In the realm of Graph Neural Networks (GNNs), two exciting research directions have recently emerged: Subgraph GNNs and Graph Transformers. In this paper, we propose an architecture that integrates both approaches, dubbed Subgraphormer, which combines the enhanced expressive power, message-passing mechanisms, and aggregation schemes from Subgraph GNNs with attention and positional encodings, arguably the most important components in Graph Transformers. Our method is based on an intriguing new connection we reveal between Subgraph GNNs and product graphs, suggesting that Subgraph GNNs can be formulated as Message Passing Neural Networks (MPNNs) operating on a product of the graph with itself. We use this formulation to design our architecture: first, we devise an attention mechanism based on the connectivity of the product graph. Following this, we propose a novel and efficient positional encoding scheme for Subgraph GNNs, which we derive as a positional encoding for the product graph. Our experimental results demonstrate significant performance improvements over both Subgraph GNNs and Graph Transformers on a wide range of datasets.

翻译：在图神经网络领域，近期涌现出两个激动人心的研究方向：子图GNN与图Transformer。本文提出一种融合两种方法的架构——Subgraphormer，它结合了子图GNN的增强表达能力、消息传递机制与聚合方案，以及图Transformer中最为关键的注意力机制与位置编码组件。我们的方法基于子图GNN与乘积图之间发现的全新关联，表明子图GNN可被表述为作用在原始图与其自身乘积上的消息传递神经网络（MPNN）。我们利用这一表述设计架构：首先，基于乘积图的连通性设计注意力机制；其次，提出一种新颖高效的位置编码方案，该方案源自对乘积图的位置编码。实验结果表明，本文方法在广泛的数据集上均显著优于纯子图GNN与纯图Transformer。