Distributed-Order Fractional Graph Operating Network

TL;DR

DRAGON introduces a novel continuous GNN framework using distributed-order fractional calculus, enabling flexible modeling of complex graph dynamics and demonstrating superior performance across various tasks.

Contribution

It presents the first framework incorporating learnable distributions over derivative orders in fractional GNNs, capturing intricate dynamics beyond traditional models.

Findings

Superior performance on multiple graph learning tasks

Flexible modeling of complex graph dynamics

Effective capture of non-Markovian processes

Abstract

We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.