2020/09/30 by Fangda Gu, Heng Chang, Wenwu Zhu +2 · 1 citation
Computer Science · Mathematics · #cs.LG #stat.ML
published as Advances in Neural Information Processing Systems 33 (2020) 11984-11995 · Accepted by NeurIPS 2020 at: https://papers.nips.cc/paper/2020/hash/8b5c8441a8ff8e151b191c53c1842a38-Abstract.html
arxiv created 2021/06/01 · arxiv updated 2021/06/02
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.