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

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

Halle B #87
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Thu 9 May 1:45 a.m. PDT — 3:45 a.m. PDT


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{}.

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