Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND
Authors: Qiyu Kang,Kai Zhao,Qinxu Ding,Feng Ji,Xuhao Li,Wenfei Liang,Yang Song,Wee Peng Tay
Presentation: ICLR 2024,Spotlight

Abstract: We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. 
We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process.
We demonstrate analytically that oversmoothing can be mitigated in this setting.
Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs.
The code is available at \url{https://github.com/zknus/ICLR2024-FROND}.