  Representation learning over temporal networks has drawn considerable
attention in recent years. Efforts are mainly focused on modeling structural
dependencies and temporal evolving regularities in Euclidean space which,
however, underestimates the inherent complex and hierarchical properties in
many real-world temporal networks, leading to sub-optimal embeddings. To
explore these properties of a complex temporal network, we propose a hyperbolic
temporal graph network (HTGN) that fully takes advantage of the exponential
capacity and hierarchical awareness of hyperbolic geometry. More specially,
HTGN maps the temporal graph into hyperbolic space, and incorporates hyperbolic
graph neural network and hyperbolic gated recurrent neural network, to capture
the evolving behaviors and implicitly preserve hierarchical information
simultaneously. Furthermore, in the hyperbolic space, we propose two important
modules that enable HTGN to successfully model temporal networks: (1)
hyperbolic temporal contextual self-attention (HTA) module to attend to
historical states and (2) hyperbolic temporal consistency (HTC) module to
ensure stability and generalization. Experimental results on multiple
real-world datasets demonstrate the superiority of HTGN for temporal graph
embedding, as it consistently outperforms competing methods by significant
margins in various temporal link prediction tasks. Specifically, HTGN achieves
AUC improvement up to 9.98% for link prediction and 11.4% for new link
prediction. Moreover, the ablation study further validates the representational
ability of hyperbolic geometry and the effectiveness of the proposed HTA and
HTC modules.
