Word embeddings represent language vocabularies as clouds of $d$-dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of representing the semantic meaning of each token. Specifically, we use the notion of persistent homology from topological data analysis (TDA) to measure the distances between language pairs from the shape of their unlabeled embeddings. These distances quantify the degree of non-isometry of the embeddings. To distinguish whether these differences are random training errors or capture real information about the languages, we use the computed distance matrices to construct language phylogenetic trees over 81 Indo-European languages. Careful evaluation shows that our reconstructed trees exhibit strong and statistically-significant similarities to the reference.

翻译：词嵌入将语言词汇表示为$d$维点云。本研究不关注单个词汇的语义表征，而是探究这些点云的整体形状如何传递信息。具体而言，我们运用拓扑数据分析中的持续同调方法，通过未标注词嵌入的几何形态来度量语言对之间的距离。这些距离量化了词嵌入的非等距程度。为区分这些差异是随机训练误差还是真实反映了语言特性，我们基于计算得到的距离矩阵为81种印欧语系语言构建了谱系树。严谨的评估表明，重建的谱系树与参照树之间具有显著且统计意义的高度相似性。