# Improving the Accuracy-Robustness Trade-Off of Classifiers via Adaptive Smoothing

arXiv: https://arxiv.org/abs/2301.12554 · HTML: https://mlsanity.com/paper/2301.12554/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 77 of its 100 references that are in the map.
- First posted on arXiv 29 Jan 2023.

## Builds on (most cited first, 30 of 77)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)

## Built on by (most cited first, 18 of 18)

- [Securely Fine-tuning Pre-trained Encoders Against Adversarial Examples](https://mlsanity.com/paper/2403.10801/) (2024)
- [MixedNUTS: Training-Free Accuracy-Robustness Balance via Nonlinearly Mixed Classifiers](https://mlsanity.com/paper/2402.02263/) (2024)
- [Adversarial Training on Purification (AToP): Advancing Both Robustness and Generalization](https://mlsanity.com/paper/2401.16352/) (2024)
- [One Surrogate to Fool Them All: Universal, Transferable, and Targeted Adversarial Attacks with CLIP](https://mlsanity.com/paper/2505.19840/) (2025)
- [Adversarial Guided Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2403.16067/) (2024)
- [Optimizing Robustness and Accuracy in Mixture of Experts: A Dual-Model Approach](https://mlsanity.com/paper/2502.06832/) (2025)
- [OODRobustBench: a Benchmark and Large-Scale Analysis of Adversarial Robustness under Distribution Shift](https://mlsanity.com/paper/2310.12793/) (2023)
- [A Random Ensemble of Encrypted Vision Transformers for Adversarially Robust Defense](https://mlsanity.com/paper/2402.07183/) (2024)
- [Towards Million-Scale Adversarial Robustness Evaluation With Stronger Individual Attacks](https://mlsanity.com/paper/2411.15210/) (2024)
- [Criticality Leveraged Adversarial Training (CLAT) for Boosted Performance via Parameter Efficiency](https://mlsanity.com/paper/2408.10204/) (2024)
- [Stop Walking in Circles! Bailing Out Early in Projected Gradient Descent](https://mlsanity.com/paper/2503.19347/) (2025)
- [Blending adversarial training and representation-conditional purification via aggregation improves adversarial robustness](https://mlsanity.com/paper/2306.06081/) (2023)
- [Enhancing Output Diversity Improves Conjugate Gradient-based Adversarial Attacks](https://mlsanity.com/paper/2408.03972/) (2024)
- [Disentangling Safe and Unsafe Corruptions via Anisotropy and Locality](https://mlsanity.com/paper/2501.18098/) (2025)
- [Model-Free Adversarial Purification via Coarse-To-Fine Tensor Network Representation](https://mlsanity.com/paper/2502.17972/) (2025)
- [HALO: Robust Out-of-Distribution Detection via Joint Optimisation](https://mlsanity.com/paper/2502.19755/) (2025)
- [Lipschitz bounds for integral kernels](https://mlsanity.com/paper/2604.02887/) (2026)
- [Frame the adversary: a structure-aware attack methodology](https://mlsanity.com/paper/2609.31128/) (2026)

## Abstract (arXiv)

While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This paper significantly alleviates this accuracy-robustness trade-off by mixing the output probabilities of a standard classifier and a robust classifier, where the standard network is optimized for clean accuracy and is not robust in general. We show that the robust base classifier's confidence difference for correct and incorrect examples is the key to this improvement. In addition to providing intuitions and empirical evidence, we theoretically certify the robustness of the mixed classifier under realistic assumptions. Furthermore, we adapt an adversarial input detector into a mixing network that adaptively adjusts the mixture of the two base models, further reducing the accuracy penalty of achieving robustness. The proposed flexible method, termed "adaptive smoothing", can work in conjunction with existing or even future methods that improve clean accuracy, robustness, or adversary detection. Our empirical evaluation considers strong attack methods, including AutoAttack and adaptive attack. On the CIFAR-100 dataset, our method achieves an 85.21% clean accuracy while maintaining a 38.72% ℓ_∞-AutoAttacked (ε = 8/255) accuracy, becoming the second most robust method on the RobustBench CIFAR-100 benchmark as of submission, while improving the clean accuracy by ten percentage points compared with all listed models. The code that implements our method is available at https://github.com/Bai-YT/AdaptiveSmoothing.