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[2602.18858] Hyperbolic Busemann Neural Networks
Summary
The paper introduces Hyperbolic Busemann Neural Networks, which enhance neural network components by adapting them to hyperbolic space, improving efficiency and effectiveness in various tasks.
Why It Matters
This research is significant as it addresses the limitations of traditional neural networks in handling hierarchical data structures. By leveraging hyperbolic geometry, the proposed models can better capture relationships in complex datasets, which is crucial for advancements in machine learning applications like image classification and genomics.
Key Takeaways
- Hyperbolic geometry allows for better representation of hierarchical data.
- Busemann MLR and BFC layers enhance neural network performance.
- The proposed methods show improvements in various applications like image classification and genome learning.
Computer Science > Machine Learning arXiv:2602.18858 (cs) [Submitted on 21 Feb 2026] Title:Hyperbolic Busemann Neural Networks Authors:Ziheng Chen, Bernhard Schölkopf, Nicu Sebe View a PDF of the paper titled Hyperbolic Busemann Neural Networks, by Ziheng Chen and 2 other authors View PDF HTML (experimental) 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 this https URL. Comments: Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2602.18858 [cs.LG] (or arXiv:2602.18858...