arXiv:2602.23981cs.LGcs.AI2026-02被引 1

提出全内在的双曲神经网络,提升层次数据建模能力。

Intrinsic Lorentz Neural Network

  • 用洛伦兹模型内嵌计算,避免欧氏与双曲混合操作。
  • 在CIFAR和基因数据集上超越现有双曲模型和欧氏基线。
  • 适合处理具有层次结构的数据,如生物谱系或分类体系。

现实数据常呈现潜在的层次结构,可自然用双曲几何表示。尽管近期双曲神经网络表现良好,但多数架构仍部分内在,混合使用欧氏与双曲操作或依赖外在参数化。为此,本文提出完全内在的双曲架构——内禀洛伦兹神经网络(ILNN),所有计算均在洛伦兹模型中进行。核心是新型点到超平面全连接层(FC),以闭式双曲距离替代传统欧氏仿射输出,确保决策函数符合内在曲率。围绕该层设计了内禀模块:洛伦兹批归一化(GyroLBN),结合陀螺中心化与缩放,优于LBN和GyroBN且训练更快;陀螺加性偏置;基于双伽马函数的洛伦兹补丁拼接算子,对齐特征块的期望对数半径;以及洛伦兹丢弃层。在CIFAR-10/100及两个基因组基准(TEB和GUE)上的实验表明,ILNN在性能与计算成本上均达双曲模型最优,并持续超越强欧氏基线。

原文摘要 · Abstract (English)

Real-world data frequently exhibit latent hierarchical structures, which can be naturally represented by hyperbolic geometry. Although recent hyperbolic neural networks have demonstrated promising results, many existing architectures remain partially intrinsic, mixing Euclidean operations with hyperbolic ones or relying on extrinsic parameterizations. To address it, we propose the \emph{Intrinsic Lorentz Neural Network} (ILNN), a fully intrinsic hyperbolic architecture that conducts all computations within the Lorentz model. At its core, the network introduces a novel \emph{point-to-hyperplane} fully connected layer (FC), replacing traditional Euclidean affine logits with closed-form hyperbolic distances from features to learned Lorentz hyperplanes, thereby ensuring that the resulting geometric decision functions respect the inherent curvature. Around this fundamental layer, we design intrinsic modules: GyroLBN, a Lorentz batch normalization that couples gyro-centering with gyro-scaling, consistently outperforming both LBN and GyroBN while reducing training time. We additionally proposed a gyro-additive bias for the FC output, a Lorentz patch-concatenation operator that aligns the expected log-radius across feature blocks via a digamma-based scale, and a Lorentz dropout layer. Extensive experiments conducted on CIFAR-10/100 and two genomic benchmarks (TEB and GUE) illustrate that ILNN achieves state-of-the-art performance and computational cost among hyperbolic models and consistently surpasses strong Euclidean baselines. The code is available at \href{https://github.com/Longchentong/ILNN}{\textcolor{magenta}{this url}}.

双曲神经网络层次结构洛伦兹模型内在架构

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