Amortized Optimal Transport from Sliced Potentials

2026-04-17 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

Minh-Phuc Truong and Khai Nguyen propose a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures by leveraging Kantorovich potentials derived from sliced OT. They introduce two strategies: regression-based amortization (RA-OT) and objective-based amortization (OA-OT). RA-OT formulates a functional regression model where Kantorovich potentials from the original OT problem are responses and those from sliced OT are predictors, estimated via least-squares. OA-OT estimates functional model parameters by optimizing the Kantorovich dual objective. Both approaches recover the OT plan from estimated potentials, enabling efficient solutions for repeated OT problems by reusing learned information. The models are parsimonious, independent of measure structures like the number of atoms, and achieve high accuracy, demonstrated on tasks including MNIST digit transport, color transfer, spherical supply-demand, and mini-batch OT conditional flow matching.

Key takeaway

For research scientists working with repeated optimal transport problems, adopting amortized methods like RA-OT or OA-OT can significantly improve computational efficiency. You should consider integrating these sliced potential-based approaches to rapidly approximate new solutions, especially when dealing with diverse measure pairs or large datasets, thereby accelerating iterative modeling and analysis workflows.

Key insights

Amortized optimal transport using sliced potentials efficiently solves repeated OT problems across diverse measure pairs.

Principles

• Leverage sliced OT for parsimonious models.
• Reuse learned information for efficiency.

Method

Predict optimal transport plans by formulating functional regression (RA-OT) or optimizing the Kantorovich dual objective (OA-OT) using Kantorovich potentials from sliced OT, then recover the plan.

In practice

• Apply to MNIST digit transport.
• Use for color transfer tasks.
• Solve spherical supply-demand problems.

Topics

• Optimal Transport
• Amortized Optimization
• Sliced Potentials
• Kantorovich Potentials
• Functional Regression

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.