotone DEQs. However, limited efforts are devoted to studying empirical robustness for general DEQs. To this end, we observe that an adversarially trained DEQ requires more forward steps to arrive at the equilibrium state, or even violates its fixed-point structure. Besides, the forward and backward tracks of DEQs are misaligned due to the black-box solvers. These facts cause gradient obfuscation when applying the ready-made attacks to evaluate or adversarially train DEQs. Given this, we develop approaches to estimate the intermediate gradients of DEQs and integrate them into the attacking pipelines. Our approaches facilitate fully white-box evaluations and lead to effective adversarial defense for DEQs. Extensive experiments on CIFAR-10 validate the adversarial robustness of DEQs competitive with deep networks of similar sizes.Comment: Accepted at NeurIPS 2022. Our code is available at https://github.com/minicheshire/DEQ-White-Box-Robustnes

Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser

Neural networks are vulnerable to adversarial examples, which poses a threat to their application in security sensitive systems. We propose high-level representation guided denoiser (HGD) as a defense for image classification. Standard denoiser suffers from the error amplification effect, in which small residual adversarial noise is progressively amplified and leads to wrong classifications. HGD overcomes this problem by using a loss function defined as the difference between the target model's outputs activated by the clean image and denoised image. Compared with ensemble adversarial training which is the state-of-the-art defending method on large images, HGD has three advantages. First, with HGD as a defense, the target model is more robust to either white-box or black-box adversarial attacks. Second, HGD can be trained on a small subset of the images and generalizes well to other images and unseen classes. Third, HGD can be transferred to defend models other than the one guiding it. In NIPS competition on defense against adversarial attacks, our HGD solution won the first place and outperformed other models by a large margin

Improving Adversarial Robustness of DEQs with Explicit Regulations Along the Neural Dynamics

Deep equilibrium (DEQ) models replace the multiple-layer stacking of conventional deep networks with a fixed-point iteration of a single-layer transformation. Having been demonstrated to be competitive in a variety of real-world scenarios, the adversarial robustness of general DEQs becomes increasingly crucial for their reliable deployment. Existing works improve the robustness of general DEQ models with the widely-used adversarial training (AT) framework, but they fail to exploit the structural uniquenesses of DEQ models. To this end, we interpret DEQs through the lens of neural dynamics and find that AT under-regulates intermediate states. Besides, the intermediate states typically provide predictions with a high prediction entropy. Informed by the correlation between the entropy of dynamical systems and their stability properties, we propose reducing prediction entropy by progressively updating inputs along the neural dynamics. During AT, we also utilize random intermediate states to compute the loss function. Our methods regulate the neural dynamics of DEQ models in this manner. Extensive experiments demonstrate that our methods substantially increase the robustness of DEQ models and even outperform the strong deep network baselines.Comment: Accepted at ICML 2023. Our code is available at https://github.com/minicheshire/DEQ-Regulating-Neural-Dynamic