# What Is Missing in IRM Training and Evaluation? Challenges and Solutions

arXiv: https://arxiv.org/abs/2303.02343 · HTML: https://mlsanity.com/paper/2303.02343/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 65 references that are in the map.
- First posted on arXiv 4 Mar 2023.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [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)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (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)
- [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)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [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)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)

## Built on by (most cited first, 10 of 10)

- [Defensive Unlearning with Adversarial Training for Robust Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2405.15234/) (2024)
- [Towards LLM Unlearning Resilient to Relearning Attacks: A Sharpness-Aware Minimization Perspective and Beyond](https://mlsanity.com/paper/2502.05374/) (2025)
- [An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning](https://mlsanity.com/paper/2308.00788/) (2023)
- [Invariance Makes LLM Unlearning Resilient Even to Unanticipated Downstream Fine-Tuning](https://mlsanity.com/paper/2506.01339/) (2025)
- [Towards Understanding Variants of Invariant Risk Minimization through the Lens of Calibration](https://mlsanity.com/paper/2401.17541/) (2024)
- [The Power of Few: Accelerating and Enhancing Data Reweighting with Coreset Selection](https://mlsanity.com/paper/2403.12166/) (2024)
- [BiSSL: Enhancing the Alignment Between Self-Supervised Pretraining and Downstream Fine-Tuning via Bilevel Optimization](https://mlsanity.com/paper/2410.02387/) (2024)
- [Context is Environment](https://mlsanity.com/paper/2309.09888/) (2023)
- [Robust Invariant Representation Learning by Distribution Extrapolation](https://mlsanity.com/paper/2505.16126/) (2025)
- [From Objectives to What Models Learn: A Landau Theory of Invariant Learning](https://mlsanity.com/paper/2608.09396/) (2026)

## Abstract (arXiv)

Invariant risk minimization (IRM) has received increasing attention as a way to acquire environment-agnostic data representations and predictions, and as a principled solution for preventing spurious correlations from being learned and for improving models' out-of-distribution generalization. Yet, recent works have found that the optimality of the originally-proposed IRM optimization (IRM) may be compromised in practice or could be impossible to achieve in some scenarios. Therefore, a series of advanced IRM algorithms have been developed that show practical improvement over IRM. In this work, we revisit these recent IRM advancements, and identify and resolve three practical limitations in IRM training and evaluation. First, we find that the effect of batch size during training has been chronically overlooked in previous studies, leaving room for further improvement. We propose small-batch training and highlight the improvements over a set of large-batch optimization techniques. Second, we find that improper selection of evaluation environments could give a false sense of invariance for IRM. To alleviate this effect, we leverage diversified test-time environments to precisely characterize the invariance of IRM when applied in practice. Third, we revisit (Ahuja et al. (2020))'s proposal to convert IRM into an ensemble game and identify a limitation when a single invariant predictor is desired instead of an ensemble of individual predictors. We propose a new IRM variant to address this limitation based on a novel viewpoint of ensemble IRM games as consensus-constrained bi-level optimization. Lastly, we conduct extensive experiments (covering 7 existing IRM variants and 7 datasets) to justify the practical significance of revisiting IRM training and evaluation in a principled manner.