用双曲空间建模类别原型，能更好保留艺术风格的层级结构。
Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off
- 在双曲球面（Poincare ball）中构建类别原型，比欧式空间更适配树状结构。
- 双曲原型在近邻图拓扑保持上显著优于欧式原型（亲缘召回提升15.2个百分点）。
- 适合研究层次化分类、图像检索与结构化表征的学者参考。
我们研究了在层次分类模型中对类别原型布局施加树状正则化的效果，并探讨原型所处的潜在流形（欧氏空间R^d vs. 双曲球面B^d_c）是否影响该正则化满足程度而不扭曲数据似然。两种流形仅在体积增长方式上不同：双曲空间随半径呈指数增长，对树结构嵌入的失真更小，因此在相同维度下，树状正则化应更易满足。我们在WikiArt数据集（27种风格，81,446幅画作，冻结的CLIP ViT-B/16特征）上进行了150次种子重复的正则化最大似然拟合，覆盖嵌入维度、曲率和正则化强度。结果发现唯一稳健效应是：双曲原型在潜在空间中显著更好保持了最近邻图的拓扑结构（兄弟召回@5提升8.7个百分点，堂兄弟召回提升15.2个百分点；配对t检验p < 10^-4，符号一致性0.94），且该优势在三种参考树定义（人工构建谱系、基于CLIP、基于DINOv2）下均成立。分类性能方面，欧式原型与原始编码器特征上的逻辑回归持平，表明其潜空间几何无明显贡献；仅双曲拟合在局部检索上优于k-NN编码器基线。全局树保真度比较在不同参考树间不稳定，无法确定优劣。该结果首次在真实层次分类任务中，实证区分了两类自然潜空间几何对结构正则化的影响。
原文摘要 · Abstract (English)
We study a tree-structured regularizer over class-prototype layouts in a hierarchical-classification model and ask whether the choice of latent manifold for the prototypes (Euclidean R^d vs. the Poincare ball B^d_c) affects how well that regularizer can be satisfied without distorting the data likelihood. The two manifolds differ only in their volume growth: hyperbolic space grows exponentially with radius and embeds trees with provably lower distortion than R^d of matched dimension, so the structured regularizer should be cheaper to satisfy on B^d_c. Across 150 seed-replicated regularized maximum-likelihood fits spanning embedding dimension, curvature, and regularizer strength on WikiArt (27 styles, 81,446 paintings, frozen CLIP ViT-B/16 features), we find a single robust effect: Poincare prototypes preserve the topology of the nearest-neighbor graph in latent space substantially better than matched Euclidean prototypes (sibling recall@5 +8.7 pp, cousin recall +15.2 pp; paired-t p < 10^-4, sign agreement 0.94), and the gap holds across three reference-tree definitions (hand-built lineage, CLIP-derived, and DINOv2-derived). On classification, Euclidean prototypes are tied with logistic regression on raw encoder features, indicating no detectable contribution from the latent geometry; only the hyperbolic fit improves on a k-NN encoder baseline for local retrieval. Global tree-fidelity comparisons are unstable across reference trees and we do not claim a winner. The results give an empirical separation, on a real hierarchical-classification problem, between two natural latent geometries for a class-structured regularizer.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。