用三维时空几何完美表示词汇层级结构，因果关系决定语义检索。
The Geometry of Meaning: Perfect Spacetime Representations of Hierarchical Structures
- 基于有向词对构建局部层级信号，无需全局符号结构
- 在WordNet中实现82,115个名词的无歧义完美嵌入
- 以因果性替代距离进行语义访问，具近似共形不变性
我们提出一种快速算法，将层次结构嵌入三维闵可夫斯基时空。数据相关性完全由因果结构编码。模型仅依赖有向词对——局部层级信号——无需全局符号结构。我们在《WordNet》语料上应用该方法，实现了包含歧义（一个节点对应多个层次）的哺乳动物子树的完美嵌入，使层次结构完全编码于几何中，并精确复现真实标注。进一步扩展至《WordNet》中无歧义的最大子集，包含82,115个名词词元且每个词元仅对应单一层次。引入新型检索机制，以因果性而非距离决定层次访问。结果表明，离散数据可能存在完美的三维几何表示，且所得嵌入具有近乎共形不变性，暗示与广义相对论及场论的深层关联。这些发现提示：概念、类别及其相互关系——即层次化语义本身——本质上是几何的。
原文摘要 · Abstract (English)
We show that there is a fast algorithm that embeds hierarchical structures in three-dimensional Minkowski spacetime. The correlation of data ends up purely encoded in the causal structure. Our model relies solely on oriented token pairs -- local hierarchical signals -- with no access to global symbolic structure. We apply our method to the corpus of \textit{WordNet}. We provide a perfect embedding of the mammal sub-tree including ambiguities (more than one hierarchy per node) in such a way that the hierarchical structures get completely codified in the geometry and exactly reproduce the ground-truth. We extend this to a perfect embedding of the maximal unambiguous subset of the \textit{WordNet} with 82{,}115 noun tokens and a single hierarchy per token. We introduce a novel retrieval mechanism in which causality, not distance, governs hierarchical access. Our results seem to indicate that all discrete data has a perfect geometrical representation that is three-dimensional. The resulting embeddings are nearly conformally invariant, indicating deep connections with general relativity and field theory. These results suggest that concepts, categories, and their interrelations, namely hierarchical meaning itself, is geometric.
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