mlsanityData to 14 Oct 2026

Universal Neural Optimal Transport

arXiv 2212.00133 ↗First posted 30 Nov 2022cs.LG math.OC stat.MLcited by 6

Not on the map. Why?

Abstract (arXiv)

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately predicting (entropic) OT distances and plans between discrete measures for a given cost function. UNOT builds on Fourier Neural Operators, a universal class of neural networks that map between function spaces and that are discretization-invariant, which enables our network to process measures of variable resolutions. The network is trained adversarially using a second, generating network and a self-supervised bootstrapping loss. We ground UNOT in an extensive theoretical framework. Through experiments on Euclidean and non-Euclidean domains, we show that our network not only accurately predicts OT distances and plans across a wide range of datasets, but also captures the geometry of the Wasserstein space correctly. Furthermore, we show that our network can be used as a state-of-the-art initialization for the Sinkhorn algorithm with speedups of up to 7.4×, significantly outperforming existing approaches.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 21 of its 55 references that are in the map. First posted on arXiv 30 Nov 2022.

Builds on

21 of 55 references.

References · 21

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  4. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  5. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
  6. 2018Invertible Residual Networkscited by 365
  7. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 314
  8. 2017Joint Distribution Optimal Transportation for Domain Adaptationcited by 282
  9. 2019Generalized Sliced Wasserstein Distancescited by 208
  10. 2015Learning with a Wasserstein Losscited by 196
  11. 2020Primal Wasserstein Imitation Learningcited by 121
  12. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 93
9 more
  1. 2017Reversible Architectures for Arbitrarily Deep Residual Neural Networkscited by 70
  2. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 65
  3. 2022Supervised Training of Conditional Monge Mapscited by 61
  4. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  5. 2022Meta Optimal Transportcited by 28
  6. 2018Distilled Wasserstein Learning for Word Embedding and Topic Modelingcited by 18
  7. 2020Dataset Dynamics via Gradient Flows in Probability Spacecited by 18
  8. 2022Rethinking Initialization of the Sinkhorn Algorithmcited by 14
  9. 2022On the explainable properties of 1-Lipschitz Neural Networks: An Optimal Transport Perspectivecited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  2. 2025DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flowscited by 4
  3. 2026Measure-to-measure Regression with Transformerscited by 2
  4. 2025Experts-Guided Unbalanced Optimal Transport for ISP Learning from Unpaired and/or Paired Datacited by 1
  5. 2026C-kNN-LSH: A Nearest-Neighbor Algorithm for Sequential Counterfactual Inferencecited by 0
  6. 2026Generative Modeling on Metric Graphs via Neural Optimal Transportcited by 0