Paraphrases do not explain word analogies

Many types of distributional word embeddings (weakly) encode linguistic regularities as directions (the difference between "jump" and "jumped" will be in a similar direction to that of "walk" and "walked," and so on). Several attempts have been made to explain this fact. We respond to Allen and Hospedales' recent (ICML, 2019) theoretical explanation, which claims that word2vec and GloVe will encode linguistic regularities whenever a specific relation of paraphrase holds between the four words involved in the regularity. We demonstrate that the explanation does not go through: the paraphrase relations needed under this explanation do not hold empirically.