  Representing words by vectors, or embeddings, enables computational reasoning
and is foundational to automating natural language tasks. For example, if word
embeddings of similar words contain similar values, word similarity can be
readily assessed, whereas judging that from their spelling is often impossible
(e.g. cat /feline) and to predetermine and store similarities between all words
is prohibitively time-consuming, memory intensive and subjective. We focus on
word embeddings learned from text corpora and knowledge graphs. Several
well-known algorithms learn word embeddings from text on an unsupervised basis
by learning to predict those words that occur around each word, e.g. word2vec
and GloVe. Parameters of such word embeddings are known to reflect word
co-occurrence statistics, but how they capture semantic meaning has been
unclear. Knowledge graph representation models learn representations both of
entities (words, people, places, etc.) and relations between them, typically by
training a model to predict known facts in a supervised manner. Despite steady
improvements in fact prediction accuracy, little is understood of the latent
structure that enables this.
  The limited understanding of how latent semantic structure is encoded in the
geometry of word embeddings and knowledge graph representations makes a
principled means of improving their performance, reliability or
interpretability unclear. To address this:
  1. we theoretically justify the empirical observation that particular
geometric relationships between word embeddings learned by algorithms such as
word2vec and GloVe correspond to semantic relations between words; and
  2. we extend this correspondence between semantics and geometry to the
entities and relations of knowledge graphs, providing a model for the latent
structure of knowledge graph representation linked to that of word embeddings.
