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.

我们提出了一种新颖的端到端深度学习方法，用于监督图预测。我们引入了一种原始的基于最优传输的损失函数，即部分遮蔽融合 Gromov-Wasserstein 损失函数（PM-FGW），可以直接利用图形表示（如邻接和特征矩阵）。PM-FGW 具有 SGP 所需的所有理想属性：节点排列不变性，次可微性，并通过比较它们的填充表示和遮罩向量来处理不同大小的图形。此外，我们还提出了一种灵活的基于 Transformer 的架构，可以轻松适应不同类型的输入数据。在实验部分，我们展示了该方法相对竞争对手在一个新颖而具有挑战性的合成数据集（image2graph）和两个真实世界任务（image2map 和 fingerprint2molecule）上的效率和多功能性。