# Learning Representations that Support Robust Transfer of Predictors

arXiv: https://arxiv.org/abs/2110.09940 · HTML: https://mlsanity.com/paper/2110.09940/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [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)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (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)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [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)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Deep Domain-Adversarial Image Generation for Domain Generalisation](https://mlsanity.com/paper/2003.06054/) (2020)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Learning explanations that are hard to vary](https://mlsanity.com/paper/2009.00329/) (2020)
- [Invariant Rationalization](https://mlsanity.com/paper/2003.09772/) (2020)
- [Reducing Domain Gap by Reducing Style Bias](https://mlsanity.com/paper/1910.11645/) (2019)
- [Enforcing Predictive Invariance across Structured Biomedical Domains](https://mlsanity.com/paper/2006.03908/) (2020)
- [Learning Robust Models Using The Principle of Independent Causal Mechanisms](https://mlsanity.com/paper/2010.07167/) (2020)

## Built on by (most cited first, 17 of 17)

- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)
- [Model Agnostic Sample Reweighting for Out-of-Distribution Learning](https://mlsanity.com/paper/2301.09819/) (2023)
- [WOODS: Benchmarks for Out-of-Distribution Generalization in Time Series](https://mlsanity.com/paper/2203.09978/) (2022)
- [Domain Generalization in Computational Pathology: Survey and Guidelines](https://mlsanity.com/paper/2310.19656/) (2023)
- [Empowering Graph Invariance Learning with Deep Spurious Infomax](https://mlsanity.com/paper/2407.11083/) (2024)
- [Controlling Directions Orthogonal to a Classifier](https://mlsanity.com/paper/2201.11259/) (2022)
- [Back-to-Bones: Rediscovering the Role of Backbones in Domain Generalization](https://mlsanity.com/paper/2209.01121/) (2022)
- [What Is Missing in IRM Training and Evaluation? Challenges and Solutions](https://mlsanity.com/paper/2303.02343/) (2023)
- [Class Is Invariant to Context and Vice Versa: On Learning Invariance for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2208.03462/) (2022)
- [OOD-Probe: A Neural Interpretation of Out-of-Domain Generalization](https://mlsanity.com/paper/2208.12352/) (2022)
- [Pareto Invariant Representation Learning for Multimedia Recommendation](https://mlsanity.com/paper/2308.04706/) (2023)
- [Benchmarking Domain Generalization Algorithms in Computational Pathology](https://mlsanity.com/paper/2409.17063/) (2024)
- [Robustness May be More Brittle than We Think under Different Degrees of Distribution Shifts](https://mlsanity.com/paper/2310.06622/) (2023)
- [Enhancing Fairness through Reweighting: A Path to Attain the Sufficiency Rule](https://mlsanity.com/paper/2408.14126/) (2024)
- [IENE: Identifying and Extrapolating the Node Environment for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2406.00764/) (2024)
- [Invariant Correlation of Representation with Label: Enhancing Domain Generalization in Noisy Environments](https://mlsanity.com/paper/2407.01749/) (2024)
- [Assessing Distribution Shift in Human Activity Recognition for Domain Generalization](https://mlsanity.com/paper/2606.24781/) (2026)

## Abstract (arXiv)

Ensuring generalization to unseen environments remains a challenge. Domain shift can lead to substantially degraded performance unless shifts are well-exercised within the available training environments. We introduce a simple robust estimation criterion -- transfer risk -- that is specifically geared towards optimizing transfer to new environments. Effectively, the criterion amounts to finding a representation that minimizes the risk of applying any optimal predictor trained on one environment to another. The transfer risk essentially decomposes into two terms, a direct transfer term and a weighted gradient-matching term arising from the optimality of per-environment predictors. Although inspired by IRM, we show that transfer risk serves as a better out-of-distribution generalization criterion, both theoretically and empirically. We further demonstrate the impact of optimizing such transfer risk on two controlled settings, each representing a different pattern of environment shift, as well as on two real-world datasets. Experimentally, the approach outperforms baselines across various out-of-distribution generalization tasks. Code is available at urlhttps://github.com/Newbeeer/TRM.