mlsanityData to 7 Oct 2026

Spectral GNN via Two-dimensional (2-D) Graph Convolution

arXiv 2404.04559 ↗First posted 6 Apr 2024cs.LG cs.NA eess.SPcited by 3

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Abstract (arXiv)

Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph learning. As an essential part of spectral GNNs, spectral graph convolution extracts crucial frequency information in graph data, leading to superior performance of spectral GNNs in downstream tasks. However, in this paper, we show that existing spectral GNNs remain critical drawbacks in performing the spectral graph convolution. Specifically, considering the spectral graph convolution as a construction operation towards target output, we prove that existing popular convolution paradigms cannot construct the target output with mild conditions on input graph signals, causing spectral GNNs to fall into suboptimal solutions. To address the issues, we rethink the spectral graph convolution from a more general two-dimensional (2-D) signal convolution perspective and propose a new convolution paradigm, named 2-D graph convolution. We prove that 2-D graph convolution unifies existing graph convolution paradigms, and is capable to construct arbitrary target output. Based on the proposed 2-D graph convolution, we further propose ChebNet2D, an efficient and effective GNN implementation of 2-D graph convolution through applying Chebyshev interpolation. Extensive experiments on benchmark datasets demonstrate both effectiveness and efficiency of the ChebNet2D.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 37 of its 63 references that are in the map. First posted on arXiv 6 Apr 2024.

Builds on

37 of 63 references.

References · 37

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25 more
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Cited by year

Citing papers per year: 2024: 2; 2025: 1.

3 papers.

  1. 2024ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filterscited by 5
  2. 2025Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarseningcited by 2
  3. 2024Polynomial Selection in Spectral Graph Neural Networks: An Error-Sum of Function Slices Approachcited by 1