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

Junchao Lin, Zenan Ling, Zhanbo Feng, Feng Zhou, Jingwen Xu, Robert C Qiu

Keywords: implicit deep learning, deep equilibrium models, implicit graph neural networks

TL;DR: We developed a solver for implicit graph neural networks with a tiny graph neural network.

Abstract: 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.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 2887