Spectral Neural Graph Sparsification

2025-10-31

AI Summary

Graph neural networks (GNNs) face fundamental trade-offs between modeling accuracy and computational efficiency due to reliance on fixed graph structures and susceptibility to oversmoothing. To address this, we propose Spectral-Preserving Networks (SPN), a differentiable graph sparsification framework that jointly optimizes graph topology and node features. SPN introduces a joint graph evolution layer coupled with a spectral consistency loss, enabling co-adaptive evolution of graph structure and feature representations while preserving critical spectral properties of the original graph. By integrating spectral graph theory with end-to-end learning, SPN embeds spectral-domain regularization to ensure structural fidelity during sparsification. Extensive experiments demonstrate that SPN achieves state-of-the-art performance across multiple benchmark datasets in downstream tasks—including community detection and influence propagation—outperforming existing methods significantly. Notably, SPN exhibits superior generalization and robustness in node-level sparsification scenarios.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning, they remain constrained by reliance on fixed structures and susceptibility to over-smoothing. We propose the Spectral Preservation Network, a new framework for graph representation learning that generates reduced graphs serving as faithful proxies of the original, enabling downstream tasks such as community detection, influence propagation, and information diffusion at a reduced computational cost. The Spectral Preservation Network introduces two key components: the Joint Graph Evolution layer and the Spectral Concordance loss. The former jointly transforms both the graph topology and the node feature matrix, allowing the structure and attributes to evolve adaptively across layers and overcoming the rigidity of static neighborhood aggregation. The latter regularizes these transformations by enforcing consistency in both the spectral properties of the graph and the feature vectors of the nodes. We evaluate the effectiveness of Spectral Preservation Network on node-level sparsification by analyzing well-established metrics and benchmarking against state-of-the-art methods. The experimental results demonstrate the superior performance and clear advantages of our approach.

Problem

• Overcoming fixed graph structure limitations in neural networks
• Reducing computational cost for graph-based downstream tasks
• Addressing over-smoothing in Graph Convolutional Networks

Innovation

• Joint Graph Evolution layer transforms topology and features
• Spectral Concordance loss enforces spectral and feature consistency
• Generates reduced graphs as faithful proxies for original