# Gradient Matching for Domain Generalization

arXiv: https://arxiv.org/abs/2104.09937 · HTML: https://mlsanity.com/paper/2104.09937/

## Key facts

- Cited by 258 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 61 references that are in the map.
- First posted on arXiv 20 Apr 2021.

## Builds on (most cited first, 30 of 36)

- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Approximating CNNs with Bag-of-local-Features models works surprisingly well on ImageNet](https://mlsanity.com/paper/1904.00760/) (2019)
- [Domain Generalization for Object Recognition with Multi-task Autoencoders](https://mlsanity.com/paper/1508.07680/) (2015)

## Built on by (most cited first, 30 of 258)

- [Prompt-aligned Gradient for Prompt Tuning](https://mlsanity.com/paper/2205.14865/) (2022)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization](https://mlsanity.com/paper/2110.10832/) (2021)
- [Domain Generalization by Mutual-Information Regularization with Pre-trained Models](https://mlsanity.com/paper/2203.10789/) (2022)
- [Sharpness-Aware Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2303.10353/) (2023)
- [OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.03721/) (2021)
- [Sparse Mixture-of-Experts are Domain Generalizable Learners](https://mlsanity.com/paper/2206.04046/) (2022)
- [Shortcut Learning of Large Language Models in Natural Language Understanding](https://mlsanity.com/paper/2208.11857/) (2022)
- [Discover and Cure: Concept-aware Mitigation of Spurious Correlation](https://mlsanity.com/paper/2305.00650/) (2023)
- [C-Mixup: Improving Generalization in Regression](https://mlsanity.com/paper/2210.05775/) (2022)
- [SAND-mask: An Enhanced Gradient Masking Strategy for the Discovery of Invariances in Domain Generalization](https://mlsanity.com/paper/2106.02266/) (2021)
- [AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation](https://mlsanity.com/paper/2304.12566/) (2023)
- [Improved Test-Time Adaptation for Domain Generalization](https://mlsanity.com/paper/2304.04494/) (2023)
- [Spawrious: A Benchmark for Fine Control of Spurious Correlation Biases](https://mlsanity.com/paper/2303.05470/) (2023)
- [Robust and Interpretable Medical Image Classifiers via Concept Bottleneck Models](https://mlsanity.com/paper/2310.03182/) (2023)
- [ITSA: An Information-Theoretic Approach to Automatic Shortcut Avoidance and Domain Generalization in Stereo Matching Networks](https://mlsanity.com/paper/2201.02263/) (2022)
- [PASTA: Proportional Amplitude Spectrum Training Augmentation for Syn-to-Real Domain Generalization](https://mlsanity.com/paper/2212.00979/) (2022)
- [Towards Open-Set Test-Time Adaptation Utilizing the Wisdom of Crowds in Entropy Minimization](https://mlsanity.com/paper/2308.06879/) (2023)
- [Pareto Invariant Risk Minimization: Towards Mitigating the Optimization Dilemma in Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07766/) (2022)
- [Invariant and Transportable Representations for Anti-Causal Domain Shifts](https://mlsanity.com/paper/2207.01603/) (2022)
- [Learning Domain Invariant Prompt for Vision-Language Models](https://mlsanity.com/paper/2212.04196/) (2022)
- [Understanding and Improving Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2304.11327/) (2023)
- [Rich Feature Construction for the Optimization-Generalization Dilemma](https://mlsanity.com/paper/2203.15516/) (2022)
- [UMIX: Improving Importance Weighting for Subpopulation Shift via Uncertainty-Aware Mixup](https://mlsanity.com/paper/2209.08928/) (2022)
- [Domain Generalization using Pretrained Models without Fine-tuning](https://mlsanity.com/paper/2203.04600/) (2022)
- [Semantic-Discriminative Mixup for Generalizable Sensor-based Cross-domain Activity Recognition](https://mlsanity.com/paper/2206.06629/) (2022)
- [Learning to Retain while Acquiring: Combating Distribution-Shift in Adversarial Data-Free Knowledge Distillation](https://mlsanity.com/paper/2302.14290/) (2023)
- [Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2306.02879/) (2023)
- [RegMixup: Mixup as a Regularizer Can Surprisingly Improve Accuracy and Out Distribution Robustness](https://mlsanity.com/paper/2206.14502/) (2022)

## Abstract (arXiv)

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.