Residual Hyperbolic Graph Convolution Networks

• URL: http://arxiv.org/abs/2412.03825v1
• Date: Thu, 05 Dec 2024 02:38:45 GMT
• Title: Residual Hyperbolic Graph Convolution Networks
• Authors: Yangkai Xue, Jindou Dai, Zhipeng Lu, Yuwei Wu, Yunde Jia,
• Abstract summary: Hyperbolic graph convolutional networks (HGCNs) have demonstrated representational capabilities of modeling hierarchical-structured graphs. Over-smoothing may occur as the number of model layers increases, limiting the representation capabilities of most current HGCN models. We propose residual hyperbolic graph convolutional networks (R-HGCNs) to address the over-smoothing problem.
• Score: 24.380072966869932
• License:
• Abstract: Hyperbolic graph convolutional networks (HGCNs) have demonstrated representational capabilities of modeling hierarchical-structured graphs. However, as in general GCNs, over-smoothing may occur as the number of model layers increases, limiting the representation capabilities of most current HGCN models. In this paper, we propose residual hyperbolic graph convolutional networks (R-HGCNs) to address the over-smoothing problem. We introduce a hyperbolic residual connection function to overcome the over-smoothing problem, and also theoretically prove the effectiveness of the hyperbolic residual function. Moreover, we use product manifolds and HyperDrop to facilitate the R-HGCNs. The distinctive features of the R-HGCNs are as follows: (1) The hyperbolic residual connection preserves the initial node information in each layer and adds a hyperbolic identity mapping to prevent node features from being indistinguishable. (2) Product manifolds in R-HGCNs have been set up with different origin points in different components to facilitate the extraction of feature information from a wider range of perspectives, which enhances the representing capability of R-HGCNs. (3) HyperDrop adds multiplicative Gaussian noise into hyperbolic representations, such that perturbations can be added to alleviate the over-fitting problem without deconstructing the hyperbolic geometry. Experiment results demonstrate the effectiveness of R-HGCNs under various graph convolution layers and different structures of product manifolds.

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