# Mixing Classifiers to Alleviate the Accuracy-Robustness Trade-Off

arXiv: https://arxiv.org/abs/2311.15165 · HTML: https://mlsanity.com/paper/2311.15165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 57 references that are in the map.
- First posted on arXiv 26 Nov 2023.

## Builds on (most cited first, 30 of 51)

- [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)
- [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)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [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)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [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)
- [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)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Adversarial Robustness: From Self-Supervised Pre-Training to Fine-Tuning](https://mlsanity.com/paper/2003.12862/) (2020)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)

## Built on by (most cited first, 2 of 2)

- [MixedNUTS: Training-Free Accuracy-Robustness Balance via Nonlinearly Mixed Classifiers](https://mlsanity.com/paper/2402.02263/) (2024)
- [Laws of Learning Dynamics and the Core of Learners](https://mlsanity.com/paper/2602.05026/) (2026)

## Abstract (arXiv)

Deep neural classifiers have recently found tremendous success in data-driven control systems. However, existing models suffer from a trade-off between accuracy and adversarial robustness. This limitation must be overcome in the control of safety-critical systems that require both high performance and rigorous robustness guarantees. In this work, we develop classifiers that simultaneously inherit high robustness from robust models and high accuracy from standard models. Specifically, we propose a theoretically motivated formulation that mixes the output probabilities of a standard neural network and a robust neural network. Both base classifiers are pre-trained, and thus our method does not require additional training. Our numerical experiments verify that the mixed classifier noticeably improves the accuracy-robustness trade-off and identify the confidence property of the robust base classifier as the key leverage of this more benign trade-off. Our theoretical results prove that under mild assumptions, when the robustness of the robust base model is certifiable, no alteration or attack within a closed-form ℓp radius on an input can result in the misclassification of the mixed classifier.