IGNN-Solver: A Graph Neural Solver for Implicit Graph Neural Networks

Implicit graph neural networks (IGNNs), which exhibit strong expressive power with a single layer, have recently demonstrated remarkable performance in capturing long-range dependencies (LRD) in underlying graphs while effectively mitigating the over-smoothing problem. However, IGNNs rely on computationally expensive fixed-point iterations, which lead to significant speed and scalability limitations, hindering their application to large-scale graphs. To achieve fast fixed-point solving for IGNNs, we propose a novel graph neural solver, IGNN-Solver, which leverages the generalized Anderson Acceleration method, parameterized by a small GNN, and learns iterative updates as a graph-dependent temporal process. Extensive experiments demonstrate that the IGNN-Solver significantly accelerates inference, achieving a $1.5\times$ to $8\times$ speedup without sacrificing accuracy. Moreover, this advantage becomes increasingly pronounced as the graph scale grows, facilitating its large-scale deployment in real-world applications.

@article{lin2025_2410.08524,
  title={ IGNN-Solver: A Graph Neural Solver for Implicit Graph Neural Networks },
  author={ Junchao Lin and Zenan Ling and Zhanbo Feng and Jingwen Xu and Minxuan Liao and Feng Zhou and Tianqi Hou and Zhenyu Liao and Robert C. Qiu },
  journal={arXiv preprint arXiv:2410.08524},
  year={ 2025 }
}