# Representation via Representations: Domain Generalization via Adversarially Learned Invariant Representations

arXiv: https://arxiv.org/abs/2006.11478 · HTML: https://mlsanity.com/paper/2006.11478/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2020.

## Built on by (most cited first, 26 of 26)

- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)
- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [Domain Adversarial Neural Networks for Domain Generalization: When It Works and How to Improve](https://mlsanity.com/paper/2102.03924/) (2021)
- [An Empirical Framework for Domain Generalization in Clinical Settings](https://mlsanity.com/paper/2103.11163/) (2021)
- [Invariant Causal Mechanisms through Distribution Matching](https://mlsanity.com/paper/2206.11646/) (2022)
- [MADG: Margin-based Adversarial Learning for Domain Generalization](https://mlsanity.com/paper/2311.08503/) (2023)
- [DomainAdaptor: A Novel Approach to Test-time Adaptation](https://mlsanity.com/paper/2308.10297/) (2023)
- [HappyMap: A Generalized Multi-calibration Method](https://mlsanity.com/paper/2303.04379/) (2023)
- [Last-Layer Fairness Fine-tuning is Simple and Effective for Neural Networks](https://mlsanity.com/paper/2304.03935/) (2023)
- [Towards Artificial General Intelligence (AGI) in the Internet of Things (IoT): Opportunities and Challenges](https://mlsanity.com/paper/2309.07438/) (2023)
- [FIFA: Making Fairness More Generalizable in Classifiers Trained on Imbalanced Data](https://mlsanity.com/paper/2206.02792/) (2022)
- [PAC-Bayesian Domain Adaptation Bounds for Multiclass Learners](https://mlsanity.com/paper/2207.05685/) (2022)
- [Reinforcement Learning with Stepwise Fairness Constraints](https://mlsanity.com/paper/2211.03994/) (2022)
- [Intra- & Extra-Source Exemplar-Based Style Synthesis for Improved Domain Generalization](https://mlsanity.com/paper/2307.00648/) (2023)
- [Learning Invariant Representations with Missing Data](https://mlsanity.com/paper/2112.00881/) (2021)
- [Exploring Flat Minima for Domain Generalization with Large Learning Rates](https://mlsanity.com/paper/2309.06337/) (2023)
- [How Many Domains Suffice for Domain Generalization? A Tight Characterization via the Domain Shattering Dimension](https://mlsanity.com/paper/2506.16704/) (2025)
- [Explainability-aided Domain Generalization for Image Classification](https://mlsanity.com/paper/2104.01742/) (2021)
- [Discovery of New Multi-Level Features for Domain Generalization via Knowledge Corruption](https://mlsanity.com/paper/2109.04320/) (2021)
- [Generalizing Vision-Language Models with Dedicated Prompt Guidance](https://mlsanity.com/paper/2512.02421/) (2025)
- [Meta-TTT: A Meta-learning Minimax Framework For Test-Time Training](https://mlsanity.com/paper/2410.01709/) (2024)
- [Power side-channel leakage localization through adversarial training of deep neural networks](https://mlsanity.com/paper/2410.22425/) (2024)
- [Should Bias be Eliminated? A General Framework to Use Bias for OOD Generalization](https://mlsanity.com/paper/2507.17001/) (2025)
- [Universal Adaptive Environment Discovery](https://mlsanity.com/paper/2510.12547/) (2025)

## Abstract (arXiv)

We investigate the power of censoring techniques, first developed for learning em fair representations, to address domain generalization. We examine em adversarial censoring techniques for learning invariant representations from multiple "studies" (or domains), where each study is drawn according to a distribution on domains. The mapping is used at test time to classify instances from a new domain. In many contexts, such as medical forecasting, domain generalization from studies in populous areas (where data are plentiful), to geographically remote populations (for which no training data exist) provides fairness of a different flavor, not anticipated in previous work on algorithmic fairness. We study an adversarial loss function for k domains and precisely characterize its limiting behavior as k grows, formalizing and proving the intuition, backed by experiments, that observing data from a larger number of domains helps. The limiting results are accompanied by non-asymptotic learning-theoretic bounds. Furthermore, we obtain sufficient conditions for good worst-case prediction performance of our algorithm on previously unseen domains. Finally, we decompose our mappings into two components and provide a complete characterization of invariance in terms of this decomposition. To our knowledge, our results provide the first formal guarantees of these kinds for adversarial invariant domain generalization.