This work proposes DIVE (distributional inclusion vector embeddings), an unsupervised method for hypernymy discovery that preserves the inclusion property of old fashioned sparse BOW representations (i.e., that hypernyms tend to have higher counts in more varies contexts than hyponyms).  The learned representations are evaluated on a large set of datasets and are shown to work well.  The work is very thorough, and almost reads as a systematic study in places.  Unfortunately, this makes it hard to follow sometimes,  and although the work is generally interesting,  I am left to wonder about its novelty and general impact on the field. The main proposition essentially comes down to a slight tweak in word2vec's SGNS method:  instead of shifting the PMI value of word co-occurrences by 1/k, we shift by #w/(k*|D|/|V|) and add a non-negativity constraint, i.e., we explicitly force Eq. 2 to be true in perfect reconstructions.  This makes sense and I am surprised nobody has done it before.  It feels like a minor tweak,  however, and any major improvement seems to be largely dependent on the scoring function, rather than on this slightly different objective.  Consequently, I feel like the paper is in two minds about what it wants to be: a systematic study of hypernymy detection methods, or an introduction of a novel algorithm for learning distributional inclusion embeddings. I like the main ideas of this work and I think it's great that the study is so thorough,  but I don't think it should be accepted in its current form.  Main concerns:- Presentation: the experiments show that (1) DIVE outperforms GE, HyperScore and H-Feature baselines;  (2) which scoring function works best for DIVE;  (3) DIVE outperforms SBOW in many cases, but not always, though better on average;  and (4) we can use DIVE for WSD (only shown qualitatively).  The paper spans 13 pages, excluding appendices,  which is rather long.  I feel that (2), (3) and (4) are part of a systematic study/review paper,  while (1) could be interesting in and of itself, if it included a full comparison against alternative methods.  The way results are presented in the tables is confusing,  and it's unclear why only one baseline is included in each case. - Comparison: it appears that there are methods missing from the results tables.  On HyperLex, for example, results as high as 0.512 (Poincare embeddings), 0.540 (HyperVec) and 0.686 (LEAR) have been reported,  while the highest result in the paper is 34.5.  That's a big difference.  On Weeds' BLESS, it's 68.6 versus e.g. 0.75 for Kiela et al. (unsupervised, using images) and 0.850 for HyperVec.  If these results were omitted due to space, I think experiment (2) and (4) can safely be moved to the appendix.  Especially for something that hinges on being a review paper, such as this work, it is important to be complete. In short, I think the presentation doesn't help;  I am left to wonder what the main contribution is of the work;  and I think the comparison to previous work is incomplete. Questions:- Why use WaCkypedia?  It's old and, by now, small.  It would be interesting to try all scoring functions and types of model (PPMI, PPMI with shift, PPMI with inclusion shift) trained on the exact same corpus and same negatives, and showing that it works best there. - General question: Is Vendrov's test set only yes/no, e.g. if I set the threshold really low, I get 100% accuracy, or does it contain negatives?  Same for BLESS.  If so how valuable is this evaluation? - To what extent are the baselines tuned in the semi-supervised case?  If the numbers are from papers, that should be mentioned.  It would be better to use the same corpus, and the same amount of attention to tuning the results, for both cases. Minor/Typos:- Medicl - "From the recent review (Santus et al) ... suggested by the review study (Vulic et al)" this way of citing reviews isn't very pretty