Topological Polysemy (TPS), a persistent-homology-based singularity measure, correlates with real word-sense counts in a trained fastText embedding, and not with frequency

Jakubowski, Gašić & Zibrowius (2020) model word-embedding space as a "pinched manifold" in which polysemous words sit at singular/glued points, and define Topological Polysemy (TPS) via degree-0 persistent homology (Wasserstein norm of punctured-neighborhood persistence diagrams) computed directly on real self-trained fastText embeddings (65M-token SemEval-2010 corpus). TPS correlates with SemEval-2010 gold-standard sense-cluster counts (Pearson r=0.424, p<10^-3, 100 words) and, more weakly but significantly, with WordNet synset counts (r=0.085-0.122, 62,049 words) — and explicitly does NOT correlate with word frequency (r=-0.006), ruling out a frequency confound. A quantified topological-shape claim on real trained embeddings, clearing criterion (a); no causal intervention performed. See [[pinched-manifold]].