# Invariant Risk Minimization Is A Total Variation Model

arXiv: https://arxiv.org/abs/2405.01389 · HTML: https://mlsanity.com/paper/2405.01389/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Heterogeneous Risk Minimization](https://mlsanity.com/paper/2105.03818/) (2021)
- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)
- [In-N-Out: Pre-Training and Self-Training using Auxiliary Information for Out-of-Distribution Robustness](https://mlsanity.com/paper/2012.04550/) (2020)
- [Meta-Learning for Few-Shot Land Cover Classification](https://mlsanity.com/paper/2004.13390/) (2020)

## Built on by (most cited first, 5 of 5)

- [Out-of-distribution Generalization for Total Variation based Invariant Risk Minimization](https://mlsanity.com/paper/2502.19665/) (2025)
- [Generalizable Multimodal Large Language Model Editing via Invariant Trajectory Learning](https://mlsanity.com/paper/2601.19700/) (2026)
- [Feed Two Birds with One Scone: Exploiting Function-Space Regularization for Both OOD Robustness and ID Fine-Tuning Performance](https://mlsanity.com/paper/2509.05328/) (2025)
- [Environment-Conditioned Tail Reweighting for Invariant Learning under Mixed Shifts](https://mlsanity.com/paper/2601.22944/) (2026)
- [A Lightweight, Transferable, and Self-Adaptive Framework for Intelligent DC Arc-Fault Detection in Photovoltaic Systems](https://mlsanity.com/paper/2603.25749/) (2026)

## Abstract (arXiv)

Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical essence of IRM remains to be properly explained. We verify that IRM is essentially a total variation based on L2 norm (TV-ℓ2) of the learning risk with respect to the classifier variable. Moreover, we propose a novel IRM framework based on the TV-ℓ1 model. It not only expands the classes of functions that can be used as the learning risk and the feature extractor, but also has robust performance in denoising and invariant feature preservation based on the coarea formula. We also illustrate some requirements for IRM-TV-ℓ1 to achieve out-of-distribution generalization. Experimental results show that the proposed framework achieves competitive performance in several benchmark machine learning scenarios.