Amortized Optimal Transport from Sliced Potentials

2026-04-16 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Researchers have introduced a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures. This approach leverages Kantorovich potentials derived from sliced OT and includes two distinct amortization strategies: regression-based amortization (RA-OT) and objective-based amortization (OA-OT). RA-OT formulates a functional regression model, using Kantorovich potentials from original OT as responses and sliced OT potentials as predictors, estimated via least-squares. OA-OT, conversely, estimates functional model parameters by optimizing the Kantorovich dual objective. Both methods recover the predicted OT plan from estimated potentials, enabling efficient solutions for repeated OT problems by reusing learned information. The models are parsimonious, independent of measure-specific structures like the number of atoms in discrete cases, and demonstrate high accuracy on tasks such as MNIST digit transport, color transfer, spherical supply-demand transportation, and mini-batch OT conditional flow matching.

Key takeaway

For research scientists working with repeated optimal transport problems, these new amortized methods offer a path to significantly more efficient solutions. By leveraging sliced OT and either regression-based or objective-based amortization, you can achieve high accuracy while reducing computational overhead, especially for tasks like conditional flow matching or large-scale data transfer. Consider integrating RA-OT or OA-OT into your workflow to accelerate complex OT computations.

Key insights

Amortized optimal transport methods efficiently predict OT plans by reusing learned Kantorovich potentials from sliced OT.

Principles

• Amortization reuses prior information.
• Sliced OT provides structural advantages.
• Parsimony improves model efficiency.

Method

The method involves either functional regression (RA-OT) or Kantorovich dual objective optimization (OA-OT) to estimate potentials, from which the OT plan is recovered.

In practice

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

Topics

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

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

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.