Technical Report: The Graph Spectral Token -- Enhancing Graph Transformers with Spectral Information

TL;DR

This paper introduces the Graph Spectral Token, a novel method to incorporate spectral information into graph transformers, significantly improving their performance on large graph benchmarks by capturing global graph structure.

Contribution

The paper proposes the Graph Spectral Token to encode spectral information directly into transformer models, enhancing their ability to leverage global graph structure.

Findings

GraphTrans-Spec improves over 10% on large graph benchmarks.

SubFormer-Spec shows strong performance across multiple datasets.

Method maintains efficiency comparable to message-passing GNNs.

Abstract

Graph Transformers have emerged as a powerful alternative to Message-Passing Graph Neural Networks (MP-GNNs) to address limitations such as over-squashing of information exchange. However, incorporating graph inductive bias into transformer architectures remains a significant challenge. In this report, we propose the Graph Spectral Token, a novel approach to directly encode graph spectral information, which captures the global structure of the graph, into the transformer architecture. By parameterizing the auxiliary [CLS] token and leaving other tokens representing graph nodes, our method seamlessly integrates spectral information into the learning process. We benchmark the effectiveness of our approach by enhancing two existing graph transformers, GraphTrans and SubFormer. The improved GraphTrans, dubbed GraphTrans-Spec, achieves over 10% improvements on large graph benchmark datasets while maintaining efficiency comparable to MP-GNNs. SubFormer-Spec demonstrates strong performance across various datasets.