text: This paper presents a new method for detecting hypernymy by extending the distributional inclusion hypothesis to low-rank embeddings. The first half of the paper is written superbly, providing a sober account of the state-of-the-art in hypernymy detection via distributional semantics, and a clear, well-motivated explanation of the main algorithm (DIVE). The reformulation of PMI is interesting; the authors essentially replace P(w) with the uniform distribution (this should be stated explicitly in the paper, BTW). They then augment SGNS to reflect this change by dynamically selecting the number of negatively-sampled contexts according to the target word (w). This is a clever trick. I was also very happy to see that the authors evaluated on virtually every lexical inference dataset available. However, the remainder of the paper describing the experiments and their results was extremely difficult to parse. First of all, the line between the authors' contribution and prior art is blurry, because they seem to be introducing new metrics for measuring hypernymy as part of the experiments. There are also too many moving parts: datasets, evaluation metrics, detection metrics, embedding methods, hyperparameters, etc. These need to be organized, controlled for, and clearly explained. I have two major concerns regarding the experiments, beyond intelligibility. First, the authors used a specific corpus (with specific preprocessing) to train their vectors, but compared their results to those reported in other papers, which are not based on the same data. This invalidates these comparisons. Instead, the other methods should be replicated and rerun on exactly the same corpus. I would also recommend using a much larger corpus, since 50M tokens is considered quite small when training word embeddings. My second concern is that summation (dS) is doing all the heavy lifting. In Table 2, we can see that the difference is only 0.1 between dS and W * dS (where W is also not trained using DIVE). Since dS is basically a proxy for difference in word frequency, could it be that the proposed method is just computing which word is more general? This looks awfully familiar to Levy et al's prototypical hypernym result. Miscellaneous Comments: - There's a very recent paper on using vector norms for detecting hypernymy that might be worth contrasting with: https://arxiv.org/pdf/1710.06371.pdf - Micro-averaging these datasets is problematic, because some of the datasets based on WordNet are much larger than the hand-annotated ones, and will likely drown them out. Because these datasets are so different, I think it is critical to look at the details and not only at the averages. - PMI filtering needs to be controlled/ablated in the experiments. - While explaining equation 6, the authors say that the gradients for x and y are similar; this is not true, because k is a function of x (or y), and if one appears more often in general (not necessarily with c), then the gradients will be different as well.