# Understanding and Improving Feature Learning for Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2304.11327 · HTML: https://mlsanity.com/paper/2304.11327/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 22 Apr 2023.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [On Feature Learning in the Presence of Spurious Correlations](https://mlsanity.com/paper/2210.11369/) (2022)
- [Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization](https://mlsanity.com/paper/2110.10832/) (2021)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Learning explanations that are hard to vary](https://mlsanity.com/paper/2009.00329/) (2020)
- [Toward Understanding the Feature Learning Process of Self-supervised Contrastive Learning](https://mlsanity.com/paper/2105.15134/) (2021)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [Benign Overfitting in Two-layer Convolutional Neural Networks](https://mlsanity.com/paper/2202.06526/) (2022)

## Built on by (most cited first, 30 of 35)

- [A Sober Look at the Robustness of CLIPs to Spurious Features](https://mlsanity.com/paper/2403.11497/) (2024)
- [Towards Stable Backdoor Purification through Feature Shift Tuning](https://mlsanity.com/paper/2310.01875/) (2023)
- [Spurious Feature Diversification Improves Out-of-distribution Generalization](https://mlsanity.com/paper/2309.17230/) (2023)
- [Federated Learning from Vision-Language Foundation Models: Theoretical Analysis and Method](https://mlsanity.com/paper/2409.19610/) (2024)
- [Improving Group Robustness on Spurious Correlation Requires Preciser Group Inference](https://mlsanity.com/paper/2404.13815/) (2024)
- [Safety Reasoning with Guidelines](https://mlsanity.com/paper/2502.04040/) (2025)
- [FOOGD: Federated Collaboration for Both Out-of-distribution Generalization and Detection](https://mlsanity.com/paper/2410.11397/) (2024)
- [How Interpretable Are Interpretable Graph Neural Networks?](https://mlsanity.com/paper/2406.07955/) (2024)
- [Features are fate: a theory of transfer learning in high-dimensional regression](https://mlsanity.com/paper/2410.08194/) (2024)
- [Feature contamination: Neural networks learn uncorrelated features and fail to generalize](https://mlsanity.com/paper/2406.03345/) (2024)
- [FuseFL: One-Shot Federated Learning through the Lens of Causality with Progressive Model Fusion](https://mlsanity.com/paper/2410.20380/) (2024)
- [Mitigating Simplicity Bias in Deep Learning for Improved OOD Generalization and Robustness](https://mlsanity.com/paper/2310.06161/) (2023)
- [Enhancing Evolving Domain Generalization through Dynamic Latent Representations](https://mlsanity.com/paper/2401.08464/) (2024)
- [How does promoting the minority fraction affect generalization? A theoretical study of the one-hidden-layer neural network on group imbalance](https://mlsanity.com/paper/2403.07310/) (2024)
- [Provably Neural Active Learning Succeeds via Prioritizing Perplexing Samples](https://mlsanity.com/paper/2406.03944/) (2024)
- [Learning Diverse Features in Vision Transformers for Improved Generalization](https://mlsanity.com/paper/2308.16274/) (2023)
- [TIF: Learning Temporal Invariance in Android Malware Detectors](https://mlsanity.com/paper/2502.05098/) (2025)
- [On the Role of Label Noise in the Feature Learning Process](https://mlsanity.com/paper/2505.18909/) (2025)
- [Measure-Theoretic Anti-Causal Representation Learning](https://mlsanity.com/paper/2510.18052/) (2025)
- [Generalizable Prompt Learning of CLIP: A Brief Overview](https://mlsanity.com/paper/2503.01263/) (2025)
- [Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2506.05957/) (2025)
- [CausalEvolve: Towards Open-Ended Discovery with Causal Scratchpad](https://mlsanity.com/paper/2603.14575/) (2026)
- [Weighted Risk Invariance: Domain Generalization under Invariant Feature Shift](https://mlsanity.com/paper/2407.18428/) (2024)
- [Noise-Aware Generalization: Robustness to In-Domain Noise and Out-of-Domain Generalization](https://mlsanity.com/paper/2504.02996/) (2025)
- [Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning](https://mlsanity.com/paper/2509.24332/) (2025)
- [Revisiting Spurious Correlation in Domain Generalization](https://mlsanity.com/paper/2406.11517/) (2024)
- [Simple yet Effective Node Property Prediction on Edge Streams under Distribution Shifts](https://mlsanity.com/paper/2504.00328/) (2025)
- [Robust Context-Aware Object Recognition](https://mlsanity.com/paper/2510.00618/) (2025)
- [Let Samples Speak: Mitigating Spurious Correlation by Exploiting the Clusterness of Samples](https://mlsanity.com/paper/2512.22874/) (2025)
- [Structure-agnostic Causal Representation Learning](https://mlsanity.com/paper/2610.00968/) (2026)

## Abstract (arXiv)

A common explanation for the failure of out-of-distribution (OOD) generalization is that the model trained with empirical risk minimization (ERM) learns spurious features instead of invariant features. However, several recent studies challenged this explanation and found that deep networks may have already learned sufficiently good features for OOD generalization. Despite the contradictions at first glance, we theoretically show that ERM essentially learns both spurious and invariant features, while ERM tends to learn spurious features faster if the spurious correlation is stronger. Moreover, when fed the ERM learned features to the OOD objectives, the invariant feature learning quality significantly affects the final OOD performance, as OOD objectives rarely learn new features. Therefore, ERM feature learning can be a bottleneck to OOD generalization. To alleviate the reliance, we propose Feature Augmented Training (FeAT), to enforce the model to learn richer features ready for OOD generalization. FeAT iteratively augments the model to learn new features while retaining the already learned features. In each round, the retention and augmentation operations are performed on different subsets of the training data that capture distinct features. Extensive experiments show that FeAT effectively learns richer features thus boosting the performance of various OOD objectives.