发表机构
BIFOLD; Technische Universität Berlin; Nanyang Technological University; University of Toronto; Vector Institute for Artificial Intelligence; RIKEN Center for AIP（柏林智能与数据科学基础研究所; 柏林工业大学; 南洋理工大学; 多伦多大学; 向量人工智能研究所; 理化学研究所先进智能研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对双曲神经网络提出几何感知相关性传播规则LRP-radial-all，满足几何表示不变性与零曲率一致性，在多个数据集上实现高效且保真的特征归因。
AI 中文摘要
双曲神经网络引入了需要在相关性传播中显式处理的几何操作。即使局部相关性守恒，等效的几何实现也可能产生不同的特征归因。我们通过几何表示不变性（GRI，即实现不变性的特化）以及零曲率一致性来研究该问题，后者要求当几何模块趋近于恒等映射时，相关性传播保持一致。我们针对以原点为中心的径向模块提出了LRP-radial-all规则，将几何缩放视为调制，并将相关性完全分配给信号分支。该规则守恒相关性，对等效的径向分解具有不变性，并满足零曲率一致性，从而为特定的庞加莱-洛伦兹对数映射构造实现GRI。相比之下，保守的LRP-half基线可能违反这两个一致性标准。在双曲MNIST、sEEG和CIFAR-10分类器上的实验评估了归因保真度、定性解释和运行时间。LRP-radial-all在数据集上实现了具有竞争力的归因保真度，其运行时间与Gradient×Input相当，且显著低于Integrated Gradients。这些发现推动了几何感知传播规则的发展，该规则区分了等效计算中的相关性守恒与一致性。
英文摘要
Hyperbolic neural networks introduce geometric operations that require explicit treatment in relevance propagation. Equivalent geometric realizations can produce different feature attributions, even when local relevance is conserved. We study this problem through Geometric Representation Invariance (GRI), a specialization of Implementation Invariance, and zero-curvature consistency, which requires identity relevance propagation when a geometric module approaches the identity. We propose LRP-radial-all for origin-centered radial modules, treating geometric scaling as modulation and assigning relevance entirely to the signal branch. The rule conserves relevance, is invariant to equivalent radial factorizations, and satisfies zero-curvature consistency, yielding GRI for a specified Poincaré-Lorentz logarithmic-map construction. In contrast, a conservative LRP-half baseline can violate both consistency criteria. Experiments on hyperbolic MNIST, sEEG, and CIFAR-10 classifiers assess attribution fidelity, qualitative explanations, and runtime. LRP-radial-all achieves competitive attribution fidelity across datasets with runtime comparable to Gradient$\times$Input and substantially lower than Integrated Gradients. These findings motivate geometry-aware propagation rules that distinguish relevance conservation from consistency across equivalent computations.
