SoK: Certified Robustness for Deep Neural Networks
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Abstract (arXiv)
Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on a wide range of tasks. However, recent studies have shown that DNNs are vulnerable to adversarial attacks, which have brought great concerns when deploying these models to safety-critical applications such as autonomous driving. Different defense approaches have been proposed against adversarial attacks, including: a) empirical defenses, which can usually be adaptively attacked again without providing robustness certification; and b) certifiably robust approaches, which consist of robustness verification providing the lower bound of robust accuracy against any attacks under certain conditions and corresponding robust training approaches. In this paper, we systematize certifiably robust approaches and related practical and theoretical implications and findings. We also provide the first comprehensive benchmark on existing robustness verification and training approaches on different datasets. In particular, we 1) provide a taxonomy for the robustness verification and training approaches, as well as summarize the methodologies for representative algorithms, 2) reveal the characteristics, strengths, limitations, and fundamental connections among these approaches, 3) discuss current research progresses, theoretical barriers, main challenges, and future directions for certifiably robust approaches for DNNs, and 4) provide an open-sourced unified platform to evaluate 20+ representative certifiably robust approaches.
Key facts. Cited by 100 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Sep 2020.
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Citing papers per year: 2021: 9; 2022: 8; 2023: 34; 2024: 31; 2025: 7; 2026: 11.
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- 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
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- 2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
- 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
- 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
- 2022LOT: Layer-wise Orthogonal Training on Improving ℓ2 Certified Robustnesscited by 32
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- 2024CTBENCH: A Library and Benchmark for Certified Trainingcited by 13
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- 2023Efficient Query-Based Attack against ML-Based Android Malware Detection under Zero Knowledge Settingcited by 10
- 2023Improving the Robustness of Transformer-based Large Language Models with Dynamic Attentioncited by 10
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- 2023Hierarchical Randomized Smoothingcited by 9
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- 2023Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networkscited by 6
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- 2024ControlLoc: Physical-World Hijacking Attack on Visual Perception in Autonomous Drivingcited by 5
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- 2026Uncovering the Limits of Proof Sharing for Neural Networks19 Aug 2026
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- 2026Probabilistic Verification of Voice Anti-Spoofing Models11 Mar 2026
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- 2025Provably Robust Adaptation for Language-Empowered Foundation Models9 Oct 2025
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- 2024ARQ: A Mixed-Precision Quantization Framework for Accurate and Certifiably Robust DNNs31 Oct 2024
- 2024Tightening convex relaxations of trained neural networks: a unified approach for convex and S-shaped activations30 Oct 2024
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- 2024Adversarial Robustification via Text-to-Image Diffusion Models26 Jul 2024
- 2024Automated Design of Linear Bounding Functions for Sigmoidal Nonlinearities in Neural Networks14 Jun 2024
- 2024ControlLoc: Physical-World Hijacking Attack on Visual Perception in Autonomous Driving9 Jun 2024
- 2024SlowPerception: Physical-World Latency Attack against Visual Perception in Autonomous Driving9 Jun 2024
- 2024CTBENCH: A Library and Benchmark for Certified Training7 Jun 2024
- 2024CR-UTP: Certified Robustness against Universal Text Perturbations on Large Language Models4 Jun 2024
- 2024Towards General Robustness Verification of MaxPool-based Convolutional Neural Networks via Tightening Linear Approximation2 Jun 2024
- 2024Confronting the Reproducibility Crisis: A Case Study of Challenges in Cybersecurity AI29 May 2024
- 2024Certifying Adapters: Enabling and Enhancing the Certification of Classifier Adversarial Robustness25 May 2024
- 2024How Does Bayes Error Limit Probabilistic Robust Accuracy23 May 2024
- 2024Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errors19 May 2024
- 2024RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothing14 May 2024
- 2024Espresso: Robust Concept Filtering in Text-to-Image Models30 Apr 2024
- 2024Certification of Speaker Recognition Models to Additive Perturbations29 Apr 2024
- 2024Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximation20 Apr 2024
- 2024How Real Is Real? A Human Evaluation Framework for Unrestricted Adversarial Examples19 Apr 2024
- 2024Fortify the Guardian, Not the Treasure: Resilient Adversarial Detectors18 Apr 2024
- 2024Ti-Patch: Tiled Physical Adversarial Patch for no-reference video quality metrics15 Apr 2024
- 2024Improving Robustness to Model Inversion Attacks via Sparse Coding Architectures21 Mar 2024
- 2024NLP Verification: Towards a General Methodology for Certifying Robustness15 Mar 2024
- 2024COMMIT: Certifying Robustness of Multi-Sensor Fusion Systems against Semantic Attacks4 Mar 2024
- 2024Trust Regions for Explanations via Black-Box Probabilistic Certification17 Feb 2024
- 2024PROSAC: Provably Safe Certification for Machine Learning Models under Adversarial Attacks4 Feb 2024
- 2024Security and Privacy Challenges of Large Language Models: A Survey30 Jan 2024
- 2023Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks27 Dec 2023
50 newest of 100 All 100 (JSON)
- 2023DiffSmooth: Certifiably Robust Learning via Diffusion Models and Local Smoothingcited by 20
- 2024Espresso: Robust Concept Filtering in Text-to-Image Modelscited by 14
- 2023Multi-scale Diffusion Denoised Smoothingcited by 9
- 2023Raising the Bar for Certified Adversarial Robustness with Diffusion Modelscited by 7
- 2024Adversarial Robustification via Text-to-Image Diffusion Modelscited by 3
- 2024Adversarial Robustification via Text-to-Image Diffusion Models26 Jul 2024
- 2024Espresso: Robust Concept Filtering in Text-to-Image Models30 Apr 2024
- 2023Multi-scale Diffusion Denoised Smoothing25 Oct 2023
- 2023DiffSmooth: Certifiably Robust Learning via Diffusion Models and Local Smoothing28 Aug 2023
- 2023Raising the Bar for Certified Adversarial Robustness with Diffusion Models17 May 2023
- 2022MM-BD: Post-Training Detection of Backdoor Attacks with Arbitrary Backdoor Pattern Types Using a Maximum Margin Statisticcited by 53
- 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
- 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
- 2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
- 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
- 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
- 2022LOT: Layer-wise Orthogonal Training on Improving ℓ2 Certified Robustnesscited by 32
- 2023Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attackscited by 32
- 2021Certified Robustness to Programmable Transformations in LSTMscited by 18
- 2023Wasserstein distributional robustness of neural networkscited by 15
- 20231-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustnesscited by 15
- 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
12 most cited of 87 All 87 (JSON)
- 2026Uncovering the Limits of Proof Sharing for Neural Networks19 Aug 2026
- 2026Certified Training for Convolutional Perturbations20 Jul 2026
- 2026Fast SDP certification of neural networks : towards large multi-class datasets3 Jul 2026
- 2026Convex training of Lipschitz-regularized shallow neural networks17 Jun 2026
- 2026CEAR: Certified Ensemble Adversarial Robustness in DNNs31 May 2026
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026AI Security Research Should Better Incentivize Defense Research22 May 2026
- 2026Lipschitz Optimization for Formal Verification of Homographies22 May 2026
- 2026Provable Robustness against Backdoor Attacks via the Primal-Dual Perspective on Differential Privacy20 May 2026
- 2026Probabilistic Verification of Voice Anti-Spoofing Models11 Mar 2026
- 2026Cascading Robustness Verification: Toward Efficient Model-Agnostic Certification4 Feb 2026
- 2025Provably Robust Adaptation for Language-Empowered Foundation Models9 Oct 2025
12 newest of 87 All 87 (JSON)