Structured Optimal Transport

TL;DR

This paper introduces a nonlinear generalization of optimal transport that captures complex structures beyond traditional metrics, enabling faster algorithms and improved performance in domain adaptation and NLP tasks.

Contribution

The authors develop a novel nonlinear optimal transport model that incorporates additional structure and demonstrate its computational advantages and practical benefits.

Findings

Enhanced structured couplings improve domain adaptation.

The model captures richer data relationships.

Algorithms achieve faster convergence.

Abstract

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) optimal transport that is able to reflect much additional structure. We demonstrate how to leverage the geometry of this new model for fast algorithms, and explore connections and properties. Illustrative experiments highlight the benefit of the induced structured couplings for tasks in domain adaptation and natural language processing.