arXiv:2605.05759v2 Announce Type: replace Abstract: It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of universality for higher-order signals. To go beyond this bound, we propose the Full-Spectrum GNNs (FSpecGNNs), a second-order generalization of classical spectral GNNs. FSpecGNN advances spectral filtering from two perspectives: (1) it lifts signals from the node domain to the node-pair domain; and (2) it exten
The continuous drive for more powerful and efficient AI models necessitates advances in fundamental graph neural network architectures, particularly for complex high-dimensional data.
Improved expressive power and scalability in GNNs unlock new capabilities for AI in modeling relationships and structures, impacting diverse fields from drug discovery to social network analysis.
Traditional spectral GNNs, limited by the 1-dimensional Weisfeiler-Lehman test, are being surpassed by new architectures like FSpecGNNs that can model higher-order signals by lifting to the node-pair domain.
- · AI researchers
- · Deep learning practitioners
- · Industries relying on complex data analysis
- · Graph AI platform providers
- · Legacy GNN architectures
- · Applications bottlenecked by current GNN expressivity
More accurate and nuanced AI models for relational data become feasible, improving predictive capabilities.
The ability to analyze higher-order signals could lead to breakthroughs in areas requiring complex interaction modeling, such as material science or systemic risk assessment.
Advances in fundamental AI algorithms contribute to the broader availability of sophisticated AI tools, potentially accelerating adoption across various sectors and industries.
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