# Robustness and Accuracy Could Be Reconcilable by (Proper) Definition

arXiv: https://arxiv.org/abs/2202.10103 · HTML: https://mlsanity.com/paper/2202.10103/

## Key facts

- Cited by 111 papers in the map (data through 14 Oct 2026).
- Builds on 80 of its 108 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 30 of 80)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [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)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Adversarial Examples Improve Image Recognition](https://mlsanity.com/paper/1911.09665/) (2019)

## Built on by (most cited first, 30 of 111)

- [On Evaluating Adversarial Robustness of Large Vision-Language Models](https://mlsanity.com/paper/2305.16934/) (2023)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Revisiting Adversarial Training for ImageNet: Architectures, Training and Generalization across Threat Models](https://mlsanity.com/paper/2303.01870/) (2023)
- [How Deep Learning Sees the World: A Survey on Adversarial Attacks & Defenses](https://mlsanity.com/paper/2305.10862/) (2023)
- [Robust Evaluation of Diffusion-Based Adversarial Purification](https://mlsanity.com/paper/2303.09051/) (2023)
- [Decoupled Kullback-Leibler Divergence Loss](https://mlsanity.com/paper/2305.13948/) (2023)
- [Improving Fast Adversarial Training with Prior-Guided Knowledge](https://mlsanity.com/paper/2304.00202/) (2023)
- [DISCO: Adversarial Defense with Local Implicit Functions](https://mlsanity.com/paper/2212.05630/) (2022)
- [Randomized Adversarial Training via Taylor Expansion](https://mlsanity.com/paper/2303.10653/) (2023)
- [Improving Generalization of Adversarial Training via Robust Critical Fine-Tuning](https://mlsanity.com/paper/2308.02533/) (2023)
- [Enhancing Adversarial Robustness via Score-Based Optimization](https://mlsanity.com/paper/2307.04333/) (2023)
- [Improving the Accuracy-Robustness Trade-Off of Classifiers via Adaptive Smoothing](https://mlsanity.com/paper/2301.12554/) (2023)
- [MimicDiffusion: Purifying Adversarial Perturbation via Mimicking Clean Diffusion Model](https://mlsanity.com/paper/2312.04802/) (2023)
- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [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)
- [Defenses in Adversarial Machine Learning: A Survey](https://mlsanity.com/paper/2312.08890/) (2023)
- [Towards Lightweight Black-Box Attacks against Deep Neural Networks](https://mlsanity.com/paper/2209.14826/) (2022)
- [Adversarial Training Should Be Cast as a Non-Zero-Sum Game](https://mlsanity.com/paper/2306.11035/) (2023)
- [Mitigating Accuracy-Robustness Trade-off via Balanced Multi-Teacher Adversarial Distillation](https://mlsanity.com/paper/2306.16170/) (2023)
- [Uncovering Adversarial Risks of Test-Time Adaptation](https://mlsanity.com/paper/2301.12576/) (2023)
- [MIMIR: Masked Image Modeling for Mutual Information-based Adversarial Robustness](https://mlsanity.com/paper/2312.04960/) (2023)
- [Adversarial Training Can Provably Improve Robustness: Theoretical Analysis of Feature Learning Process Under Structured Data](https://mlsanity.com/paper/2410.08503/) (2024)
- [DAT: Improving Adversarial Robustness via Generative Amplitude Mix-up in Frequency Domain](https://mlsanity.com/paper/2410.12307/) (2024)
- [Mitigating Adversarial Vulnerability through Causal Parameter Estimation by Adversarial Double Machine Learning](https://mlsanity.com/paper/2307.07250/) (2023)
- [Enhancing Robust Fairness via Confusional Spectral Regularization](https://mlsanity.com/paper/2501.13273/) (2025)
- [Robustness and Cybersecurity in the EU Artificial Intelligence Act](https://mlsanity.com/paper/2502.16184/) (2025)
- [Detecting Brittle Decisions for Free: Leveraging Margin Consistency in Deep Robust Classifiers](https://mlsanity.com/paper/2406.18451/) (2024)
- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [Shedding More Light on Robust Classifiers under the lens of Energy-based Models](https://mlsanity.com/paper/2407.06315/) (2024)

## Abstract (arXiv)

The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for the origin of this trade-off in adversarial training and find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance -- an overcorrection towards smoothness. Given this, we advocate employing local equivariance to describe the ideal behavior of a robust model, leading to a self-consistent robust error named SCORE. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty via robust optimization. By simply substituting KL divergence with variants of distance metrics, SCORE can be efficiently minimized. Empirically, our models achieve top-rank performance on RobustBench under AutoAttack. Besides, SCORE provides instructive insights for explaining the overfitting phenomenon and semantic input gradients observed on robust models. Code is available at https://github.com/P2333/SCORE.