# Multiplicative Reweighting for Robust Neural Network Optimization

arXiv: https://arxiv.org/abs/2102.12192 · HTML: https://mlsanity.com/paper/2102.12192/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 93 of its 137 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 30 of 93)

- [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)
- [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)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [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)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)

## Built on by (most cited first, 4 of 4)

- [To Aggregate or Not? Learning with Separate Noisy Labels](https://mlsanity.com/paper/2206.07181/) (2022)
- [Detecting Label Errors by using Pre-Trained Language Models](https://mlsanity.com/paper/2205.12702/) (2022)
- [Constrained Instance and Class Reweighting for Robust Learning under Label Noise](https://mlsanity.com/paper/2111.05428/) (2021)
- [SLaM: Student-Label Mixing for Distillation with Unlabeled Examples](https://mlsanity.com/paper/2302.03806/) (2023)

## Abstract (arXiv)

Neural networks are widespread due to their powerful performance. Yet, they degrade in the presence of noisy labels at training time. Inspired by the setting of learning with expert advice, where multiplicative weights (MW) updates were recently shown to be robust to moderate data corruptions in expert advice, we propose to use MW for reweighting examples during neural networks optimization. We theoretically establish the convergence of our method when used with gradient descent and prove its advantages in 1d cases. We then validate empirically our findings for the general case by showing that MW improves neural networks' accuracy in the presence of label noise on CIFAR-10, CIFAR-100 and Clothing1M. We also show the impact of our approach on adversarial robustness.