Graph Optimal Transport for Cross-Domain Alignment

TL;DR

This paper introduces Graph Optimal Transport (GOT), a novel framework that formulates cross-domain alignment as a graph matching problem using optimal transport, improving interpretability and performance across multiple tasks.

Contribution

GOT uniquely combines Wasserstein and Gromov-Wasserstein distances for flexible, interpretable cross-domain alignment within neural networks, advancing beyond existing attention-based methods.

Findings

GOT outperforms baselines in image-text retrieval and VQA.

GOT improves results in machine translation and text summarization.

The inferred transport plan offers sparse, interpretable alignments.

Abstract

Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention mechanisms to simulate soft alignment, with no training signals to explicitly encourage alignment. The learned attention matrices are also dense and lacks interpretability. We propose Graph Optimal Transport (GOT), a principled framework that germinates from recent advances in Optimal Transport (OT). In GOT, cross-domain alignment is formulated as a graph matching problem, by representing entities into a dynamically-constructed graph. Two types of OT distances are considered: (i) Wasserstein distance (WD) for node (entity) matching; and (ii) Gromov-Wasserstein distance (GWD) for edge (structure) matching. Both WD and GWD can be incorporated into existing neural network models, effectively acting as a drop-in regularizer. The inferred transport plan also yields sparse and self-normalized alignment, enhancing the interpretability of the learned model. Experiments show consistent outperformance of GOT over baselines across a wide range of tasks, including image-text retrieval, visual question answering, image captioning, machine translation, and text summarization.