Successful deep learning models often involve training neural network architectures that contain more parameters than the number of training samples. Such overparametrized models have been extensively studied in recent years, and the virtues of overparametrization have been established from both the statistical perspective, via the double-descent phenomenon, and the computational perspective via the structural properties of the optimization landscape.
Despite the remarkable success of deep learning architectures in the overparametrized regime, it is also well known that these models are highly vulnerable to small adversarial perturbations in their inputs. Even when adversarially trained, their performance on perturbed inputs (robust generalization) is considerably worse than their best attainable performance on benign inputs (standard generalization). It is thus imperative to understand how overparametrization fundamentally affects robustness.
In this paper, we will provide a precise characterization of the role of overparametrization on robustness by focusing on random features regression models (two-layer neural networks with random first layer weights). We consider a regime where the sample size, the input dimension and the number of parameters grow in proportion to each other, and derive an asymptotically exact formula for the robust generalization error when the model is adversarially trained. Our developed theory reveals the nontrivial effect of overparametrization on robustness and indicates that for adversarially trained random features models, high overparametrization can hurt robust generalization.
Overparametrization has become a de facto standard in machine learning. Despite numerous efforts, our understanding of how and where overparametrization helps model accuracy and robustness is still limited. To this end, here we conduct an empirical investigation to systemically study and replicate previous findings in this area, in particular the study by Madry et al. Together with this study, our findings support the "universal law of robustness" recently proposed by Bubeck et al. We argue that while critical for robust perception, overparametrization may not be enough to achieve full robustn…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
Adversarial training is a popular method to give neural nets robustness against adversarial perturbations. In practice adversarial training leads to low robust training loss. However, a rigorous explanation for why this happens under natural conditions is still missing. Recently a convergence theory for standard (non-adversarial) supervised training was developed by various groups for {\em very overparametrized} nets. It is unclear how to extend these results to adversarial training because of the min-max objective. Recently, a first step towards this direction was made by Gao et al. using too…
University of Southern California（南加利福尼亚大学）；University of Pennsylvania（宾夕法尼亚大学）
Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent \emph{adversarial training} methods have been effective at improving robustness to perturbed inputs (robust accuracy), often this benefit is accompanied by a decrease in accuracy on benign inputs (standard accuracy), leading to a tradeoff between often competing objectives. Complicating matters further, recent empirical evidence suggest that a variety of other factors (size and quality of training data, model size, etc.) a…
Many modern machine learning classifiers are shown to be vulnerable to adversarial perturbations of the instances. Despite a massive amount of work focusing on making classifiers robust, the task seems quite challenging. In this work, through a theoretical study, we investigate the adversarial risk and robustness of classifiers and draw a connection to the well-known phenomenon of concentration of measure in metric measure spaces. We show that if the metric probability space of the test instance is concentrated, any classifier with some initial constant error is inherently vulnerable to advers…
McGill University（麦吉尔大学）；University of Minnesota（明尼苏达大学）
In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networks. The adversarial robustness regularization combines adversarial training, which we show to be equivalent to Total Variation regularization, with Lipschitz regularization. We demonstrate empirically that the regularized models are more robust, and that gradient norms of images …
The adversarial training procedure proposed by Madry et al. (2018) is one of the most effective methods to defend against adversarial examples in deep neural networks (DNNs). In our paper, we shed some lights on the practicality and the hardness of adversarial training by showing that the effectiveness (robustness on test set) of adversarial training has a strong correlation with the distance between a test point and the manifold of training data embedded by the network. Test examples that are relatively far away from this manifold are more likely to be vulnerable to adversarial attacks. Conse…
Deep neural networks have been successful in diverse discriminative classification tasks, although, they are poorly calibrated often assigning high probability to misclassified predictions. Potential consequences could lead to trustworthiness and accountability of the models when deployed in real applications, where predictions are evaluated based on their confidence scores. Existing solutions suggest the benefits attained by combining deep neural networks and Bayesian inference to quantify uncertainty over the models' predictions for ambiguous datapoints. In this work we propose to validate a…
University of Nevada, Reno（内华达大学里诺分校）；IBM Research（IBM研究院）；University of Virginia（弗吉尼亚大学）
Data heterogeneity has been identified as one of the key features in federated learning but often overlooked in the lens of robustness to adversarial attacks. This paper focuses on characterizing and understanding its impact on backdooring attacks in federated learning through comprehensive experiments using synthetic and the LEAF benchmarks. The initial impression driven by our experimental results suggests that data heterogeneity is the dominant factor in the effectiveness of attacks and it may be a redemption for defending against backdooring as it makes the attack less efficient, more chal…
Fermi National Accelerator Laboratory（费米国家加速器实验室）；Space Telescope Science Institute（空间望远镜科学研究所）；Argonne National Laboratory（阿贡国家实验室）；Kavli Institute for Cosmological Physics（宇宙物理研究所）；University of Chicago（芝加哥大学）
Deep learning models are being increasingly adopted in wide array of scientific domains, especially to handle high-dimensionality and volume of the scientific data. However, these models tend to be brittle due to their complexity and overparametrization, especially to the inadvertent adversarial perturbations that can appear due to common image processing such as compression or blurring that are often seen with real scientific data. It is crucial to understand this brittleness and develop models robust to these adversarial perturbations. To this end, we study the effect of observational noise …
Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not constrained by the size of the classifier's architecture. Here, we extend the work of Li et al. \cite{li2018second}, studying how the choice of divergence between smoothing measures affects the final robustness guarantee, and how the choice of smoothing measure itself can lead to guarantees in differing threat models. To this end, we develop a method to certify ro…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Peking University（北京大学）
Neural networks (NNs) are known to be vulnerable against adversarial perturbations, and thus there is a line of work aiming to provide robustness certification for NNs, such as randomized smoothing, which samples smoothing noises from a certain distribution to certify the robustness for a smoothed classifier. However, as shown by previous work, the certified robust radius in randomized smoothing suffers from scaling to large datasets ("curse of dimensionality"). To overcome this hurdle, we propose a Double Sampling Randomized Smoothing (DSRS) framework, which exploits the sampled probability f…
Southern University of Science and Technology（南方科技大学）；City University of Hong Kong（香港城市大学）；University of Surrey（萨里大学）
Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial n…
Recently, more and more works have proposed to drive evolutionary algorithms using machine learning models.Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models.Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality.To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial n…
ENS Paris-Saclay（巴黎萨克雷高等师范学院）；Kyoto University（京都大学）；RIKEN AIP（理化学研究所先进智能项目中心）；University of Technology Sydney（悉尼科技大学）；Carnegie Mellon University（卡内基梅隆大学）；Zhejiang University（浙江大学）
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for high-dimensional data, which solves high-dimensional OT problems using feature selection to avoid the curse of dimensionality. Specifically, we find a transport plan with discriminative features. To this end, we formulate the FROT problem as a min--max optimization problem. We then propose a convex formulation of the FROT problem and solve it using a Frank--Wolfe-based o…
It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust training error can be near zero via some methods, all existing algorithms lead to a high robust generalization error. In this paper, we provide a theoretical understanding of this puzzling phenomenon from the perspective of expressive power for deep neural networks. Specifically, for binary classification problems with well-separated data, we show that, for ReLU networks, while mild over-parameteri…
