# When Will Gradient Regularization Be Harmful?

arXiv: https://arxiv.org/abs/2406.09723 · HTML: https://mlsanity.com/paper/2406.09723/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 14 Jun 2024.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Implicit Gradient Regularization](https://mlsanity.com/paper/2009.11162/) (2020)
- [Efficient Sharpness-aware Minimization for Improved Training of Neural Networks](https://mlsanity.com/paper/2110.03141/) (2021)
- [Penalizing Gradient Norm for Efficiently Improving Generalization in Deep Learning](https://mlsanity.com/paper/2202.03599/) (2022)
- [Training Tips for the Transformer Model](https://mlsanity.com/paper/1804.00247/) (2018)
- [Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Bias](https://mlsanity.com/paper/2210.02720/) (2022)
- [Randomized Sharpness-Aware Training for Boosting Computational Efficiency in Deep Learning](https://mlsanity.com/paper/2203.09962/) (2022)

## Built on by (most cited first, 3 of 3)

- [Towards LLM Unlearning Resilient to Relearning Attacks: A Sharpness-Aware Minimization Perspective and Beyond](https://mlsanity.com/paper/2502.05374/) (2025)
- [Gradient Regularization Mitigates Reward Hacking in Reinforcement Learning from Human Feedback and Verifiable Rewards](https://mlsanity.com/paper/2602.18037/) (2026)
- [Insights from Gradient Dynamics: Gradient Autoscaled Normalization](https://mlsanity.com/paper/2509.03677/) (2025)

## Abstract (arXiv)

Gradient regularization (GR), which aims to penalize the gradient norm atop the loss function, has shown promising results in training modern over-parameterized deep neural networks. However, can we trust this powerful technique? This paper reveals that GR can cause performance degeneration in adaptive optimization scenarios, particularly with learning rate warmup. Our empirical and theoretical analyses suggest this is due to GR inducing instability and divergence in gradient statistics of adaptive optimizers at the initial training stage. Inspired by the warmup heuristic, we propose three GR warmup strategies, each relaxing the regularization effect to a certain extent during the warmup course to ensure the accurate and stable accumulation of gradients. With experiments on Vision Transformer family, we confirm the three GR warmup strategies can effectively circumvent these issues, thereby largely improving the model performance. Meanwhile, we note that scalable models tend to rely more on the GR warmup, where the performance can be improved by up to 3% on Cifar10 compared to baseline GR. Code is available at hrefhttps://github.com/zhaoyang-0204/gnphttps://github.com/zhaoyang-0204/gnp.