This work studies sparse adversarial perturbations, including both unstructured and structured ones. We propose a framework based on a white-box PGD-like attack method named Sparse-PGD to effectively and efficiently generate such perturbations. Furthermore, we combine Sparse-PGD with a black-box attack to comprehensively and more reliably evaluate the models' robustness against unstructured and structured sparse adversarial perturbations. Moreover, the efficiency of Sparse-PGD enables us to conduct adversarial training to build robust models against various sparse perturbations. Extensive experiments demonstrate that our proposed attack algorithm exhibits strong performance in different scenarios. More importantly, compared with other robust models, our adversarially trained model demonstrates state-of-the-art robustness against various sparse attacks.

This work studies fast adversarial training against sparse adversarial perturbations bounded by $l_0$ norm. We first demonstrate the unique challenges of employing $1$-step attacks on $l_0$ bounded perturbations, especially catastrophic overfitting (CO) that cannnot be properly addressed by existing fast adversarial training method for other $l_p$ norms ($p \geq 1$). We highlight that CO in $l_0$ adversarial training arises from sub-optimal perturbation locations of $1$-step attack. Some strategies like multi-$\epsilon$ can mitigate this sub-optimality to some extent, they lead to unstable training in turn. Theoretical and numerical analyses also reveal that the loss landscape of $l_0$ adversarial training is more craggy than its $l_\infty$, $l_2$ and $l_1$ counterparts, which exaggerates CO. To address this issue, we adopt soft labels and the trade-off loss function to smooth the adversarial loss landscape. Extensive experiments demonstrate our method can overcome the challenge of CO, achieve state-of-the-art performance, and narrow the performance gap between $1$-step and multi-step adversarial training against sparse attacks.

Existing machine unlearning (MU) approaches exhibit significant sensitivity to hyperparameters, requiring meticulous tuning that limits practical deployment. In this work, we first empirically demonstrate the instability and suboptimal performance of existing popular MU methods when deployed in different scenarios. To address this issue, we propose Dual Optimizer (DualOptim), which incorporates adaptive learning rate and decoupled momentum factors. Empirical and theoretical evidence demonstrates that DualOptim contributes to effective and stable unlearning. Through extensive experiments, we show that DualOptim can significantly boost MU efficacy and stability across diverse tasks, including image classification, image generation, and large language models, making it a versatile approach to empower existing MU algorithms.

Dataset distillation (DD) methods have demonstrated remarkable performance for neural networks trained with very limited training data. However, a significant challenge arises in the form of architecture overfitting: the distilled training dataset synthesized by a specific network architecture (i.e., training network) generates poor performance when trained by other network architectures (i.e., test networks), especially when the test networks have a larger capacity than the training network. This article introduces a series of approaches to mitigate this issue. Among them, DropPath renders the large model to be an implicit ensemble of its subnetworks, and knowledge distillation (KD) ensures each subnetwork acts similar to the small but well-performing teacher network. These methods, characterized by their smoothing effects, significantly mitigate architecture overfitting. We conduct extensive experiments to demonstrate the effectiveness and generality of our methods. Particularly, across various scenarios involving different tasks and different sizes of distilled data, our approaches significantly mitigate architecture overfitting. Furthermore, our approaches achieve comparable or even superior performance when the test network is larger than the training network. Codes are available at https://github.com/CityU-MLO/mitigate_architecture_overfitting.

This work studies sparse adversarial perturbations bounded by $l_0$ norm. We propose a white-box PGD-like attack method named sparse-PGD to effectively and efficiently generate such perturbations. Furthermore, we combine sparse-PGD with a black-box attack to comprehensively and more reliably evaluate the models' robustness against $l_0$ bounded adversarial perturbations. Moreover, the efficiency of sparse-PGD enables us to conduct adversarial training to build robust models against sparse perturbations. Extensive experiments demonstrate that our proposed attack algorithm exhibits strong performance in different scenarios. More importantly, compared with other robust models, our adversarially trained model demonstrates state-of-the-art robustness against various sparse attacks. Codes are available at https://github.com/CityU-MLO/sPGD.

Adversarial training is a popular method to robustify models against adversarial attacks. However, it exhibits much more severe overfitting than training on clean inputs. In this work, we investigate this phenomenon from the perspective of training instances, i.e., training input-target pairs. Based on a quantitative metric measuring the relative difficulty of an instance in the training set, we analyze the model's behavior on training instances of different difficulty levels. This lets us demonstrate that the decay in generalization performance of adversarial training is a result of fitting hard adversarial instances. We theoretically verify our observations for both linear and general nonlinear models, proving that models trained on hard instances have worse generalization performance than ones trained on easy instances, and that this generalization gap increases with the size of the adversarial budget. Finally, we investigate solutions to mitigate adversarial overfitting in several scenarios, including fast adversarial training and fine-tuning a pretrained model with additional data. Our results demonstrate that using training data adaptively improves the model's robustness.

We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an $l_1$ norm. We demonstrate that achieving robustness against $l_1$-bounded perturbations is more challenging than in the $l_2$ or $l_\infty$ cases, because adversarial training against $l_1$-bounded perturbations is more likely to suffer from catastrophic overfitting and yield training instabilities. Our analysis links these issues to the coordinate descent strategy used in existing methods. We address this by introducing Fast-EG-$l_1$, an efficient adversarial training algorithm based on Euclidean geometry and free of coordinate descent. Fast-EG-$l_1$ comes with no additional memory costs and no extra hyper-parameters to tune. Our experimental results on various datasets demonstrate that Fast-EG-$l_1$ yields the best and most stable robustness against $l_1$-bounded adversarial attacks among the methods of comparable computational complexity. Code and the checkpoints are available at https://github.com/IVRL/FastAdvL.

While adversarial training and its variants have shown to be the most effective algorithms to defend against adversarial attacks, their extremely slow training process makes it hard to scale to large datasets like ImageNet. The key idea of recent works to accelerate adversarial training is to substitute multi-step attacks (e.g., PGD) with single-step attacks (e.g., FGSM). However, these single-step methods suffer from catastrophic overfitting, where the accuracy against PGD attack suddenly drops to nearly 0% during training, and the network totally loses its robustness. In this work, we study the phenomenon from the perspective of training instances. We show that catastrophic overfitting is instance-dependent, and fitting instances with larger input gradient norm is more likely to cause catastrophic overfitting. Based on our findings, we propose a simple but effective method, Adversarial Training with Adaptive Step size (ATAS). ATAS learns an instance-wise adaptive step size that is inversely proportional to its gradient norm. Our theoretical analysis shows that ATAS converges faster than the commonly adopted non-adaptive counterparts. Empirically, ATAS consistently mitigates catastrophic overfitting and achieves higher robust accuracy on CIFAR10, CIFAR100, and ImageNet when evaluated on various adversarial budgets. Our code is released at https://github.com/HuangZhiChao95/ATAS.

Training certifiable neural networks enables us to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to obtain a provable adversarial-free region in the neighborhood of the input data by a polyhedral envelope, which yields more fine-grained certified robustness than existing methods. We further introduce polyhedral envelope regularization (PER) to encourage larger adversarial-free regions and thus improve the provable robustness of the models. We demonstrate the flexibility and effectiveness of our framework on standard benchmarks; it applies to networks of different architectures and with general activation functions. Compared with state of the art, PER has negligible computational overhead; it achieves better robustness guarantees and accuracy on the clean data in various settings.

Robustness to adversarial attacks was shown to require a larger model capacity, and thus a larger memory footprint. In this paper, we introduce an approach to obtain robust yet compact models by pruning randomly-initialized binary networks. Unlike adversarial training, which learns the model parameters, we initialize the model parameters as either +1 or −1, keep them fixed, and find a subnetwork structure that is robust to attacks. Our method confirms the Strong Lottery Ticket Hypothesis in the presence of adversarial attacks, and extends this to binary networks. Furthermore, it yields more compact networks with competitive performance than existing works by 1) adaptively pruning different network layers; 2) exploiting an effective binary initialization scheme; 3) incorporating a last batch normalization layer to improve training stability. Our experiments demonstrate that our approach not only always outperforms the state-of-the-art robust binary networks, but also can achieve accuracy better than full-precision ones on some datasets. Finally, we show the structured patterns of our pruned binary networks.

We analyze the influence of adversarial training on the loss landscape of machine learning models. To this end, we first provide analytical studies of the properties of adversarial loss functions under different adversarial budgets. We then demonstrate that the adversarial loss landscape is less favorable to optimization, due to increased curvature and more scattered gradients. Our conclusions are validated by numerical analyses, which show that training under large adversarial budgets impede the escape from suboptimal random initialization, cause non-vanishing gradients and make the models' minima found sharper. Based on these observations, we show that a periodic adversarial scheduling (PAS) strategy can effectively overcome these challenges, yielding better results than vanilla adversarial training while being much less sensitive to the choice of learning rate.

Generative adversarial networks (GANs) are known to achieve the state-of-the-art performance on various generative tasks, but these results come at the expense of a notoriously difficult training phase. Current training strategies typically draw a connection to optimization theory, whose scope is restricted to local convergence due to the presence of non-convexity. In this work, we tackle the training of GANs by rethinking the problem formulation from the mixed Nash Equilibria (NE) perspective. Via a classical lifting trick, we show that essentially all existing GAN objectives can be relaxed into their mixed strategy forms, whose global optima can be solved via sampling, in contrast to the exclusive use of optimization framework in previous work. We further propose a mean-approximation sampling scheme, which allows to systematically exploit methods for bi-affine games to delineate novel, practical training algorithms of GANs. Finally, we provide experimental evidence that our approach yields comparable or superior results to contemporary training algorithms, and outperforms classical methods such as SGD, Adam, and RMSProp.

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to study the decision boundary of neural network models. We formulate our target as an optimization problem with nonlinear constraints. Then, a framework applicable for general feedforward neural networks is proposed to bound the output logits so that the relaxed problem can be solved by the augmented Lagrangian method. Our experiments show the non-uniform bounds have larger volumes than uniform ones. Compared with normal models, the robust models have even larger non-uniform bounds and better interpretability. Further, the geometric similarity of the non-uniform bounds gives a quantitative, data-agnostic metric of input features’ robustness.