Hyperbolic Deep Neural Networks: A Survey

Recently, hyperbolic deep neural networks (HDNNs) have been gaining momentum as the deep representations in the hyperbolic space provide high fidelity embeddings with few dimensions, especially for data possessing hierarchical structure. Such a hyperbolic neural architecture is quickly extended to different scientific fields, including natural language processing, single-cell RNA-sequence analysis, graph embedding, financial analysis, and computer vision. The promising results demonstrate its superior capability, significant compactness of the model, and a substantially better physical interpretability than its counterpart in the euclidean space. To stimulate future research, this paper presents a comprehensive review of the literature around the neural components in the construction of HDNN, as well as the generalization of the leading deep approaches to the hyperbolic space. It also presents current applications of various tasks, together with insightful observations and identifying open questions and promising future directions.

Automated summary

Hyperbolic deep neural networks (HDNNs) have shown superior performance and better physical interpretability in hierarchical structured data, and have been widely applied in different scientific fields. This paper provides a comprehensive review of the neural components in HDNN, demonstrating the potential of extending leading deep approaches to hyperbolic space and applications in various tasks.