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Discovering Environments with XRM
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Proposes Cross-Risk Minimization (XRM), which trains twin networks on random data halves that imitate confident held-out mistakes of their sibling, to discover environments without human annotations and without early stopping.
Problem
Automatic environment discovery for out-of-distribution and sub-population shift generalization without human environment annotations, avoiding the need for a human-annotated validation set to tune classifier capacity and early stopping.
Approach
Twin networks trained on complementary random halves flip training labels toward their sibling's confident held-out predictions (an echo chamber that amplifies spurious correlation); a model-selection rule counts label flips, and a cross-mistake formula assigns environments to all train and validation examples.
Key results
- XRM+GroupDRO reaches 88.1% worst-group accuracy on Waterbirds without group labels, matching human-annotated GroupDRO (86.5%).
- Across the Waterbirds, CelebA, MultiNLI and CivilComments quartet, XRM-based environments give 80.4% average worst-group accuracy versus 80.6% with human annotations and 67.3% with no annotations.
- On ColorMNIST, XRM+GroupDRO raises worst-group accuracy from about 10% (no annotations) to 69.7%, comparable to human annotations at 10.1% only for ERM baseline; GroupDRO with human annotations gets 10.1%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use XRM-inferred environments instead of no environment annotations with GroupDRO | GroupDRO · Sub-population shift benchmarks (Average, four datasets) | worst-group accuracy: 67.3% -> 80.4% | Helped |
| Use XRM-inferred environments instead of human annotations with GroupDRO | GroupDRO · Sub-population shift benchmarks (Average, four datasets) | worst-group accuracy: 80.6% -> 80.4% | No clear effect |
| Use XRM-inferred environments with CORAL instead of human annotations | CORAL · DomainBed benchmarks (five datasets) | worst test environment accuracy | Mixed |
| Use XRM-inferred environments instead of ground-truth annotations with GroupDRO | GroupDRO · Dominoes MF | worst-group accuracy: 85.28 -> 86.68 | Helped |
| Use XRM-inferred environments instead of ground-truth annotations with GroupDRO | GroupDRO · Dominoes MC | worst-group accuracy: 69.43 -> 68.78 | Hurt |
| Use XRM + GroupDRO rather than ERM | ColorMNIST CMNIST · CMNIST | test accuracy: 0.37 ± 0.10 -> 0.71 ± 0.02 | Helped |
| Use XRM + GroupDRO rather than ERM | ColorMNIST InverseCMNIST · InverseCMNIST | test accuracy: 0.67 ± 0.02 -> 0.82 ± 0.02 | Helped |
| Use XRM + GroupDRO rather than ERM | ColorMNIST InveCOLOR · InveCOLOR | test accuracy: 0.75 ± 0.01 -> 0.40 ± 0.01 | Hurt |
| Use XRM + GroupDRO rather than ERM | ColorMNIST MCOLOR · MCOLOR | test accuracy: 0.85 ± 0.01 -> 0.57 ± 0.01 | Hurt |
| Remove holding-out of data during twin training (ablation) | XRM · Environment discovery and downstream OOD generalization | performance | Hurt |
| Remove label flipping during twin training (ablation) | XRM · Environment discovery and downstream OOD generalization | performance | Hurt |
Surprising findings
- Deliberately flipping training labels toward held-out predictions, rather than avoiding label noise, is what produces useful environments.
- XRM fails on ColorMNIST variants where the invariant feature is simple and weakly correlated (accuracy 0.40 vs ERM 0.75), so it targets cases where the fastest-learned feature is spurious.
Limitations
- Impossibility of learning invariant predictors without environment annotations in general; XRM can fail when the invariant feature is the fastest-learned one (e.g., InverseCMNIST vs InverseMCOLOR are indistinguishable from pooled data).
- Always splits data into two environments per label, which may not match the true number of environments.
- Discovered environments may not align with human annotations (e.g., NMI near zero for some PACS classes), with only empirical justification.
Experimental setup
Datasets: Waterbirds CelebA MultiNLI CivilComments ColorMNIST MetaShift ImageNetBG DomainBed CIFAR-10 Dominoes
Benchmarks: Waterbirds CelebA MultiNLI CivilComments ColorMNIST MetaShift ImageNetBG DomainBed Dominoes
Metrics: worst-group accuracy average accuracy
Baselines: ERM GroupDRO LfF EIIL JTT CnC AFR LS BAM CORAL
Builds on: group distributionally robust optimization just train twice learning from failure CrossSplit CORAL
Closest papers by meaning
- OOD-Chameleon: Is Algorithm Selection for OOD Generalization Learnable? (ICML 2025 · similarity 0.84)
- Enhancing Graph Invariant Learning from a Negative Inference Perspective (ICML 2025 · similarity 0.84)
- Environment-Robust Representation Learning with Empirical Bayes (NeurIPS 2026 · similarity 0.83)
- Improving Generalization of Dynamic Graph Learning via Environment Prompt (NeurIPS 2024 · similarity 0.83)
- Context is Environment (ICLR 2024 · similarity 0.83)
- Environment Inference for Learning Generalizable Dynamical System (NeurIPS 2025 · similarity 0.83)
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