Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark

Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Alexander Filippov, Evgeny Burnaev

Результат исследований: Глава в книге, отчете, сборнике статейМатериалы для конференциирецензирование

Аннотация

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we address this issue for quadratic-cost transport—specifically, computation of the Wasserstein-2 distance, a commonly-used formulation of optimal transport in machine learning. To overcome the challenge of computing ground truth transport maps between continuous measures needed to assess these solvers, we use input-convex neural networks (ICNN) to construct pairs of measures whose ground truth OT maps can be obtained analytically. This strategy yields pairs of continuous benchmark measures in high-dimensional spaces such as spaces of images. We thoroughly evaluate existing optimal transport solvers using these benchmark measures. Even though these solvers perform well in downstream tasks, many do not faithfully recover optimal transport maps. To investigate the cause of this discrepancy, we further test the solvers in a setting of image generation. Our study reveals crucial limitations of existing solvers and shows that increased OT accuracy does not necessarily correlate to better results downstream.

Язык оригиналаАнглийский
Название основной публикацииAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
РедакторыMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
ИздательNeural information processing systems foundation
Страницы14593-14605
Число страниц13
ISBN (электронное издание)9781713845393
СостояниеОпубликовано - 2021
Событие35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Продолжительность: 6 дек. 202114 дек. 2021

Серия публикаций

НазваниеAdvances in Neural Information Processing Systems
Том18
ISSN (печатное издание)1049-5258

Конференция

Конференция35th Conference on Neural Information Processing Systems, NeurIPS 2021
ГородVirtual, Online
Период6/12/2114/12/21

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