# Domain Adaptation and Entanglement: an Optimal Transport Perspective

arXiv: https://arxiv.org/abs/2503.08155 · HTML: https://mlsanity.com/paper/2503.08155/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [A DIRT-T Approach to Unsupervised Domain Adaptation](https://mlsanity.com/paper/1802.08735/) (2018)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [Theoretical Analysis of Domain Adaptation with Optimal Transport](https://mlsanity.com/paper/1610.04420/) (2016)
- [Support and Invertibility in Domain-Invariant Representations](https://mlsanity.com/paper/1903.03448/) (2019)
- [f-Domain-Adversarial Learning: Theory and Algorithms](https://mlsanity.com/paper/2106.11344/) (2021)
- [d-SNE: Domain Adaptation using Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1905.12775/) (2019)
- [KL Guided Domain Adaptation](https://mlsanity.com/paper/2106.07780/) (2021)
- [An Information-theoretic Approach to Distribution Shifts](https://mlsanity.com/paper/2106.03783/) (2021)
- [Mapping conditional distributions for domain adaptation under generalized target shift](https://mlsanity.com/paper/2110.15057/) (2021)
- [Information-Theoretic Analysis of Unsupervised Domain Adaptation](https://mlsanity.com/paper/2210.00706/) (2022)
- [On f-Divergence Principled Domain Adaptation: An Improved Framework](https://mlsanity.com/paper/2402.01887/) (2024)

## Built on by (most cited first, 6 of 6)

- [Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation](https://mlsanity.com/paper/2512.00308/) (2025)
- [DMGD: Train-Free Dataset Distillation with Semantic-Distribution Matching in Diffusion Models](https://mlsanity.com/paper/2605.03877/) (2026)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [OT Score: An OT based Confidence Score for Prototype-Assisted Source Free Unsupervised Domain Adaptation](https://mlsanity.com/paper/2505.11669/) (2025)
- [When Does a Skill Add Value? Task-Conditional Gain Prediction for Selective Skill Use](https://mlsanity.com/paper/2609.32274/) (2026)
- [Revisiting On-policy Adversarial Black-Box Distillation: Calibrating Groupwise Reward Geometry for Effective Advantage Construction](https://mlsanity.com/paper/2609.39757/) (2026)

## Abstract (arXiv)

Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS has been studied extensively in the field of domain adaptation. For deep neural networks, a popular framework for unsupervised domain adaptation (UDA) is domain matching, in which algorithms try to align the marginal distributions in the feature or output space. The current theoretical understanding of these methods, however, is limited and existing theoretical results are not precise enough to characterize their performance in practice. In this paper, we derive new bounds based on optimal transport that analyze the UDA problem. Our new bounds include a term which we dub as entanglement, consisting of an expectation of Wasserstein distance between conditionals with respect to changing data distributions. Analysis of the entanglement term provides a novel perspective on the unoptimizable aspects of UDA. In various experiments with multiple models across several DS scenarios, we show that this term can be used to explain the varying performance of UDA algorithms.