Specformer: Spectral Graph Neural Networks Meet Transformers

• URL: http://arxiv.org/abs/2303.01028v1
• Date: Thu, 2 Mar 2023 07:36:23 GMT
• Title: Specformer: Spectral Graph Neural Networks Meet Transformers
• Authors: Deyu Bo and Chuan Shi and Lele Wang and Renjie Liao
• Abstract summary: Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. We introduce Specformer, which effectively encodes the set of all eigenvalues and performs self-attention in the spectral domain. By stacking multiple Specformer layers, one can build a powerful spectral GNN.
• Score: 51.644312964537356
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. However, most existing spectral graph filters are scalar-to-scalar functions, i.e., mapping a single eigenvalue to a single filtered value, thus ignoring the global pattern of the spectrum. Furthermore, these filters are often constructed based on some fixed-order polynomials, which have limited expressiveness and flexibility. To tackle these issues, we introduce Specformer, which effectively encodes the set of all eigenvalues and performs self-attention in the spectral domain, leading to a learnable set-to-set spectral filter. We also design a decoder with learnable bases to enable non-local graph convolution. Importantly, Specformer is equivariant to permutation. By stacking multiple Specformer layers, one can build a powerful spectral GNN. On synthetic datasets, we show that our Specformer can better recover ground-truth spectral filters than other spectral GNNs. Extensive experiments of both node-level and graph-level tasks on real-world graph datasets show that our Specformer outperforms state-of-the-art GNNs and learns meaningful spectrum patterns. Code and data are available at https://github.com/bdy9527/Specformer.

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