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.

翻译：我们提出了一种新颖的基于深度学习的端到端监督图预测（SGP）方法。引入了一种基于最优传输（OT）的原创损失函数——部分遮蔽融合格罗莫夫-瓦瑟斯坦损失（PM-FGW），该损失可直接利用邻接矩阵和特征矩阵等图表示形式。PM-FGW具备SGP所需的全部理想性质：节点排列不变性、次可微性，并通过比较图的填充表示及其遮蔽向量，能够处理不同尺寸的图。此外，我们提出了一种灵活的基于Transformer的架构，可轻松适配不同类型的输入数据。在实验部分，三个不同任务（一个新颖且具有挑战性的合成数据集image2graph，以及两个实际任务image2map与fingerprint2molecule）展示了该方法相较于竞争方法的有效性和通用性。