# An Empirical Study of Invariant Risk Minimization

arXiv: https://arxiv.org/abs/2004.05007 · HTML: https://mlsanity.com/paper/2004.05007/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2020.

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

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- [DPU: Dynamic Prototype Updating for Multimodal Out-of-Distribution Detection](https://mlsanity.com/paper/2411.08227/) (2024)
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- [OccamNets: Mitigating Dataset Bias by Favoring Simpler Hypotheses](https://mlsanity.com/paper/2204.02426/) (2022)
- [An Empirical Study on Distribution Shift Robustness From the Perspective of Pre-Training and Data Augmentation](https://mlsanity.com/paper/2205.12753/) (2022)
- [Detecting Spurious Correlations with Sanity Tests for Artificial Intelligence Guided Radiology Systems](https://mlsanity.com/paper/2103.03048/) (2021)
- [What Is Missing in IRM Training and Evaluation? Challenges and Solutions](https://mlsanity.com/paper/2303.02343/) (2023)
- [FedGen: Generalizable Federated Learning for Sequential Data](https://mlsanity.com/paper/2211.01914/) (2022)
- [Meta-Learned Invariant Risk Minimization](https://mlsanity.com/paper/2103.12947/) (2021)
- [Causal Learning for Socially Responsible AI](https://mlsanity.com/paper/2104.12278/) (2021)
- [Contextualizing Meta-Learning via Learning to Decompose](https://mlsanity.com/paper/2106.08112/) (2021)
- [DADM: Dual Alignment of Domain and Modality for Face Anti-spoofing](https://mlsanity.com/paper/2503.00429/) (2025)
- [Environment Diversification with Multi-head Neural Network for Invariant Learning](https://mlsanity.com/paper/2308.08778/) (2023)
- [Multi-dimensional domain generalization with low-rank structures](https://mlsanity.com/paper/2309.09555/) (2023)
- [Out-of-Distribution Generalization in Text Classification: Past, Present, and Future](https://mlsanity.com/paper/2305.14104/) (2023)
- [Invariant Representation via Decoupling Style and Spurious Features from Images](https://mlsanity.com/paper/2312.06226/) (2023)
- [Enhancing Fairness through Reweighting: A Path to Attain the Sufficiency Rule](https://mlsanity.com/paper/2408.14126/) (2024)
- [PEPR: Privileged Event-based Predictive Regularization for Domain Generalization](https://mlsanity.com/paper/2602.04583/) (2026)
- [FL Games: A federated learning framework for distribution shifts](https://mlsanity.com/paper/2205.11101/) (2022)
- [FAIRM: Learning invariant representations for algorithmic fairness and domain generalization with minimax optimality](https://mlsanity.com/paper/2404.01608/) (2024)

## Abstract (arXiv)

Invariant risk minimization (IRM) (Arjovsky et al., 2019) is a recently proposed framework designed for learning predictors that are invariant to spurious correlations across different training environments. Yet, despite its theoretical justifications, IRM has not been extensively tested across various settings. In an attempt to gain a better understanding of the framework, we empirically investigate several research questions using IRMv1, which is the first practical algorithm proposed to approximately solve IRM. By extending the ColoredMNIST experiment in different ways, we find that IRMv1 (i) performs better as the spurious correlation varies more widely between training environments, (ii) learns an approximately invariant predictor when the underlying relationship is approximately invariant, and (iii) can be extended to an analogous setting for text classification.