Implicit Graph Neural Networks
This addresses a bottleneck in graph learning for tasks requiring long-range dependencies, representing an incremental improvement over existing GNN methods.
The paper tackled the problem of capturing long-range dependencies in graph-structured data with Graph Neural Networks (GNNs) by proposing Implicit Graph Neural Networks (IGNN), which use fixed-point equilibrium equations, and experiments showed that IGNNs consistently outperform state-of-the-art GNN models.
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture long-range dependencies in underlying graphs. To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving implicitly defined "state" vectors. We use the Perron-Frobenius theory to derive sufficient conditions that ensure well-posedness of the framework. Leveraging implicit differentiation, we derive a tractable projected gradient descent method to train the framework. Experiments on a comprehensive range of tasks show that IGNNs consistently capture long-range dependencies and outperform the state-of-the-art GNN models.