Research map / Learning theory and algorithms / Optimal transport
Neural optimal transport
Learn transport maps and distributions with neural, generative and loss-based formulations.
99 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Optimal transport, keyword cluster “optimal transport · transport ot · sinkhorn”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
19 papers in 2023–24 and 42 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 22.6% to 29.6%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2017 · Co-clustering through Optimal Transport (ICML 2017 · 7 citations)
- 2018 · Neural Architecture Search with Bayesian Optimisation and Optimal Transport (NeurIPS 2018 · 262 citations)
- 2019 · Obtaining Fairness using Optimal Transport Theory (ICML 2019 · 51 citations)
- 2020 · Distribution Matching for Crowd Counting (NeurIPS 2020 · 169 citations)
- 2021 · A Generalized Loss Function for Crowd Counting and Localization (CVPR 2021 · 210 citations)
- 2022 · Bending Graphs: Hierarchical Shape Matching Using Gated Optimal Transport (CVPR 2022 · 19 citations)
- 2023 · User-Controllable Arbitrary Style Transfer via Entropy Regularization (AAAI 2023 · 10 citations)
- 2024 · Hierarchical Multi-Marginal Optimal Transport for Network Alignment (AAAI 2024 · 15 citations)
- 2025 · OPTICAL: Leveraging Optimal Transport for Contribution Allocation in Dataset Distillation (CVPR 2025 · 3 citations)
- 2026 · Departures: Distributional Transport for Single-Cell Perturbation Prediction with Neural Schrödinger Bridges (AAAI 2026 · 1 citation)
Earliest papers here
- Co-clustering through Optimal Transport (ICML 2017 · 7 citations)
- Neural Architecture Search with Bayesian Optimisation and Optimal Transport (NeurIPS 2018 · 262 citations)
- Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport (NeurIPS 2018 · 31 citations)
What has been tried
65 papers here report 586 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 9%, hurt 17%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase the number of clusters M | ACM(A)-500 and DBLP(A)-500 · High-order Hits@10 | Mixed | Hierarchical Multi-Marginal Optimal Transport for Network Alignment (AAAI 2024 · 15 citations) | |
| Tuning λX and λH on iris | iris · accuracy | Mixed | An Optimal Transport View for Subspace Clustering and Spectral Clustering (AAAI 2024 · 6 citations) | |
| Vary the regularization parameter among the reported values | One-peak PDE · error | No clear effect | Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs (ICLR 2024 · 5 citations) | |
| Use the proposed Gaussian kernel instead of N/A, a linear kernel, or a single Gaussian kernel | CIFAR-10, IPC 10 · accuracy | 49.5; 47.8; 49.8 -> 50.2 | Helped | OPTICAL: Leveraging Optimal Transport for Contribution Allocation in Dataset Distillation (CVPR 2025 · 3 citations) |
| Add the growth term | Gene regulatory network, t=4 · W2 | 0.877 (± 0.011) -> 0.168 (± 0.007) | Helped | Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport (ICLR 2025 · 3 citations) |
| cache label-to-label costs between validation and training batches | data valuation · runtime | Helped | SAVA: Scalable Learning-Agnostic Data Valuation (ICLR 2025 · 2 citations) | |
| Choose δ by cross-validation instead of fixing δ=10⁻² | Kernelized IVS · ∇Ŝ (mean) | 6.502 -> 5.079 | Helped | Automatic Outlier Rectification via Optimal Transport (NeurIPS 2024 · 2 citations) |
| Add whitening to gradient distance estimation | nuScenes · LDS | 0.007 -> 0.028; 0.010 -> 0.065; 0.017 -> 0.098 | Helped | TAROT: Targeted Data Selection via Optimal Transport (ICML 2025 · 0 citations) |
| Increase the mirror-covariate penalty from η = 0 to η = 50 | STAR Neymanian confidence upper bound · relative sample size | 1.0 -> 0.951 | Helped | Tightening Causal Bounds via Covariate-Aware Optimal Transport (ICML 2025 · 0 citations) |
| Increase batch size for OT-CPCC | CIFAR100 · TestCPCC | Helped | Learning Structured Representations by Embedding Class Hierarchy with Fast Optimal Transport (ICLR 2025 · 0 citations) | |
| add the regularization term | LDW-CPS test · Wasserstein distance | 13625.83 -> 3767.62 | Helped | Generative Conditional Distributions by Neural (Entropic) Optimal Transport (ICML 2024 · 0 citations) |
| Remove the prior-knowledge penalty (set λ2 = 0) | Linear regression · excess risk | 0.057 -> 4.914 | Hurt | Outlier-Robust Distributionally Robust Optimization via Unbalanced Optimal Transport (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 18 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 4 of 18 papers
- CIFAR-10 · 4 of 18 papers
- FashionMNIST · 3 of 18 papers
- CIFAR-100 · 3 of 18 papers
- SVHN · 2 of 18 papers
- ImageNet-100 · 2 of 18 papers
- SNAREseq · 2 of 18 papers
- MMLU · 2 of 18 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 61 papers; from OpenAlex and the papers' affiliations).
- Stanford University · 5 papers
- Amazon · 2 papers
- Meta · 2 papers
- University of Science and Technology of China · 2 papers
- Massachusetts Institute of Technology · 2 papers
- University of Southern California · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Transport map estimation (77 papers)
- Sinkhorn and entropic OT algorithms (69 papers)
- Schrodinger bridge matching (11 papers)
Elsewhere in the topic
- Wasserstein barycenters and GW (55 papers)
- Sliced Wasserstein variants (50 papers)
- Wasserstein losses for generative models (23 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).