Hyperbolic Busemann Neural Networks
This work provides a novel method for handling hierarchical data in neural networks, which is incremental but offers practical gains for domains like genomics and network analysis.
The paper tackles the problem of representing hierarchical and tree-structured data by introducing Busemann MLR and Busemann FC layers that operate directly in hyperbolic space, resulting in improved effectiveness and efficiency in experiments on tasks like image classification and link prediction.
Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural networks require intrinsic and efficient components that operate directly in hyperbolic space. In this work, we lift two core components of neural networks, Multinomial Logistic Regression (MLR) and Fully Connected (FC) layers, into hyperbolic space via Busemann functions, resulting in Busemann MLR (BMLR) and Busemann FC (BFC) layers with a unified mathematical interpretation. BMLR provides compact parameters, a point-to-horosphere distance interpretation, batch-efficient computation, and a Euclidean limit, while BFC generalizes FC and activation layers with comparable complexity. Experiments on image classification, genome sequence learning, node classification, and link prediction demonstrate improvements in effectiveness and efficiency over prior hyperbolic layers. The code is available at https://github.com/GitZH-Chen/HBNN.