Neural Estimation for Scaling Entropic Multimarginal Optimal Transport
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912406198812672 |
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| author | Tsur, Dor Goldfeld, Ziv Greenewald, Kristjan Permuter, Haim |
| author_facet | Tsur, Dor Goldfeld, Ziv Greenewald, Kristjan Permuter, Haim |
| contents | Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational speedups via the multimarginal Sinkhorn algorithm, whose time complexity, for a dataset size $n$ and $k$ marginals, generally scales as $O(n^k)$. However, this dependence on the dataset size $n$ is computationally prohibitive for many machine learning problems. In this work, we propose a new computational framework for entropic MOT, dubbed Neural Entropic MOT (NEMOT), that enjoys significantly improved scalability. NEMOT employs neural networks trained using mini-batches, which transfers the computational complexity from the dataset size to the size of the mini-batch, leading to substantial gains. We provide formal guarantees on the accuracy of NEMOT via non-asymptotic error bounds. We supplement these with numerical results that demonstrate the performance gains of NEMOT over Sinkhorn's algorithm, as well as extensions to neural computation of multimarginal entropic Gromov-Wasserstein alignment. In particular, orders-of-magnitude speedups are observed relative to the state-of-the-art, with a notable increase in the feasible number of samples and marginals. NEMOT seamlessly integrates as a module in large-scale machine learning pipelines, and can serve to expand the practical applicability of entropic MOT for tasks involving multimarginal data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural Estimation for Scaling Entropic Multimarginal Optimal Transport Tsur, Dor Goldfeld, Ziv Greenewald, Kristjan Permuter, Haim Machine Learning Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational speedups via the multimarginal Sinkhorn algorithm, whose time complexity, for a dataset size $n$ and $k$ marginals, generally scales as $O(n^k)$. However, this dependence on the dataset size $n$ is computationally prohibitive for many machine learning problems. In this work, we propose a new computational framework for entropic MOT, dubbed Neural Entropic MOT (NEMOT), that enjoys significantly improved scalability. NEMOT employs neural networks trained using mini-batches, which transfers the computational complexity from the dataset size to the size of the mini-batch, leading to substantial gains. We provide formal guarantees on the accuracy of NEMOT via non-asymptotic error bounds. We supplement these with numerical results that demonstrate the performance gains of NEMOT over Sinkhorn's algorithm, as well as extensions to neural computation of multimarginal entropic Gromov-Wasserstein alignment. In particular, orders-of-magnitude speedups are observed relative to the state-of-the-art, with a notable increase in the feasible number of samples and marginals. NEMOT seamlessly integrates as a module in large-scale machine learning pipelines, and can serve to expand the practical applicability of entropic MOT for tasks involving multimarginal data. |
| title | Neural Estimation for Scaling Entropic Multimarginal Optimal Transport |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.00573 |