用布塞曼函数构建新型双曲神经网络层，提升层次数据建模效率
Hyperbolic Busemann Neural Networks
- 用布塞曼函数将MLR和全连接层迁移到双曲空间
- 在图像分类等任务上优于已有双曲网络，参数更紧凑
- 适合处理树状结构数据，如基因序列与社交网络
双曲空间因其指数级体积增长特性，天然适合表示层次化与树状结构数据。为充分利用这一优势，神经网络需具备直接在双曲空间中操作的内在且高效组件。本文通过布塞曼函数，将多类逻辑回归（MLR）和全连接（FC）层迁移至双曲空间，提出布塞曼MLR（BMLR）与布塞曼FC（BFC）层，具有统一的数学解释。BMLR实现参数紧凑、点到超球面距离解释、批处理高效计算及欧氏极限；BFC则在复杂度相当的前提下推广了全连接与激活层功能。在图像分类、基因组序列学习、节点分类和链接预测任务上的实验表明，该方法在有效性和效率上均优于先前双曲层。代码已开源：https://github.com/GitZH-Chen/HBNN。
原文摘要 · Abstract (English)
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.
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