  The number of senses of a given word, or polysemy, is a very subjective
notion, which varies widely across annotators and resources. We propose a novel
method to estimate polysemy, based on simple geometry in the contextual
embedding space. Our approach is fully unsupervised and purely data-driven. We
show through rigorous experiments that our rankings are well correlated (with
strong statistical significance) with 6 different rankings derived from famous
human-constructed resources such as WordNet, OntoNotes, Oxford, Wikipedia etc.,
for 6 different standard metrics. We also visualize and analyze the correlation
between the human rankings. A valuable by-product of our method is the ability
to sample, at no extra cost, sentences containing different senses of a given
word. Finally, the fully unsupervised nature of our method makes it applicable
to any language.
  Code and data are publicly available at
https://github.com/ksipos/polysemy-assessment .
  The paper was accepted as a long paper at EACL 2021.
