# Improving Robustness with Adaptive Weight Decay

arXiv: https://arxiv.org/abs/2210.00094 · HTML: https://mlsanity.com/paper/2210.00094/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 72 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 30 of 47)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [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)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [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)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [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)
- [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)
- [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)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Using DeepSpeed and Megatron to Train Megatron-Turing NLG 530B, A Large-Scale Generative Language Model](https://mlsanity.com/paper/2201.11990/) (2022)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)

## Built on by (most cited first, 13 of 13)

- [AlphaDecay: Module-wise Weight Decay for Heavy-Tailed Balancing in LLMs](https://mlsanity.com/paper/2506.14562/) (2025)
- [Cautious Weight Decay](https://mlsanity.com/paper/2510.12402/) (2025)
- [No More Adam: Learning Rate Scaling at Initialization is All You Need](https://mlsanity.com/paper/2412.11768/) (2024)
- [CoLo-CAM: Class Activation Mapping for Object Co-Localization in Weakly-Labeled Unconstrained Videos](https://mlsanity.com/paper/2303.09044/) (2023)
- [FedLWS: Federated Learning with Adaptive Layer-wise Weight Shrinking](https://mlsanity.com/paper/2503.15111/) (2025)
- [OUI Need to Talk About Weight Decay: A New Perspective on Overfitting Detection](https://mlsanity.com/paper/2504.17160/) (2025)
- [Improving Deep Learning Optimization through Constrained Parameter Regularization](https://mlsanity.com/paper/2311.09058/) (2023)
- [Low-Rank Adversarial PGD Attack](https://mlsanity.com/paper/2410.12607/) (2024)
- [Recovering Plasticity of Neural Networks via Soft Weight Rescaling](https://mlsanity.com/paper/2507.04683/) (2025)
- [Privacy-Preserving Explainable AIoT Application via SHAP Entropy Regularization](https://mlsanity.com/paper/2511.09775/) (2025)
- [Learning to Forget: Continual Learning with Adaptive Weight Decay](https://mlsanity.com/paper/2604.27063/) (2026)
- [Neural Network Optimization Reimagined: Decoupled Techniques for Scratch and Fine-Tuning](https://mlsanity.com/paper/2604.22838/) (2026)
- [Bigger Text Encoders Can Hurt CLIP Zero-Shot Performance](https://mlsanity.com/paper/2609.05730/) (2026)

## Abstract (arXiv)

We propose adaptive weight decay, which automatically tunes the hyper-parameter for weight decay during each training iteration. For classification problems, we propose changing the value of the weight decay hyper-parameter on the fly based on the strength of updates from the classification loss (i.e., gradient of cross-entropy), and the regularization loss (i.e., ℓ2-norm of the weights). We show that this simple modification can result in large improvements in adversarial robustness -- an area which suffers from robust overfitting -- without requiring extra data across various datasets and architecture choices. For example, our reformulation results in 20% relative robustness improvement for CIFAR-100, and 10% relative robustness improvement on CIFAR-10 comparing to the best tuned hyper-parameters of traditional weight decay resulting in models that have comparable performance to SOTA robustness methods. In addition, this method has other desirable properties, such as less sensitivity to learning rate, and smaller weight norms, which the latter contributes to robustness to overfitting to label noise, and pruning.