Analogies Explained: Towards Understanding Word Embeddings
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Word embeddings generated by neural network methods such as word2vec (W2V) are well known to exhibit seemingly linear behaviour, e.g. the embeddings of analogy "woman is to queen as man is to king" approximately describe a parallelogram. This property is particularly intriguing since the embeddings are not trained to achieve it. Several explanations have been proposed, but each introduces assumptions that do not hold in practice. We derive a probabilistically grounded definition of paraphrasing and show it can be re-interpreted as word transformation, a mathematical description of "w_x is to w_y". From these concepts we prove existence of the linear relationship between W2V-type embeddings that underlies the analogical phenomenon, and identify explicit error terms in the relationship.
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