Hyperbolic Busemann Neural Networks

TL;DR

This paper introduces hyperbolic Busemann neural network components, BMLR and BFC layers, enabling efficient and effective learning directly in hyperbolic space for hierarchical data, with demonstrated improvements across various tasks.

Contribution

It develops Busemann-based hyperbolic neural network layers, providing a unified, efficient approach for hyperbolic deep learning with broad application potential.

Findings

Improved accuracy in image classification tasks.

Enhanced efficiency in hyperbolic neural computations.

Effective learning on hierarchical and graph-structured data.

Abstract

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.