# Learning Subset-Shared Invariances for Domain Generalization with Mixture-of-Experts

arXiv: https://arxiv.org/abs/2606.25665 · HTML: https://mlsanity.com/paper/2606.25665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 58 of its 73 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [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)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Domain Generalization for Object Recognition with Multi-task Autoencoders](https://mlsanity.com/paper/1508.07680/) (2015)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Partial success in closing the gap between human and machine vision](https://mlsanity.com/paper/2106.07411/) (2021)
- [Causality Inspired Representation Learning for Domain Generalization](https://mlsanity.com/paper/2203.14237/) (2022)
- [Efficient Domain Generalization via Common-Specific Low-Rank Decomposition](https://mlsanity.com/paper/2003.12815/) (2020)
- [Domain Generalization by Mutual-Information Regularization with Pre-trained Models](https://mlsanity.com/paper/2203.10789/) (2022)
- [Sharpness-Aware Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2303.10353/) (2023)
- [Towards Principled Disentanglement for Domain Generalization](https://mlsanity.com/paper/2111.13839/) (2021)
- [Sparse Mixture-of-Experts are Domain Generalizable Learners](https://mlsanity.com/paper/2206.04046/) (2022)
- [Stronger, Fewer, & Superior: Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation](https://mlsanity.com/paper/2312.04265/) (2023)

## Abstract (arXiv)

Domain generalization (DG) aims to learn a model from one or more source domains that generalizes to an unseen target domain without accessing target data during training. A common approach enforces invariance of representations across all source domains, assuming predictive structure is globally shared. However, we demonstrate that enforcing invariance across more domains gradually restricts the feasible representation space, discarding transferable predictive factors that are not universally shared. To address this limitation, we propose subset-shared invariance, where predictive structure is assumed stable only within domain subsets. We implement this principle with a mixture-of-experts architecture, where each expert aligns the specific domains it serves and a routing mechanism composes subset-invariant components for prediction. This creates a routing-conditioned invariance, jointly learned with the representation. To facilitate effective decomposition, we develop training objectives that encourage selective alignment, confident and balanced routing, and diverse expert specialization. Experiments on DomainBed benchmarks demonstrate improved out-of-domain generalization and greater robustness under increasing domain heterogeneity. Our results suggest that DG should move beyond enforcing a single global invariance and instead model invariance through partially shared structure across domain subsets.