End-to-end Supervised Prediction of Arbitrary-size Graphs with Partially-Masked Fused Gromov-Wasserstein Matching

We present a novel end-to-end deep learning-based approach for Supervised Graph Prediction (SGP). We introduce an original Optimal Transport (OT)-based loss, the Partially-Masked Fused Gromov-Wasserstein loss (PM-FGW), that allows to directly leverage graph representations such as adjacency and feature matrices. PM-FGW exhibits all the desirable properties for SGP: it is node permutation invariant, sub-differentiable and handles graphs of different sizes by comparing their padded representations as well as their masking vectors. Moreover, we present a flexible transformer-based architecture that easily adapts to different types of input data. In the experimental section, three different tasks, a novel and challenging synthetic dataset (image2graph) and two real-world tasks, image2map and fingerprint2molecule - showcase the efficiency and versatility of the approach compared to competitors.