# Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2109.02934 · HTML: https://mlsanity.com/paper/2109.02934/

## Key facts

- Cited by 186 papers in the map (data through 14 Oct 2026).
- Builds on 93 of its 155 references that are in the map.
- First posted on arXiv 7 Sep 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [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)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [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)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)

## Built on by (most cited first, 30 of 186)

- [Prompt-aligned Gradient for Prompt Tuning](https://mlsanity.com/paper/2205.14865/) (2022)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [WARM: On the Benefits of Weight Averaged Reward Models](https://mlsanity.com/paper/2401.12187/) (2024)
- [Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization](https://mlsanity.com/paper/2110.10832/) (2021)
- [Local Learning Matters: Rethinking Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2111.14213/) (2021)
- [NICO++: Towards Better Benchmarking for Domain Generalization](https://mlsanity.com/paper/2204.08040/) (2022)
- [Sparse Mixture-of-Experts are Domain Generalizable Learners](https://mlsanity.com/paper/2206.04046/) (2022)
- [PromptStyler: Prompt-driven Style Generation for Source-free Domain Generalization](https://mlsanity.com/paper/2307.15199/) (2023)
- [AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation](https://mlsanity.com/paper/2304.12566/) (2023)
- [SimMMDG: A Simple and Effective Framework for Multi-modal Domain Generalization](https://mlsanity.com/paper/2310.19795/) (2023)
- [Improved Test-Time Adaptation for Domain Generalization](https://mlsanity.com/paper/2304.04494/) (2023)
- [Feature Alignment and Uniformity for Test Time Adaptation](https://mlsanity.com/paper/2303.10902/) (2023)
- [Spawrious: A Benchmark for Fine Control of Spurious Correlation Biases](https://mlsanity.com/paper/2303.05470/) (2023)
- [Pareto Invariant Risk Minimization: Towards Mitigating the Optimization Dilemma in Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07766/) (2022)
- [Spanning Training Progress: Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning](https://mlsanity.com/paper/2311.13613/) (2023)
- [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)
- [Free Lunch for Domain Adversarial Training: Environment Label Smoothing](https://mlsanity.com/paper/2302.00194/) (2023)
- [Loss-Curvature Matching for Dataset Selection and Condensation](https://mlsanity.com/paper/2303.04449/) (2023)
- [Deep Active Learning by Leveraging Training Dynamics](https://mlsanity.com/paper/2110.08611/) (2021)
- [DiPrompT: Disentangled Prompt Tuning for Multiple Latent Domain Generalization in Federated Learning](https://mlsanity.com/paper/2403.08506/) (2024)
- [Out-of-Distribution Representation Learning for Time Series Classification](https://mlsanity.com/paper/2209.07027/) (2022)
- [WOODS: Benchmarks for Out-of-Distribution Generalization in Time Series](https://mlsanity.com/paper/2203.09978/) (2022)
- [Domain Generalization by Learning and Removing Domain-specific Features](https://mlsanity.com/paper/2212.07101/) (2022)
- [ALOFT: A Lightweight MLP-like Architecture with Dynamic Low-frequency Transform for Domain Generalization](https://mlsanity.com/paper/2303.11674/) (2023)
- [Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2306.02879/) (2023)
- [Flatness-Aware Minimization for Domain Generalization](https://mlsanity.com/paper/2307.11108/) (2023)
- [Decompose, Adjust, Compose: Effective Normalization by Playing with Frequency for Domain Generalization](https://mlsanity.com/paper/2303.02328/) (2023)
- [Fast-Slow Test-Time Adaptation for Online Vision-and-Language Navigation](https://mlsanity.com/paper/2311.13209/) (2023)

## Abstract (arXiv)

Learning robust models that generalize well under changes in the data distribution is critical for real-world applications. To this end, there has been a growing surge of interest to learn simultaneously from multiple training domains - while enforcing different types of invariance across those domains. Yet, all existing approaches fail to show systematic benefits under controlled evaluation protocols. In this paper, we introduce a new regularization - named Fishr - that enforces domain invariance in the space of the gradients of the loss: specifically, the domain-level variances of gradients are matched across training domains. Our approach is based on the close relations between the gradient covariance, the Fisher Information and the Hessian of the loss: in particular, we show that Fishr eventually aligns the domain-level loss landscapes locally around the final weights. Extensive experiments demonstrate the effectiveness of Fishr for out-of-distribution generalization. Notably, Fishr improves the state of the art on the DomainBed benchmark and performs consistently better than Empirical Risk Minimization. Our code is available at https://github.com/alexrame/fishr.