Papers › Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND

Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND

26 Apr 2024arXiv:2404.17099archive 2025-07-28

Qiyu Kang, Kai Zhao, Qinxu Ding, Feng Ji, Xuhao Li, Wenfei Liang, Yang song, Wee Peng Tay

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}.

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GLmethod zknus/torchfde/torchfde/riemann_liouville_solver.py official repository ran no licence file found · pointer only · 4b77efb8ffa16337 · report
Predictor zknus/torchfde/torchfde/explicit_solver.py official repository ran no licence file found · pointer only · ae5d259ba0676d48 · report
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split_data zknus/iclr2024-frond/src/data.py official repository unverified no licence file found · pointer only · 58130ac3739b817c · report

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Graph Neural NetworkGraph Representation LearningRepresentation Learning

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DiffusionGraph Neural Network

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