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Implicit Graph Neural Networks

Fangda Gu · Heng Chang · Wenwu Zhu · Somayeh Sojoudi · Laurent El Ghaoui

Poster Session 6 #1842

Keywords: [ Deep Learning ] [ Applications -> Computer Vision; Applications -> Denoising; Deep Learning -> Deep Autoencoders; Deep Learning ] [ Predictive Mod ]


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.

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