Amortized Optimal Transport from Sliced Potentials
Quick summary
arXiv:2604.15114v2 Announce Type: replace-cross Abstract: We 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. We introduce two amortization strategies: regression-based amortization (RA-OT) and objective-based amortization (OA-OT). In RA-OT, we formulate a functional regression model that treats Kantorovich potentials from the original OT problem as responses and those obtained from sliced OT as predictors, and estimate these models via least-squares methods.
Key takeaways
- arXiv:2604.15114v2 Announce Type: replace-cross Abstract: We 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.
- We introduce two amortization strategies: regression-based amortization (RA-OT) and objective-based amortization (OA-OT).
- In RA-OT, we formulate a functional regression model that treats Kantorovich potentials from the original OT problem as responses and those obtained from sliced OT as predictors, and estimate these models via least-squares methods.
Why it matters
This model development creates a new option for users and a new testing obligation for developers. A fixed evaluation set comparing quality, cost and failure behavior is more useful than launch claims.
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