This page keeps track of the highest certified accuracy reported by existing papers.

The papers that are not published on conferences or journals, such as preprints, are in gray text.

For probabilistic certification, we only take the results into account if certification confidence \(\ge 99.9\%\).

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Expressive Losses for Verified Robustness via Convex Combinations 98.43% Deterministic ICLR 2024 Approach name: CC-IBP
2 Certified Training: Small Boxes are All You Need 98.22% Deterministic ICLR 2023 Approach name: SABR
3 Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective 98.14% Deterministic NeurIPS 2022 SortNet
4 Fast certified robust training with short warmup 97.95% Deterministic NeurIPS 2021
5 Boosting the certified robustness of L-infinity distance nets 97.95% Deterministic ICLR 2022
6 Robustra: training provable robust neural networks over reference adversarial space 97.91% Deterministic IJCAI 2019
7 Scalable verified training for provably robust image classification 97.77% Deterministic ICCV 2019 Train on TPU
8 Towards stable and efficient training of verifiably robust neural networks 97.76% Deterministic ICLR 2020
9 Towards certifying L-infinity robustness using neural networks with L-inf-dist neurons 97.70% Deterministic ICML 2021 Reported by this paper
10 MixTrain: Scalable Training of Verifiably Robust Neural Networks 97.1% Deterministic *preprint
11 Scaling provable adversarial defenses 96.33% Deterministic NeurIPS 2018
12 Provable Defenses against Adversarial Examples via the Convex Outer Adversarial Polytope 94.18% Deterministic ICML 2018

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Towards Evaluating and Training Verifiably Robust Neural Networks 94.02% Deterministic CVPR 2021
2 Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective 93.40% Deterministic NeurIPS 2022 SortNet
3 Certified Training: Small Boxes are All You Need 93.40% Deterministic ICLR 2023 Approach name: SABR
4 Boosting the certified robustness of L-infinity distance nets 93.20% Deterministic ICLR 2022
5 Fast certified robust training with short warmup 93.10% Deterministic NeurIPS 2021
6 Towards certifying L-infinity robustness using neural networks with L-inf-dist neurons 93.09% Deterministic ICML 2021
7 Towards stable and efficient training of verifiably robust neural networks 92.98% Deterministic ICLR 2020
8 Scalable verified training for provably robust image classification 91.95% Deterministic ICCV 2019 Train on TPU
9 Provably robust boosted decision stumps and trees against adversarial attacks 87.54% Deterministic NeurIPS 2019 Non-neural-network approach
10 Adversarial training and provable defenses: bridging the gap 85.7% Deterministic ICLR 2020
11 Robustra: training provable robust neural networks over reference adversarial space 83.09% Deterministic IJCAI 2019
12 Training for faster adversarial robustness verification via inducing ReLU stability 80.68% Deterministic ICLR 2019
13 MixTrain: Scalable Training of Verifiably Robust Neural Networks 58.4% Deterministic *preprint
14 Scaling provable adversarial defenses 56.90% Deterministic NeurIPS 2018

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Provably robust deep learning via adversarially trained smoothed classifiers 68.2% Probabilistic NeurIPS 2019 combine adversarial training, self-training, and unlabeled data
2 Unlabeled data improves adversarial robustness 63.8% Probabilistic NeurIPS 2019 use unlabeled data
3 Expressive Losses for Verified Robustness via Convex Combinations 63.78% Deterministic ICLR 2024 Approach name: CC-IBP
4 Certified Training: Small Boxes are All You Need 62.84% Deterministic ICLR 2023 Approach name: SABR
5 IBP Regularization for Verified Adversarial Robustness via Branch-and-Bound 61.97% Deterministic ICML 2022 Workshop on Formal Verification of Machine Learning
6 Adversarial training and provable defenses: bridging the gap 60.5% Deterministic ICLR 2020
7 Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective 56.94% Deterministic NeurIPS 2022 SortNet + MLP
8 Towards Evaluating and Training Verifiably Robust Neural Networks 56.63% Deterministic CVPR 2021
9 Robustra: training provable robust neural networks over reference adversarial space 56.32% Deterministic IJCAI 2019
10 Boosting the certified robustness of L-infinity distance nets 54.12% Deterministic ICLR 2022
11 Towards stable and efficient training of verifiably robust neural networks 53.97% Deterministic ICLR 2020
12 Scaling provable adversarial defenses 53.89% Deterministic NeurIPS 2018
13 Fast certified robust training with short warmup 52.85% Deterministic NeurIPS 2021
14 Scalable verified training for provably robust image classification 50.02% Deterministic ICCV 2019 Train on TPU

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Raising the Bar for Certified Adversarial Robustness with Diffusion Models 41.78% Deterministic *preprint SortNet with EDM-generated data
2 Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective 40.39% Deterministic NeurIPS 2022 SortNet
3 Boosting the certified robustness of L-infinity distance nets 40.06% Deterministic ICLR 2022
4 Expressive Losses for Verified Robustness via Convex Combinations 35.44% Deterministic ICLR 2024 Approach name: MTL-IBP
5 Towards certifying L-infinity robustness using neural networks with L-inf-dist neurons 35.42% Deterministic ICML 2021
6 Certified Training: Small Boxes are All You Need 35.13% Deterministic ICLR 2023 Approach name: SABR
7 Fast certified robust training with short warmup 34.97% Deterministic NeurIPS 2021
8 Towards Evaluating and Training Verifiably Robust Neural Networks 34.92% Deterministic CVPR 2021
9 Automatic perturbation analysis for scalable certified robustness and beyond 33.38% Deterministic NeurIPS 2020
10 Towards stable and efficient training of verifiably robust neural networks 33.06% Deterministic ICLR 2020
11 Scalable verified training for provably robust image classification 32.04% Deterministic ICCV 2019 Train on TPU
12 Robustra: training provable robust neural networks over reference adversarial space 25.13% Deterministic IJCAI 2019
13 Scaling provable adversarial defenses 21.78% Deterministic NeurIPS 2018

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Expressive Losses for Verified Robustness via Convex Combinations 26.39% Deterministic ICLR 2024 Approach name: CC-IBP
2 Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective 18.18% Deterministic NeurIPS 2022 SortNet+MLP (2x larger)
3 Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond 15.86% Deterministic NeurIPS 2020
4 Scalable verified training for provably robust image classification 14.85% Deterministic ICCV 2019 WideResNet, reported by Auto-LiRPA paper

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Expressive Losses for Verified Robustness via Convex Combinations 13.30% Deterministic ICLR 2024 Approach name: Exp-IBP
2 Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective 9.54% Deterministic NeurIPS 2022 SortNet+MLP (2x larger)
3 Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond 8.73% Deterministic NeurIPS 2020
4 Scalable verified training for provably robust image classification 6.13% Deterministic ICCV 2019 based on arXiv version (1810.12715)

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Provably robust deep learning via adversarially trained smoothed classifiers 38.2% Probabilistic NeurIPS 2019 translated from \(\ell_2\) certification, combine adversarial training, self-training, and unlabeled data
2 Certified adversarial robustness via randomized smoothing 28.6% Probabilistic ICML 2019 translated from \(\ell_2\) certification

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Provably Adversarially Robust Nearest Prototype Classifiers 73.0% Deterministic ICML 2022 Non-neural-network approach
2 SmoothMix: training confidence-calibrated smoothed classifiers for certified robustness 70.7% Probabilistic NeurIPS 2021 under larger attack radius \(\epsilon=1.75\)
3 Consistency regularization for certified robustness of smoothed classifiers 70.5% Probabilistic NeurIPS 2020 under larger attack radius \(\epsilon=1.75\)
4 Second-Order Provable Defenses against Adversarial Attacks 69.79% Deterministic ICML 2020 ! a loose certification --- certified accuracy against only the class with second largest logit, but not all non-ground-truth classes; non-relu neural networks
5 Certified adversarial robustness with additive noise 69.0% Probabilistic NeurIPS 2019
6 Globally-robust neural networks 62.8% Deterministic ICML 2021
7 Lipschitz-certifiable training with a tight outer bound 47.95% Deterministic NeurIPS 2020
8 Scaling provable adversarial defenses 44.53% Deterministic NeurIPS 2018

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 A Recipe for Improved Certifiable Robustness: Capacity and Data 78.1% Deterministic *preprint
2 Scaling in Depth: Unlocking Robustness Certification on ImageNet 70.1% Deterministic NeurIPS 2023 With data-agumentation using a DDPM model. Without the DDPM augmentation for the dataset, it reports 66.9%.
3 Raising the Bar for Certified Adversarial Robustness with Diffusion Models 69.05% Deterministic *preprint LOT with EDM-generated data
4 Certified adversarial robustness with additive noise 65.6% Probabilistic NeurIPS 2019
5 LOT: Layer-wise Orthogonal Training on Improving l2 Certified Robustness 64.49% Deterministic NeurIPS 2022
6 Householder activations for provable robustness against adversarial attacks 62.96% Deterministic ICLR 2022
7 Orthogonalizing convolutional layers with the cayley transform 59.16% Deterministic ICLR 2021
8 Globally-robust neural networks 58.4% Deterministic ICML 2021 "Scaling in Depth: Unlocking Robustness Certification on ImageNet" reproduced 60.0%
9 Scaling provable adversarial defenses 51.96% Deterministic NeurIPS 2018
10 Lipschitz-certifiable training with a tight outer bound 51.30% Deterministic NeurIPS 2020
Many records from CIFAR-10,  \(\ell_2\),   \(\epsilon=0.25\) imply stronger baselines in this setting. To avoid duplication, these stronger baselines are not listed here.

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Provably robust deep learning via adversarially trained smoothed classifiers 81% Probabilistic NeurIPS 2019 combine adversarial training, self-training, and unlabeled data
2 (Certified!!) Adversarial Robustness for Free! 79.3% Probabilistic ICLR 2023 based on denoising with large diffusion models
3 DensePure: Understanding Diffusion Models towards Adversarial Robustness 76.6% Probabilistic ICLR 2023 based on denoising with large diffusion models
4 Unlabeled data improves adversarial robustness 72% Probabilistic NeurIPS 2019 parse from Figure 1(a)
5 Macer: attack-free and scalable robust training via maximizing certified radius 71% Probabilistic ICLR 2020
6 Boosting Randomized Smoothing with Variance Reduced Classifiers 70.6% Probabilistic ICLR 2022 From Table 8
7 On the certified robustness for ensemble models and beyond 70.4% Probabilistic ICLR 2022
8 A Recipe for Improved Certifiable Robustness: Capacity and Data 69.5% Deterministic *preprint
9 Robust and Accurate -- Compositional Architectures for Randomized Smoothing 69.0% Probabilistic *preprint parse from Table 8
10 Consistency regularization for certified robustness of smoothed classifiers 68.8% Probabilistic NeurIPS 2020
11 SmoothMix: training confidence-calibrated smoothed classifiers for certified robustness 67.9% Probabilistic NeurIPS 2021
12 Certified adversarial robustness via randomized smoothing 60% Probabilistic ICML 2019 parse from Figure 6 (top)

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Provably robust deep learning via adversarially trained smoothed classifiers 40% Probabilistic NeurIPS 2019 combine adversarial training, self-training, and unlabeled data
2 On the certified robustness for ensemble models and beyond 39.5% Probabilistic ICLR 2022
3 Boosting Randomized Smoothing with Variance Reduced Classifiers 38.8% Probabilistic ICLR 2022 From Table 8
4 Macer: attack-free and scalable robust training via maximizing certified radius 38% Probabilistic ICLR 2020
5 Consistency regularization for certified robustness of smoothed classifiers 37.8% Probabilistic NeurIPS 2020
6 Robust and Accurate -- Compositional Architectures for Randomized Smoothing 37.8% Probabilistic *preprint parse from Table 10
7 DensePure: Understanding Diffusion Models towards Adversarial Robustness 37.4% Probabilistic ICLR 2023 based on denoising with large diffusion models
8 SmoothMix: training confidence-calibrated smoothed classifiers for certified robustness 37.2% Probabilistic NeurIPS 2021
9 (Certified!!) Adversarial Robustness for Free! 35.5% Probabilistic ICLR 2023 based on denoising with large diffusion models
10 A Recipe for Improved Certifiable Robustness: Capacity and Data 35.1% Deterministic *preprint
11 Certified adversarial robustness via randomized smoothing 22% Probabilistic ICML 2019 parse from Figure 6 (top)

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 On the certified robustness for ensemble models and beyond 20.3% Probabilistic ICLR 2022
2 Boosting Randomized Smoothing with Variance Reduced Classifiers 19.8% Probabilistic ICLR 2022 From Table 8
3 Consistency regularization for certified robustness of smoothed classifiers 19.5% Probabilistic NeurIPS 2020
4 Provably robust deep learning via adversarially trained smoothed classifiers 19% Probabilistic NeurIPS 2019 combine adversarial training, self-training, and unlabeled data
5 Macer: attack-free and scalable robust training via maximizing certified radius 19% Probabilistic ICLR 2020

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 DensePure: Understanding Diffusion Models towards Adversarial Robustness 67.0% Probabilistic ICLR 2023 based on denoising with large diffusion models
2 (Certified!!) Adversarial Robustness for Free! 54.3% Probabilistic ICLR 2023 based on denoising with large diffusion models
3 Provably robust deep learning via adversarially trained smoothed classifiers 45% Probabilistic NeurIPS 2019 combine adversarial training, self-training, and unlabeled data
4 Boosting Randomized Smoothing with Variance Reduced Classifiers 44.6% Probabilistic ICLR 2022 From Table 8
5 On the certified robustness for ensemble models and beyond 44.4% Probabilistic ICLR 2022
6 Consistency regularization for certified robustness of smoothed classifiers 44% Probabilistic NeurIPS 2020
7 SmoothMix: training confidence-calibrated smoothed classifiers for certified robustness 43% Probabilistic NeurIPS 2021
8 Macer: attack-free and scalable robust training via maximizing certified radius 43% Probabilistic ICLR 2020
9 Robust and Accurate -- Compositional Architectures for Randomized Smoothing 42.2% Probabilistic *preprint parse from Table 1
10 Certified adversarial robustness via randomized smoothing 39% Probabilistic ICML 2019 parse from Figure 6 (bottom)
11 Black-box certification with randomized smoothing: A functional optimization based framework 39% Probabilistic NeurIPS 2020
12 Scaling in Depth: Unlocking Robustness Certification on ImageNet 14.20% Deterministic NeurIPS 2023

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 DensePure: Understanding Diffusion Models towards Adversarial Robustness 42.2% Probabilistic ICLR 2023 based on denoising with large diffusion models
2 On the certified robustness for ensemble models and beyond 30.4% Probabilistic ICLR 2022
3 (Certified!!) Adversarial Robustness for Free! 29.5% Probabilistic ICLR 2023 based on denoising with large diffusion models
4 Boosting Randomized Smoothing with Variance Reduced Classifiers 28.6% Probabilistic ICLR 2022 From Table 8
5 Provably robust deep learning via adversarially trained smoothed classifiers 28% Probabilistic NeurIPS 2019 combine adversarial training, self-training, and unlabeled data
6 Macer: attack-free and scalable robust training via maximizing certified radius 27% Probabilistic ICLR 2020
7 SmoothMix: training confidence-calibrated smoothed classifiers for certified robustness 26% Probabilistic NeurIPS 2021
8 Consistency regularization for certified robustness of smoothed classifiers 24% Probabilistic NeurIPS 2020
9 Black-box certification with randomized smoothing: A functional optimization based framework 21% Probabilistic NeurIPS 2020
10 Certified adversarial robustness via randomized smoothing 19% Probabilistic ICML 2019 parse from Figure 6 (bottom)

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Improved, deterministic smoothing for l1 certified robustness 63.07% Deterministic ICML 2021
2 Randomized smoothing of all shapes and sizes 63% Probabilistic ICML 2020 combine adversarial training, self-training, and unlabeled data
3 L1 adversarial robustness certificates: a randomized smoothing approach 39% Probabilistic *preprint parse from Figure 6
4 Black-box certification with randomized smoothing: A functional optimization based framework 34% Probabilistic NeurIPS 2020
5 Certified robustness to adversarial examples with differential privacy 18% Probabilistic S&P 2019 parse from Figures 7 and 8 of this paper since the original paper does not provide certified accuray under this setting

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Improved, deterministic smoothing for l1 certified robustness 51.33% Deterministic ICML 2021
2 Randomized smoothing of all shapes and sizes 48% Probabilistic ICML 2020 combine adversarial training, self-training, and unlabeled data
3 Black-box certification with randomized smoothing: A functional optimization based framework 17% Probabilistic NeurIPS 2020
4 L1 adversarial robustness certificates: a randomized smoothing approach 16% Probabilistic *preprint parse from Figure 6
5 Certified robustness to adversarial examples with differential privacy 5% Probabilistic S&P 2019 parse from Figures 7 and 8 of this paper since the original paper does not provide certified accuray under this setting

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Randomized smoothing of all shapes and sizes 55% Probabilistic ICML 2020 combine adversarial training, self-training, and unlabeled data
2 Improved, deterministic smoothing for l1 certified robustness 49% Deterministic ICML 2021
3 Black-box certification with randomized smoothing: A functional optimization based framework 42% Probabilistic NeurIPS 2020
4 L1 adversarial robustness certificates: a randomized smoothing approach 40% Probabilistic *preprint parse from Figure 6
5 Certified robustness to adversarial examples with differential privacy 25% Probabilistic S&P 2019 parse from Figures 7 and 8 of this paper since the original paper does not provide certified accuray under this setting

Rank Paper Name Reported Certified Accuracy Certification Type Venue Comment
1 Randomized smoothing of all shapes and sizes 48% Probabilistic ICML 2020 combine adversarial training, self-training, and unlabeled data
2 Improved, deterministic smoothing for l1 certified robustness 45% Deterministic ICML 2021
3 Black-box certification with randomized smoothing: A functional optimization based framework 30% Probabilistic NeurIPS 2020
4 L1 adversarial robustness certificates: a randomized smoothing approach 26% Probabilistic *preprint parse from Figure 6
5 Certified robustness to adversarial examples with differential privacy 16% Probabilistic S&P 2019 parse from Figures 7 and 8 of this paper since the original paper does not provide certified accuray under this setting
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