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 tiny GNN, and learns iterative updates as a graph-dependent temporal process. To improve effectiveness on large-scale graph tasks, we further integrate sparsification and storage compression methods, specifically tailored for the IGNN-Solver, into its design. Distinct from previous solvers and IGNN variants, IGNN-Solver treats the solver itself as a learnable, graph-aware dynamical system, enabling solver-level acceleration. Extensive experiments demonstrate that the IGNN-Solver significantly accelerates inference on both small- and large-scale tasks, achieving a 1.5× to 8× speedup without sacrificing accuracy. This advantage becomes more pronounced as the graph scale grows, facilitating its large-scale deployment in real-world applications.