# Neural Estimation for Scaling Entropic Multimarginal Optimal Transport arXiv: https://arxiv.org/abs/2506.00573 · HTML: https://mlsanity.com/paper/2506.00573/ ## Key facts - Cited by 2 papers in the map (data through 14 Oct 2026). - Builds on 30 of its 57 references that are in the map. - First posted on arXiv 31 May 2025. ## Builds on (most cited first, 30 of 30) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013) - [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018) - [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017) - [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019) - [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017) - [Gromov-Wasserstein Alignment of Word Embedding Spaces](https://mlsanity.com/paper/1809.00013/) (2018) - [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018) - [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019) - [Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with ℓ1 and ℓ0 Controls](https://mlsanity.com/paper/1607.07819/) (2016) - [Score-based Generative Neural Networks for Large-Scale Optimal Transport](https://mlsanity.com/paper/2110.03237/) (2021) - [Scalable Bayes via Barycenter in Wasserstein Space](https://mlsanity.com/paper/1508.05880/) (2015) - [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014) - [Multi-marginal Wasserstein GAN](https://mlsanity.com/paper/1911.00888/) (2019) - [On the Complexity of Approximating Multimarginal Optimal Transport](https://mlsanity.com/paper/1910.00152/) (2019) - [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023) - [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021) - [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022) - [Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenters](https://mlsanity.com/paper/2305.16557/) (2023) - [Polynomial-time algorithms for Multimarginal Optimal Transport problems with structure](https://mlsanity.com/paper/2008.03006/) (2020) - [Non-Asymptotic Performance Guarantees for Neural Estimation of mathsff-Divergences](https://mlsanity.com/paper/2103.06923/) (2021) - [Multi-marginal optimal transport and probabilistic graphical models](https://mlsanity.com/paper/2006.14113/) (2020) - [Hardness results for Multimarginal Optimal Transport problems](https://mlsanity.com/paper/2012.05398/) (2020) - [Lower Complexity Adaptation for Empirical Entropic Optimal Transport](https://mlsanity.com/paper/2306.13580/) (2023) - [Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm](https://mlsanity.com/paper/1710.08234/) (2017) - [Multi-Marginal Gromov-Wasserstein Transport and Barycenters](https://mlsanity.com/paper/2205.06725/) (2022) - [Contrasting Multiple Representations with the Multi-Marginal Matching Gap](https://mlsanity.com/paper/2405.19532/) (2024) - [Accelerating the Sinkhorn algorithm for sparse multi-marginal optimal transport by fast Fourier transforms](https://mlsanity.com/paper/2208.03120/) (2022) - [Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs](https://mlsanity.com/paper/2208.03025/) (2022) - [Convergence rate of entropy-regularized multi-marginal optimal transport costs](https://mlsanity.com/paper/2307.03023/) (2023) ## Built on by (most cited first, 2 of 2) - [A Neural Network Algorithm for KL Divergence Estimation with Quantitative Error Bounds](https://mlsanity.com/paper/2510.05386/) (2025) - [PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction](https://mlsanity.com/paper/2605.06979/) (2026) ## Abstract (arXiv) 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(nk). 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.