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Consistency Regularization for Certified Robustness of Smoothed Classifiers

arXiv 2006.04062 ↗First posted 7 Jun 2020cs.LG stat.MLcited by 73

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Abstract (arXiv)

A recent technique of randomized smoothing has shown that the worst-case (adversarial) ℓ2-robustness can be transformed into the average-case Gaussian-robustness by "smoothing" a classifier, i.e., by considering the averaged prediction over Gaussian noise. In this paradigm, one should rethink the notion of adversarial robustness in terms of generalization ability of a classifier under noisy observations. We found that the trade-off between accuracy and certified robustness of smoothed classifiers can be greatly controlled by simply regularizing the prediction consistency over noise. This relationship allows us to design a robust training objective without approximating a non-existing smoothed classifier, e.g., via soft smoothing. Our experiments under various deep neural network architectures and datasets show that the "certified" ℓ2-robustness can be dramatically improved with the proposed regularization, even achieving better or comparable results to the state-of-the-art approaches with significantly less training costs and hyperparameters.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Jun 2020.

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Citing papers per year: 2021: 14; 2022: 16; 2023: 17; 2024: 17; 2025: 7; 2026: 2.

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2022(Certified!!) Adversarial Robustness for Free!cited by 130
2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
2021Consistency Regularization for Adversarial Robustnesscited by 42
2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 41
2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
2022DensePure: Understanding Diffusion Models towards Adversarial Robustnesscited by 33
2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
2024Your Diffusion Model is Secretly a Certifiably Robust Classifiercited by 24

38 more

2021ANCER: Anisotropic Certification via Sample-wise Volume Maximizationcited by 23
2022Double Sampling Randomized Smoothingcited by 22
2022Denoising Masked AutoEncoders Help Robust Classificationcited by 21
2023DiffSmooth: Certifiably Robust Learning via Diffusion Models and Local Smoothingcited by 20
2024Provably Unlearnable Data Examplescited by 18
2021Certified Adversarial Defenses Meet Out-of-Distribution Corruptions: Benchmarking Robustness and Simple Baselinescited by 17
2022Improving Robust Fairness via Balance Adversarial Trainingcited by 17
2024Mitigating the Curse of Dimensionality for Certified Robustness via Dual Randomized Smoothingcited by 15
2022Robust and Accurate -- Compositional Architectures for Randomized Smoothingcited by 12
2021Input-Specific Robustness Certification for Randomized Smoothingcited by 11
2022CARE: Certifiably Robust Learning with Reasoning via Variational Inferencecited by 10
2022Confidence-aware Training of Smoothed Classifiers for Certified Robustnesscited by 9
2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
2023Hierarchical Randomized Smoothingcited by 9
2023Multi-scale Diffusion Denoised Smoothingcited by 9
2024Adaptive Randomized Smoothing: Certified Adversarial Robustness for Multi-Step Defencescited by 9
2022A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunitiescited by 8
2022Accelerating Certified Robustness Training via Knowledge Transfercited by 7
2023Augment then Smooth: Reconciling Differential Privacy with Certified Robustnesscited by 6
2024Building a Domain-specific Guardrail Model in Productioncited by 6
2022(De-)Randomized Smoothing for Decision Stump Ensemblescited by 5
2022Data Models for Dataset Drift Controls in Machine Learning With Optical Imagescited by 5
2023Revisiting Intermediate Layer Distillation for Compressing Language Models: An Overfitting Perspectivecited by 5
2023Certified Adversarial Robustness Within Multiple Perturbation Boundscited by 4
2023A Recipe for Improved Certifiable Robustnesscited by 4
2024SPLITZ: Certifiable Robustness via Split Lipschitz Randomized Smoothingcited by 4
2023Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesicscited by 3
2023On the Fly Neural Style Smoothing for Risk-Averse Domain Generalizationcited by 3
2022Towards Evading the Limits of Randomized Smoothing: A Theoretical Analysiscited by 2
2022Multi-head Ensemble of Smoothed Classifiers for Certified Robustnesscited by 2
2023Pixel-wise Smoothing for Certified Robustness against Camera Motion Perturbationscited by 2
2024Certifying Adapters: Enabling and Enhancing the Certification of Classifier Adversarial Robustnesscited by 2
2024Consistency Purification: Effective and Efficient Diffusion Purification towards Certified Robustnesscited by 2
2025Learning from the Undesirable: Robust Adaptation of Language Models without Forgettingcited by 2
2021Towards Bridging the gap between Empirical and Certified Robustness against Adversarial Examplescited by 1
2021Learning Robust Controllers Via Probabilistic Model-Based Policy Searchcited by 1
2023Pretrained deep models outperform GBDTs in Learning-To-Rank under label scarcitycited by 1
2023Exploring Transferability for Randomized Smoothingcited by 1

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