Hyperbolic Busemann Neural Networks
arXiv:2602.18858v1 Announce Type: new 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 layer
arXiv:2602.18858v1 Announce Type: new 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.
Executive Summary
This article introduces Hyperbolic Busemann Neural Networks, which leverage the benefits of hyperbolic spaces to represent hierarchical and tree-structured data. The authors propose Busemann MLR and Busemann FC layers, providing a unified mathematical interpretation and demonstrating improvements in effectiveness and efficiency over prior hyperbolic layers. The results show promise in various applications, including image classification, genome sequence learning, node classification, and link prediction.
Key Points
- ▸ Introduction of Hyperbolic Busemann Neural Networks
- ▸ Proposal of Busemann MLR and Busemann FC layers
- ▸ Demonstrated improvements in effectiveness and efficiency
Merits
Improved Representation
Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data, allowing for more accurate and efficient modeling.
Unified Mathematical Interpretation
The proposed Busemann MLR and Busemann FC layers provide a unified mathematical interpretation, simplifying the understanding and implementation of hyperbolic neural networks.
Demerits
Limited Explorations
The article primarily focuses on the technical aspects of Hyperbolic Busemann Neural Networks, with limited discussion on the broader implications and potential applications.
Expert Commentary
The introduction of Hyperbolic Busemann Neural Networks marks a significant step forward in the development of geometric deep learning techniques. By leveraging the properties of hyperbolic spaces, the proposed Busemann MLR and Busemann FC layers demonstrate improved representation and efficiency. However, further research is needed to fully explore the potential applications and implications of this technology. As the field continues to evolve, it is essential to consider the broader societal and economic impacts of these advances.
Recommendations
- ✓ Further exploration of the potential applications and implications of Hyperbolic Busemann Neural Networks
- ✓ Investigation into the integration of Hyperbolic Busemann Neural Networks with other geometric deep learning techniques
