# Discovering environments with XRM

arXiv: https://arxiv.org/abs/2309.16748 · HTML: https://mlsanity.com/paper/2309.16748/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 88 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 30 of 56)

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [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)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [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)
- [Noise or Signal: The Role of Image Backgrounds in Object Recognition](https://mlsanity.com/paper/2006.09994/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)

## Built on by (most cited first, 26 of 26)

- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [The Pitfalls of Memorization: When Memorization Hurts Generalization](https://mlsanity.com/paper/2412.07684/) (2024)
- [Compositional Risk Minimization](https://mlsanity.com/paper/2410.06303/) (2024)
- [Unsupervised Concept Discovery Mitigates Spurious Correlations](https://mlsanity.com/paper/2402.13368/) (2024)
- [DRoP: Distributionally Robust Data Pruning](https://mlsanity.com/paper/2404.05579/) (2024)
- [Severing Spurious Correlations with Data Pruning](https://mlsanity.com/paper/2503.18258/) (2025)
- [Data Debiasing with Datamodels (D3M): Improving Subgroup Robustness via Data Selection](https://mlsanity.com/paper/2406.16846/) (2024)
- [Trustworthy AI: Safety, Bias, and Privacy -- A Survey](https://mlsanity.com/paper/2502.10450/) (2025)
- [AIM-Fair: Advancing Algorithmic Fairness via Selectively Fine-Tuning Biased Models with Contextual Synthetic Data](https://mlsanity.com/paper/2503.05665/) (2025)
- [Measure-Theoretic Anti-Causal Representation Learning](https://mlsanity.com/paper/2510.18052/) (2025)
- [Optimizing importance weighting in the presence of sub-population shifts](https://mlsanity.com/paper/2410.14315/) (2024)
- [FairLoRA: Unpacking Bias Mitigation in Vision Models with Fairness-Driven Low-Rank Adaptation](https://mlsanity.com/paper/2410.17358/) (2024)
- [Subgroups Matter for Robust Bias Mitigation](https://mlsanity.com/paper/2505.21363/) (2025)
- [Curriculum-enhanced GroupDRO: Challenging the Norm of Avoiding Curriculum Learning in Subpopulation Shift Setups](https://mlsanity.com/paper/2411.15272/) (2024)
- [Class-Conditional Distribution Balancing for Group Robust Classification](https://mlsanity.com/paper/2504.17314/) (2025)
- [Fine-Grained Class-Conditional Distribution Balancing for Debiased Learning](https://mlsanity.com/paper/2505.06831/) (2025)
- [Dual-Branch Cross-Projection Debiasing through Diffusion-based Disentanglement](https://mlsanity.com/paper/2606.24161/) (2026)
- [Structure-agnostic Causal Representation Learning](https://mlsanity.com/paper/2610.00968/) (2026)
- [Mind the GAP: Improving Robustness to Subpopulation Shifts with Group-Aware Priors](https://mlsanity.com/paper/2403.09869/) (2024)
- [Revisiting Mixout: An Overlooked Path to Robust Finetuning](https://mlsanity.com/paper/2510.06982/) (2025)
- [Environment-Conditioned Tail Reweighting for Invariant Learning under Mixed Shifts](https://mlsanity.com/paper/2601.22944/) (2026)
- [Bias Leaves a Gradient Trail: Label-Free Bias Identification via Gradient Probes on Concept Decompositions](https://mlsanity.com/paper/2605.28780/) (2026)
- [Discovering Latent Groups for Robust Classification](https://mlsanity.com/paper/2606.23609/) (2026)
- [ProME: Prototype-Margin Environments with Repair-Aware Selection for Group-Robust Learning](https://mlsanity.com/paper/2608.13190/) (2026)
- [Learning the Robustness Mechanism with Bilevel Optimization](https://mlsanity.com/paper/2609.35541/) (2026)

## Abstract (arXiv)

Environment annotations are essential for the success of many out-of-distribution (OOD) generalization methods. Unfortunately, these are costly to obtain and often limited by human annotators' biases. To achieve robust generalization, it is essential to develop algorithms for automatic environment discovery within datasets. Current proposals, which divide examples based on their training error, suffer from one fundamental problem. These methods introduce hyper-parameters and early-stopping criteria, which require a validation set with human-annotated environments, the very information subject to discovery. In this paper, we propose Cross-Risk-Minimization (XRM) to address this issue. XRM trains twin networks, each learning from one random half of the training data, while imitating confident held-out mistakes made by its sibling. XRM provides a recipe for hyper-parameter tuning, does not require early-stopping, and can discover environments for all training and validation data. Algorithms built on top of XRM environments achieve oracle worst-group-accuracy, addressing a long-standing challenge in OOD generalization. Code available at urlhttps://github.com/facebookresearch/XRM.