arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2303.01028cs.LGcs.AIcs.SI
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Specformer:谱图神经网络与Transformers相遇

Specformer: Spectral Graph Neural Networks Meet Transformers

University of British Columbia(不列颠哥伦比亚大学)

Deyu Bo, Chuan Shi, Lele Wang, Renjie Liao

摘要:

谱图神经网络(GNN)通过谱域图卷积来学习图表示。然而,大多数现有的谱图滤波器是标量到标量函数,即,将单个特征值映射到单个滤波值,从而忽略频谱的全局模式。此外,这些滤波器往往是基于一些固定阶多项式,这具有有限的表达性和灵活性。为了解决这些问题,我们引入了Specformer,它有效地对所有特征值的集合进行编码,并在谱域中执行自注意,从而形成可学习的集合到集合的谱滤波器。我们还设计了一个具有可学习基础的解码器,以实现非局部图卷积。重要的是,Specformer与置换是等变的。通过堆叠多个Specformer层,可以构建强大的光谱GNN。在合成数据集上,我们证明了我们的Specformer可以比其他光谱GNN更好地恢复地面实况光谱滤波器。在真实世界的图数据集上进行的节点级和图级任务的广泛实验表明,我们的Specformer优于最先进的GNN,并学习有意义的频谱模式。代码和数据可在https://github.com/bdy9527/Specformer上获得。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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