  Word embeddings represent language vocabularies as clouds of $d$-dimensional
points. We investigate how information is conveyed by the general shape of
these clouds, outside 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. We use these distance matrices to construct
language phylogenetic trees over 81 Indo-European languages. Careful evaluation
shows that our reconstructed trees exhibit strong similarities to the reference
tree.
