text: This paper presents, and analyzes, a method for learning word relationships based on co-occurrence.   In the method, relationships between pairs of words (A, B) are represented by the terms that tend to occur around co-mentions of A and B in text.   The paper shows the start of some interesting ideas,  but needs revisions and much more extensive experiments. On the plus side, the method proposed here does perform relatively well (Table 1) and probably merits further investigation.   The experiments in Table 1 can only be considered preliminary, however.   They only evaluate over a small number of relationships (three)  -- looking at 20 or so different relationships would greatly improve confidence in the conclusions. Beyond Table 1 the paper makes a number of claims that are not supported or weakly supported (the paper uses only a handful of examples as evidence).   An attempt to explain what Word2Vec is doing should be made with careful experiments over many relations and hundreds of examples,  whereas this paper presents only a handful of examples for most of its claims.   Further, whether the behavior of the proposed algorithm actually reflects what word2vec is doing is left as a significant open question. I appreciate the clarity of Assumption 1 and Proposition 1,  but ultimately this formalism is not used  and because Assumption 1 about which nouns are "semantically related" to which other nouns attempts to trivialize a complex notion (semantics) and is clearly way too strong  -- the paper would be better off without it.  Also Assumption 1 does not actually claim what the text says it claims  (the text says words outside the window are *not* semantically related, but the assumption does not actually say this)  and furthermore is soon discarded and only the frequency of noun occurrences around co-mentions is used.   I think the description of the algorithm could be retained without including Assumption 1. minor: References to numbered algorithms or assumptions should be capitalized in the text. what the introduction means about the "dynamics" of the vector equation is a little unclear A submission shouldn't have acknowledgments, and in particular with names that undermine anonymity MLE has a particular technical meaning that is not utilized here,  I would just refer to the most frequent words as "most related nouns" or similar In Table 1, are the "same dataset" results with w2v for the nouns-only corpus, or with all the other words? The argument made assuming a perfect Zipf distribution (with exponent equal to one) should be made with data. will likely by observed -> will likely be observed lions:dolphins probably ends up that way because of "sea lions" Table 4 caption: frequencies -> currencies Table 2 -- claim is that improvements from k=10 to k=20 are 'nominal' but they look non-negligible to me I did not understand how POS lying in the same subspace means that Vec(D) has to be in the span of Vecs A-C.