QDC: Quantum Diffusion Convolution Kernels on Graphs

TL;DR

This paper introduces Quantum Diffusion Convolution (QDC), a novel graph convolution kernel inspired by quantum particle diffusion, which enhances predictive accuracy in graph neural networks by rewiring graphs based on quantum dynamics.

Contribution

The paper proposes the QDC kernel that leverages quantum diffusion principles for graph convolution, along with a multiscale variant combining QDC and Laplacian messages, improving GCN performance.

Findings

QDC outperforms existing methods on benchmark datasets.

Quantum dynamics enable effective graph rewiring for better message passing.

Multiscale QDC enhances predictive accuracy across various tasks.

Abstract

Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and significant work has been dedicated to improving predictive accuracy by altering the ways of message passing. In this work, we propose a new convolution kernel that effectively rewires the graph according to the occupation correlations of the vertices by trading on the generalized diffusion paradigm for the propagation of a quantum particle over the graph. We term this new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In addition, we introduce a multiscale variant that combines messages from the QDC operator and the traditional combinatorial Laplacian. To understand our method, we explore the spectral dependence of homophily and the importance of quantum dynamics in the construction of a bandpass filter. Through these studies, as well as experiments on a range of datasets, we observe that QDC improves predictive performance on the widely used benchmark datasets when compared to similar methods.