Graph Fourier Transformer with Structure-Frequency Information

Graph Transformers (GTs) excel in graph tasks but often overlook graph-specific inductive biases. Existing methods inject structural bias via positional encoding or attention mechanisms, yet remain limited by their neglect of frequency-domain information. This paper proposes Grafourierformer, a novel architecture that integrates Graph Fourier Transform into the self-attention mechanism. Our approach constructs a structural mask from Laplacian eigenvalues and incorporates frequency-energy filtering through inverse Fourier transformation, enabling joint structure-frequency optimization. This allows adaptive emphasis on global trends and local details while suppressing redundant information. Extensive experiments demonstrate that Grafourierformer consistently outperforms both GNN and GT baselines across graph and node classification tasks, with ablations confirming the necessity of each component. The code is available at https://github.com/Arichibald/Grafourierformer.git<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>