Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.

翻译：Transformer模型已在自然语言处理和视觉领域引发性能革命，为与图神经网络（GNNs）的融合开辟了道路。增强图Transformer的一个关键挑战在于提升其区分图同构的判别能力，这对提高预测性能至关重要。为应对这一挑战，我们提出“拓扑感知图Transformer（TIGT）”——一种新型Transformer，既能增强图同构检测的判别力，又能提升图Transformer的整体性能。TIGT包含四个组件：基于图循环子图的非同构通用覆盖的拓扑位置嵌入层，确保图的唯一表示；贯穿编码器层显式编码拓扑特征的双路径消息传递层；全局注意力机制；以及用于重新校准通道级图特征以优化特征表示的图信息层。TIGT在针对区分图同构类别的合成数据集分类任务中超越了以往的图Transformer。此外，数学分析和实证评估表明，我们的模型在多个基准数据集上相较最先进的图Transformer具有竞争优势。