Hierarchical Density Order Embeddings
Table 2: KL(column||row). Cells in boldface indicate true WordNet hypernym relationships (column ⪯ row). Our model predicts a synset pair as a hypernym if the KL less than 1900, where this value is tuned based on the validation set. Most relationship pairs are correctly predicted except for the underlined cells.
['[EMPTY]', 'city', 'location', 'living_thing', 'whole', 'object', 'physical_entity']
Most hypernym relationships exhibit encapsulation behavior where the hypernym encompasses the synset that entails it. For instance, the distribution of whole.n.02 is subsumed in the distribution of physical_entity.n.01. Note that location.n.01 is not entirely encapsulated by physical_entity.n.01 under this visualization. However, we can still predict which entity should be the hypernym among the two since the KL divergence of one given another would be drastically different. This is because a large part of physical_entity.n.01 has considerable density at the locations where location.n.01 has very low density. This causes KL(physical\textunderscoreentity.n.01 || location.n.01) to be very high (5103) relative to KL(location.n.01 || physical\textunderscoreentity.n.01) (206).