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[2602.18837] L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations
Summary
The paper presents L2G-Net, a novel spectral graph neural network that utilizes Cauchy factorizations to enhance the modeling of long-range dependencies in graphs while maintaining computational efficiency.
Why It Matters
This research addresses the limitations of existing spectral methods in graph neural networks, which often struggle with long-range dependencies and computational complexity. By introducing L2G-Net, the authors provide a more efficient way to leverage spectral representations, potentially advancing applications in various fields such as social network analysis and recommendation systems.
Key Takeaways
- L2G-Net improves the efficiency of spectral graph neural networks by avoiding full eigendecompositions.
- The new method processes spectral representations of subgraphs, enhancing the modeling of long-range dependencies.
- L2G-Net demonstrates competitive performance with fewer learnable parameters compared to existing techniques.
Computer Science > Machine Learning arXiv:2602.18837 (cs) [Submitted on 21 Feb 2026] Title:L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations Authors:Samuel Fernández-Menduiña, Eduardo Pavez, Antonio Ortega View a PDF of the paper titled L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations, by Samuel Fern\'andez-Mendui\~na and 2 other authors View PDF 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 compl...