Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND
<|reference_start|>Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND: 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}.<|reference_end|>
@article{kang2024unleashing,
    title={Unleashing the Potential of Fractional Calculus in Graph Neural Networks
  with FROND},
    author={Qiyu Kang and Kai Zhao and Qinxu Ding and Feng Ji and Xuhao Li and
  Wenfei Liang and Yang Song and Wee Peng Tay},
    journal={arXiv preprint arXiv:2404.17099},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.17099},
    primaryClass={cs.LG cs.NE}
}