双曲 Busemann 神经网络
Hyperbolic Busemann Neural Networks
把 MLR 和全连接层搬到双曲空间（BMLR/BFC），为需要建模层级/树状结构的视觉表征（如类别层级分类、细粒度识别、图结构视觉数据）提供可直接替换的层，且参数更紧凑、批量计算更高效。
原文依据 we lift two core components of neural networks, Multinomial Logistic Regression (MLR) and Fully Connected (FC) layers, into hyperbolic space via Busemann functions
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论双曲空间由于具有指数级体积增长的特性，为表示层级化和树状结构数据提供了自然的几何结构。为利用这些优势，神经网络需要能够直接在双曲空间中运行的内在且高效的组件。在本工作中，我们通过 Busemann 函数将神经网络的两个核心组件——多项逻辑回归（MLR）和全连接（FC）层——提升到双曲空间，得到 Busemann MLR（BMLR）和 Busemann FC（BFC）层，并给出统一的数学解释。BMLR 具有参数紧凑、点到超球面距离的解释、批量高效计算以及欧氏极限等特性，而 BFC 以相当的复杂度推广了 FC 层和激活层。在图像分类、基因组序列学习、节点分类和链接预测上的实验表明，相较于先前的双曲层，该方法在有效性和效率上均有提升。代码见 https://github.com/GitZH-Chen/HBNN。
英文原文摘要 1014 字符
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.