# Enhance Diffusion to Improve Robust Generalization

arXiv: https://arxiv.org/abs/2306.02618 · HTML: https://mlsanity.com/paper/2306.02618/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 71 of its 100 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 71)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [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)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (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)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)

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

- [On the Role of Server Momentum in Federated Learning](https://mlsanity.com/paper/2312.12670/) (2023)
- [Two Simple Principles for Diffusion-Based Test-Time Adaptation](https://mlsanity.com/paper/2312.05274/) (2023)
- [From Incomplete Coarse-Grained to Complete Fine-Grained: A Two-Stage Framework for Spatiotemporal Data Reconstruction](https://mlsanity.com/paper/2410.05323/) (2024)

## Abstract (arXiv)

Deep neural networks are susceptible to human imperceptible adversarial perturbations. One of the strongest defense mechanisms is Adversarial Training (AT). In this paper, we aim to address two predominant problems in AT. First, there is still little consensus on how to set hyperparameters with a performance guarantee for AT research, and customized settings impede a fair comparison between different model designs in AT research. Second, the robustly trained neural networks struggle to generalize well and suffer from tremendous overfitting. This paper focuses on the primary AT framework - Projected Gradient Descent Adversarial Training (PGD-AT). We approximate the dynamic of PGD-AT by a continuous-time Stochastic Differential Equation (SDE), and show that the diffusion term of this SDE determines the robust generalization. An immediate implication of this theoretical finding is that robust generalization is positively correlated with the ratio between learning rate and batch size. We further propose a novel approach, Diffusion Enhanced Adversarial Training (DEAT), to manipulate the diffusion term to improve robust generalization with virtually no extra computational burden. We theoretically show that DEAT obtains a tighter generalization bound than PGD-AT. Our empirical investigation is extensive and firmly attests that DEAT universally outperforms PGD-AT by a significant margin.