Implicit Graph Neural Networks
Fangda Gu, Heng Chang, Wenwu Zhu, Somayeh Sojoudi, Laurent El Ghaoui
Abstract
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 state-of-the-art GNN models.
BibTeX
@inproceedings{NEURIPS2020_8b5c8441,
author = {Gu, Fangda and Chang, Heng and Zhu, Wenwu and Sojoudi, Somayeh and El Ghaoui, Laurent},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
pages = {11984--11995},
publisher = {Curran Associates, Inc.},
title = {Implicit Graph Neural Networks},
url = {https://proceedings.neurips.cc/paper_files/paper/2020/file/8b5c8441a8ff8e151b191c53c1842a38-Paper.pdf},
volume = {33},
year = {2020}
}