L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations
arXiv:2602.18837v1 Announce Type: new Abstract: Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in spectral representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce a novel factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. We use this factorization to propose a new class of spectral GNNs, which we term L2G-Net (Local-to-Global Net). Unlike existing spectral methods, which are either fully global (when they use the GFT) or local (when they use polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. O
arXiv:2602.18837v1 Announce Type: new Abstract: Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in spectral representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce a novel factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. We use this factorization to propose a new class of spectral GNNs, which we term L2G-Net (Local-to-Global Net). Unlike existing spectral methods, which are either fully global (when they use the GFT) or local (when they use polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the subgraph interface size. Experiments on benchmarks stressing non-local dependencies show that L2G-Net outperforms existing spectral techniques and is competitive with the state-of-the-art with orders of magnitude fewer learnable parameters.
Executive Summary
The article introduces L2G-Net, a novel spectral graph neural network that leverages a factorization of the graph Fourier transform into operators acting on subgraphs. This approach enables the efficient processing of spectral representations of subgraphs and their combination via structured matrices, avoiding full eigendecompositions and reducing computational complexity. L2G-Net demonstrates competitive performance with state-of-the-art methods while requiring significantly fewer learnable parameters, making it a promising solution for modeling long-range dependencies in graphs.
Key Points
- ▸ Introduction of L2G-Net, a novel spectral graph neural network
- ▸ Factorization of the graph Fourier transform into subgraph operators
- ▸ Efficient processing of spectral representations with reduced computational complexity
Merits
Efficient Spectral Processing
L2G-Net's factorization approach enables efficient processing of spectral representations, reducing computational complexity and avoiding full eigendecompositions.
Competitive Performance
L2G-Net demonstrates competitive performance with state-of-the-art methods, despite requiring significantly fewer learnable parameters.
Demerits
Limited Interpretability
The use of structured matrices and subgraph operators may limit the interpretability of L2G-Net's results and decisions.
Expert Commentary
The introduction of L2G-Net represents a significant advancement in the field of graph neural networks, as it addresses the long-standing issue of efficient spectral processing. By leveraging a factorization of the graph Fourier transform, L2G-Net enables the efficient processing of spectral representations, making it a promising solution for modeling long-range dependencies in graphs. The competitive performance of L2G-Net, despite requiring fewer learnable parameters, highlights its potential for practical applications. However, further research is needed to fully understand the implications of L2G-Net's approach and to explore its potential applications in various domains.
Recommendations
- ✓ Further evaluation of L2G-Net on diverse graph-based tasks and datasets to assess its generalizability and robustness.
- ✓ Investigation of L2G-Net's potential applications in areas like network analysis, recommendation systems, and social network analysis, with a focus on its efficiency and effectiveness.
