用几何分析法揭示多语言嵌入中的语义结构与模型缺陷
Geometric Patterns of Meaning: A PHATE Manifold Analysis of Multi-lingual Embeddings
- 通过PHATE降维技术在四个语言层级分析语义几何
- 中文部首出现几何坍塌，暴露模型混淆语义与结构的缺陷
- 阿拉伯数字呈螺旋分布，挑战传统语义分布假设
我们提出一个多层级分析框架，用于研究多语言嵌入中的语义几何结构，借助Semanscope（一种应用PHATE流形学习的可视化工具）在四个语言层次展开分析。对涵盖子字符成分、字母系统、语义领域和数值概念的多种数据集进行研究，揭示出系统性的几何模式与现有嵌入模型的关键局限。在子字符层面，纯结构元素（如中文部首）呈现几何坍塌，凸显模型难以区分语义与结构成分；在字符层面，不同书写系统展现出独特的几何特征；在词层面，英语、中文、德语的20个语义领域中，实词形成聚类-分支模式；阿拉伯数字则沿螺旋轨迹组织，违背标准分布语义假设。这些发现确立了PHATE流形学习作为研究嵌入空间语义结构及验证模型有效性的重要工具。
原文摘要 · Abstract (English)
We introduce a multi-level analysis framework for examining semantic geometry in multilingual embeddings, implemented through Semanscope (a visualization tool that applies PHATE manifold learning across four linguistic levels). Analysis of diverse datasets spanning sub-character components, alphabetic systems, semantic domains, and numerical concepts reveals systematic geometric patterns and critical limitations in current embedding models. At the sub-character level, purely structural elements (Chinese radicals) exhibit geometric collapse, highlighting model failures to distinguish semantic from structural components. At the character level, different writing systems show distinct geometric signatures. At the word level, content words form clustering-branching patterns across 20 semantic domains in English, Chinese, and German. Arabic numbers organize through spiral trajectories rather than clustering, violating standard distributional semantics assumptions. These findings establish PHATE manifold learning as an essential analytic tool not only for studying geometric structure of meaning in embedding space, but also for validating the effectiveness of embedding models in capturing semantic relationships.
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