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Neural Optimal Transport

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arxiv 2201.12220 v3 pith:25PO54O3 submitted 2022-01-28 cs.LG

Alexander Korotin , Daniil Selikhanovych , Evgeny Burnaev This is my paper · ORCID
classification cs.LG
keywords transportoptimalalgorithmneuralplansapproximatorscomputecosts
verification ladder T0 review T1 audit T2 compute T3 formal
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We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans between probability distributions. We evaluate the performance of our optimal transport algorithm on toy examples and on the unpaired image-to-image translation.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Convex relaxation approaches for high-dimensional optimal transport

    math.OC 2025-11 conditional novelty 6.0 of 10

    High-dimensional optimal transport cost can be approximated by semidefinite programs built from sparse local moments, with exponentially decaying error for Gaussian measures with sparse precision.

  2. Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs

    cs.LG 2025-05 conditional novelty 6.0 of 10

    ULOT amortizes fused unbalanced Gromov-Wasserstein optimization: a cross-attention graph network trained to minimize FUGW loss predicts near-optimal transport plans for new graph pairs at quadratic inference cost.

  3. Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation

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    A mini-batch Wasserstein gradient-flow algorithm computes scalable and label-aware Wasserstein barycenters, with empirical gains on domain adaptation.

  4. Machine Unlearning via Information Theoretic Regularization

    cs.LG 2025-02 reject novelty 5.0 of 10

    The paper introduces an auditable, information-theoretic 'marginal unlearning' definition and a rate-distortion style regularization method that can remove data points or features from models.

  5. Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric

    math.OC 2025-09 reject novelty 3.0 of 10

    A largely expository paper connecting assignment problems to optimal transport and Gromov-Wasserstein distances, with a benchmark claiming a multi-start GW heuristic finds near-optimal capacitated QAP solutions; the b...

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