Recently, there has been a raising surge of momentum for deep representation learning in hyperbolic spaces due to their high capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer it as hyperbolic deep neural network in this paper. Such a hyperbolic neural architecture potentially leads to drastically compact models with much more physical interpretability than its counterpart in Euclidean space. To stimulate future research, this paper presents a coherent and comprehensive review of the literature around the neural components in the construction of hyperbolic deep neural networks, as well as the generalization of the leading deep approaches to the hyperbolic space. It also presents current applications around various machine learning tasks on several publicly available datasets, together with insightful observations and identifying open questions and promising future directions.

No abstract

No abstract

No abstract

No abstract