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Double Sampling Randomized Smoothing
Linyi Li · Jiawei Zhang · Tao Xie · Bo Li

Tue Jul 19 08:45 AM -- 08:50 AM (PDT) @ Hall G
in Deep Learning: Robustness »
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 previous work shows, 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 from an additional smoothing distribution to tighten the robustness certification of the previous smoothed classifier. Theoretically, under mild assumptions, we prove that DSRS can certify $\Theta(\sqrt d)$ robust radius under $\ell_2$ norm where $d$ is the input dimension, which implies that DSRS may be able to break the curse of dimensionality of randomized smoothing. We instantiate DSRS for a generalized family of Gaussian smoothing and propose an efficient and sound computing method based on customized dual optimization considering sampling error. Extensive experiments on MNIST, CIFAR-10, and ImageNet verify our theory and show that DSRS certifies larger robust radii than existing baselines consistently under different settings. Code is available at https://github.com/llylly/DSRS.
Keywords: DL: Robustness · SA: Trustworthy Machine Learning

Author Information

Linyi Li (UIUC)
Jiawei Zhang (UIUC)
Tao Xie (Peking University)
Bo Li (UIUC)
Bo Li

Dr. Bo Li is an assistant professor in the Department of Computer Science at the University of Illinois at Urbana–Champaign. She is the recipient of the IJCAI Computers and Thought Award, Alfred P. Sloan Research Fellowship, AI’s 10 to Watch, NSF CAREER Award, MIT Technology Review TR-35 Award, Dean's Award for Excellence in Research, C.W. Gear Outstanding Junior Faculty Award, Intel Rising Star award, Symantec Research Labs Fellowship, Rising Star Award, Research Awards from Tech companies such as Amazon, Facebook, Intel, IBM, and eBay, and best paper awards at several top machine learning and security conferences. Her research focuses on both theoretical and practical aspects of trustworthy machine learning, which is at the intersection of machine learning, security, privacy, and game theory. She has designed several scalable frameworks for trustworthy machine learning and privacy-preserving data publishing. Her work has been featured by major publications and media outlets such as Nature, Wired, Fortune, and New York Times.

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