In this supplementary document, we provide additional materials to supplement our main submission. In Section A, we talk about the societal impacts of our work In Section B, we provide detailed experimental settings as well as further evaluation results on CIFAR-10 and ImageNet. We also provide the comparison with input transformation-based defense methods. In Section D, we give the proofs w.r.t. In Section E, we give the proofs w.r.t. The proofs of Theorem 3 are given in Section F. In Section C, we provide the analysis and evaluation of decision-based attacks. Deep neural networks (DNNs) have been successfully applied in many safety-critical tasks, such as autonomous driving, face recognition and verification, etc. And adversarial samples have posed a serious threat to machine learning systems.

The query-based black-box attacks have raised serious threats to machine learning models in many real applications. In this work, we study a lightweight defense method, dubbed Random Noise Defense (RND), which adds proper Gaussian noise to each query. We conduct the theoretical analysis about the effectiveness of RND against query-based black-box attacks and the corresponding adaptive attacks. Our theoretical results reveal that the defense performance of RND is determined by the magnitude ratio between the noise induced by RND and the noise added by the attackers for gradient estimation or local search. The large magnitude ratio leads to the stronger defense performance of RND, and it's also critical for mitigating adaptive attacks. Based on our analysis, we further propose to combine RND with a plausible Gaussian augmentation Fine-tuning (RND-GF). It enables RND to add larger noise to each query while maintaining the clean accuracy to obtain a better trade-off between clean accuracy and defense performance. Additionally, RND can be flexibly combined with the existing defense methods to further boost the adversarial robustness, such as adversarial training (AT). Extensive experiments on CIFAR-10 and ImageNet verify our theoretical findings and the effectiveness of RND and RND-GF.

Machine learning (ML) is pervasively deployed.

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For eachDk subsets, respectively, we follow the same subsampling procedure used in the singlevariate case. That is, we letq10 = 10% of the first data subset andq20 = 10% of the second data subset.

Optimizing Data Collection for Machine Learning

In Section A, we talk about the societal impacts of our work In Section B, we provide detailed experimental settings as well as further evaluation results on CIFAR-10 and ImageNet. Forreal-worldapplications,theDNNmodelaswellas the training dataset, are often hidden from users. Extensive experiments verify our theoretical analysis and showtheeffectiveness ofourdefense methods against several state-of-the-art query-based attacks. On ImageNet, [23] released the ResNet-50 model fine-tuned with Gaussian noise sampled from N(0,0.5I)andwedirectlyadoptit. The experimental results on ImageNet are shown in Figure 3 (a-d).

In this work, we study a lightweight defense method,dubbed RandomNoiseDefense (RND),whichaddsproperGaussiannoise toeachquery.