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.
@article{arxiv.2009.06211,
title = {Implicit Graph Neural Networks},
author = {Fangda Gu and Heng Chang and Wenwu Zhu and Somayeh Sojoudi and Laurent El Ghaoui},
journal= {arXiv preprint arXiv:2009.06211},
year = {2021}
}
Comments
Accepted by NeurIPS 2020 at: https://papers.nips.cc/paper/2020/hash/8b5c8441a8ff8e151b191c53c1842a38-Abstract.html