# Structured Optimal Transport

arXiv: https://arxiv.org/abs/1712.06199 · HTML: https://mlsanity.com/paper/1712.06199/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2017.

## Built on by (most cited first, 30 of 31)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels](https://mlsanity.com/paper/2312.06221/) (2023)
- [Learning Generalized Gumbel-max Causal Mechanisms](https://mlsanity.com/paper/2111.06888/) (2021)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Accelerating Sinkhorn Algorithm with Sparse Newton Iterations](https://mlsanity.com/paper/2401.12253/) (2024)
- [Re-evaluating Word Mover's Distance](https://mlsanity.com/paper/2105.14403/) (2021)
- [Hierarchical Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2112.02073/) (2021)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [Optimal Transport for Measures with Noisy Tree Metric](https://mlsanity.com/paper/2310.13653/) (2023)
- [Tree-Sliced Wasserstein Distance: A Geometric Perspective](https://mlsanity.com/paper/2406.13725/) (2024)
- [Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes](https://mlsanity.com/paper/2211.10420/) (2022)
- [Unbalanced Optimal Transport for Unbalanced Word Alignment](https://mlsanity.com/paper/2306.04116/) (2023)
- [Submodular Framework for Structured-Sparse Optimal Transport](https://mlsanity.com/paper/2406.04914/) (2024)
- [Order Constraints in Optimal Transport](https://mlsanity.com/paper/2110.07275/) (2021)
- [Distance-Based Tree-Sliced Wasserstein Distance](https://mlsanity.com/paper/2503.11050/) (2025)
- [Improving word mover's distance by leveraging self-attention matrix](https://mlsanity.com/paper/2211.06229/) (2022)
- [A Sinkhorn-type Algorithm for Constrained Optimal Transport](https://mlsanity.com/paper/2403.05054/) (2024)
- [An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascent](https://mlsanity.com/paper/2604.03782/) (2026)
- [OT-Net: A Reusable Neural Optimal Transport Solver](https://mlsanity.com/paper/2306.08233/) (2023)
- [What is the Right Notion of Distance between Predict-then-Optimize Tasks?](https://mlsanity.com/paper/2409.06997/) (2024)
- [Optimal Transportation by Orthogonal Coupling Dynamics](https://mlsanity.com/paper/2410.08060/) (2024)
- [Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomena](https://mlsanity.com/paper/2505.06123/) (2025)
- [Fully Probabilistic Design for Optimal Transport](https://mlsanity.com/paper/2212.13912/) (2022)
- [Safe Screening for Unbalanced Optimal Transport](https://mlsanity.com/paper/2307.00247/) (2023)
- [Robust Graph Matching Using An Unbalanced Hierarchical Optimal Transport Framework](https://mlsanity.com/paper/2310.12081/) (2023)
- [Geometry-Aware Normalizing Wasserstein Flows for Optimal Causal Inference](https://mlsanity.com/paper/2311.18826/) (2023)
- [Many-to-Many Matching via Sparsity Controlled Optimal Transport](https://mlsanity.com/paper/2503.24204/) (2025)
- [Bispectral OT: Dataset Comparison using Symmetry-Aware Optimal Transport](https://mlsanity.com/paper/2509.20678/) (2025)
- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)

## Abstract (arXiv)

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) optimal transport that is able to reflect much additional structure. We demonstrate how to leverage the geometry of this new model for fast algorithms, and explore connections and properties. Illustrative experiments highlight the benefit of the induced structured couplings for tasks in domain adaptation and natural language processing.