# Equivariant Disentangled Transformation for Domain Generalization under Combination Shift

arXiv: https://arxiv.org/abs/2208.02011 · HTML: https://mlsanity.com/paper/2208.02011/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 79 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Builds on (most cited first, 30 of 43)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Strike (with) a Pose: Neural Networks Are Easily Fooled by Strange Poses of Familiar Objects](https://mlsanity.com/paper/1811.11553/) (2018)
- [Generalizing to unseen domains via distribution matching](https://mlsanity.com/paper/1911.00804/) (2019)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)

## Built on by (most cited first, 1 of 1)

- [Correcting Flaws in Common Disentanglement Metrics](https://mlsanity.com/paper/2304.02335/) (2023)

## Abstract (arXiv)

Machine learning systems may encounter unexpected problems when the data distribution changes in the deployment environment. A major reason is that certain combinations of domains and labels are not observed during training but appear in the test environment. Although various invariance-based algorithms can be applied, we find that the performance gain is often marginal. To formally analyze this issue, we provide a unique algebraic formulation of the combination shift problem based on the concepts of homomorphism, equivariance, and a refined definition of disentanglement. The algebraic requirements naturally derive a simple yet effective method, referred to as equivariant disentangled transformation (EDT), which augments the data based on the algebraic structures of labels and makes the transformation satisfy the equivariance and disentanglement requirements. Experimental results demonstrate that invariance may be insufficient, and it is important to exploit the equivariance structure in the combination shift problem.