Embedding Text in Hyperbolic Spaces
Table 3: Words in order of increasing hyperbolic norm which contain the substring indicated in the top row. Their counts in the text8 corpus are also shown. Dimension size d=20.
['[BOLD] “bank”  [BOLD] Word', '[BOLD] “bank”  [BOLD] Count', '[BOLD] “bank”  [BOLD] Norm', '[BOLD] “music”  [BOLD] Word', '[BOLD] “music”  [BOLD] Count', '[BOLD] “music”  [BOLD] Norm', '[BOLD] “dog”  [BOLD] Word', '[BOLD] “dog”  [BOLD] Count', '[BOLD] “dog”  [BOLD] Norm', '[BOLD] “great”  [BOLD] Word', '[BOLD] “great”  [BOLD] Count', '[BOLD] “great”  [BOLD] Norm']
We also show the counts in the corpus of these words, which are correlated to the number of contexts they occur in. As expected, words occurring in fewer contexts have higher hyperbolic norm, and this corresponds to increased specificity as we move down the list; for example “bulldogs” has a higher norm than “dog”, and “greatest” has a higher norm than “great”. The Spearman correlation between 1/f, where f is the frequency of a word in the corpus, and the norm of its embedding is 0.77.