Enhanced Graph Neural Networks using K-Hop Gaussian Diffusion

2026-06-16

AI Summary

This work addresses the limitation of conventional graph neural networks (GNNs), which rely on single-hop neighborhood message passing and struggle to effectively integrate local and global information in graphs with high edge noise or complex topology. To overcome this, the authors propose the K-Hop Gaussian diffusion kernel as a preprocessing module that precedes standard GNN layers. By leveraging a Gaussian-weighted multi-hop diffusion mechanism, this approach balances fine-grained local structure with long-range dependencies while suppressing distant noise. The method outperforms existing diffusion strategies based on personalized PageRank (PPR) and heat kernels by better preserving local connectivity and attenuating irrelevant remote signals. Extensive experiments demonstrate consistent and significant performance gains over both traditional message-passing GNNs and current diffusion-based methods across multiple benchmark datasets, with particularly pronounced improvements in high-noise or topologically intricate graph settings.

Abstract

Most graph neural network (GNN) cores rely on graph convolutions, typically implemented as message passing between direct (single-hop) neighbors. In many real-world graphs, edges can be noisy or poorly defined, limiting information propagation to local neighborhoods. Existing diffusion kernels, such as Personalized PageRank (PPR) and Heat Kernel, alleviate this issue through global propagation, but still struggle with complex local structures and distant node noise. To address these limitations, we propose a K-Hop Gaussian (KHG) diffusion kernel as a preprocessing module for graph data. KHG introduces multi-hop diffusion with Gaussian weighting for remote nodes, balancing local and global information propagation before applying standard GNNs. Experiments on multiple benchmark datasets demonstrate that KHG significantly outperforms traditional message-passing GNNs, as well as PPR and Heat Kernel diffusion, particularly in noisy or structurally complex graphs.

Problem

• Graph Neural Networks
• Message Passing
• Diffusion Kernels
• Noisy Graphs
• Information Propagation

Innovation

• K-Hop Gaussian Diffusion
• Graph Neural Networks
• Multi-hop Diffusion
• Gaussian Weighting
• Noisy Graphs