Long-Range Graph Wavelet Networks

2025-09-08

AI Summary

Existing wavelet-based graph neural networks suffer from narrow receptive fields and weak long-range information propagation due to reliance on low-order polynomial approximations. To address this, we propose the Long-Range Graph Wavelet Network (LGWNet), the first framework that decouples wavelet filtering into two complementary components: (i) local, low-order polynomial aggregation for short-range dependencies, and (ii) a globally propagating, flexibly parameterized mechanism in the spectral domain for capturing long-range interactions. This design unifies multi-scale dependency modeling by integrating multi-resolution signal processing with spectral-domain parameterization, achieving significant receptive field expansion while preserving computational efficiency. On long-range graph benchmark tasks, LGWNet achieves state-of-the-art performance among wavelet-based methods; it also attains competitive results on standard short-range datasets, demonstrating its robust multi-scale representational capacity and generalizability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Modeling long-range interactions, the propagation of information across distant parts of a graph, is a central challenge in graph machine learning. Graph wavelets, inspired by multi-resolution signal processing, provide a principled way to capture both local and global structures. However, existing wavelet-based graph neural networks rely on finite-order polynomial approximations, which limit their receptive fields and hinder long-range propagation. We propose Long-Range Graph Wavelet Networks (LR-GWN), which decompose wavelet filters into complementary local and global components. Local aggregation is handled with efficient low-order polynomials, while long-range interactions are captured through a flexible spectral domain parameterization. This hybrid design unifies short- and long-distance information flow within a principled wavelet framework. Experiments show that LR-GWN achieves state-of-the-art performance among wavelet-based methods on long-range benchmarks, while remaining competitive on short-range datasets.

Problem

• Modeling long-range interactions in graph machine learning
• Overcoming limitations of finite-order polynomial approximations
• Unifying local and global graph structures efficiently

Innovation

• Decomposes wavelet filters into local and global components
• Uses low-order polynomials for efficient local aggregation
• Employs spectral parameterization for flexible long-range interactions