Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs

TL;DR

This paper introduces HVGNN, a novel hyperbolic variational graph neural network that models dynamic graphs with stochastic node representations, capturing uncertainty and temporal dynamics more effectively than previous methods.

Contribution

The paper presents the first hyperbolic variational GNN for dynamic graphs, incorporating a time encoding-based Temporal GNN and a hyperbolic graph variational autoencoder.

Findings

HVGNN outperforms state-of-the-art baselines on real-world datasets.

The proposed model effectively captures dynamics and uncertainty in graph representations.

A reparameterisable sampling algorithm enables gradient-based learning in hyperbolic space.

Abstract

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling uncertainty. To bridge this gap, we propose to learn dynamic graph representation in hyperbolic space, for the first time, which aims to infer stochastic node representations. Working with hyperbolic space, we present a novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TGNN) based on a theoretically grounded time encoding approach. To model the uncertainty, we devise a hyperbolic graph variational autoencoder built upon the proposed TGNN to generate stochastic node representations of hyperbolic normal distributions. Furthermore, we introduce a reparameterisable sampling algorithm for the hyperbolic normal distribution to enable the gradient-based learning of HVGNN. Extensive experiments show that HVGNN outperforms state-of-the-art baselines on real-world datasets.