In this paper, we investigate mapping the hyponymy relation of WORDNET to feature vectors. We aim to model lexical knowledge in such a way that it can be used as input in generic machine-learning models, such as phrase entailment predictors. We propose two models. The first one leverages an existing mapping of words to feature vectors (fastText), and attempts to classify such vectors as within or outside of each class. The second model is fully supervised, using solely WORDNET as a ground truth. It maps each concept to an interval or a disjunction thereof. On the first model, we approach, but not quite attain state of the art performance. The second model can achieve near-perfect accuracy.
This paper reads like the first thoughts and experiments of a physicist or mathematician who has decided to look at word representations and hyponymy. I mean that in both the positive and negative ways that this remark could be construed. On the positive side, it provides an interesting read, with a fresh perspective, willing to poke holes in rather than accepting setups that several previous researchers have used.  On the negative side, though, this paper can have an undue, work-from-scratch mathiness that doesn't really contribute insight or understanding, and the current state of the work is too preliminary. I think another researcher interested in this area could benefit from reading this paper and hearing the perspective it presents. Nevertheless, there just isn't sufficient in the way of strong, non-trivial results in the current paper to justify conference acceptance. 
Quality:
 - Pro
   o Everything is presented in a precise formalized fashion. The paper has interesting remarks and perspectives. I appreciate that the authors not only did find most existing work on modeling hyponymy but provide a detailed and quite insightful discussion of it.  (A related paper from overlapping authors to papers you do cite that maybe should have been included is Chang et al. https://arxiv.org/abs/1710.00880 – which is a bit different in trying to learn hyponyms from text not WordNet, but still clearly related.)
  -Con
   o There just isn't enough here in the way of theoretical or experimental results. In the end, two "methods" of hyponymy modeling are presented: one is a simple logistic regression, which is estimated separately PER WORD for words with 10 or more hyponyms. This performs worse than the methods of several recent papers that the author cites. The other is a construction that shows that any tree can be embedded by representing nodes as ranges of the real line. This is true, but trivial. Why don't ML/NLP researchers do this? It's because they want a representation that doesn't only represent the ISA hierarchy but also other aspects of word meaning such as meaning similarity and dimensions of relatedness. Furthermore, in general they would like to learn these representations from data rather than hand-constructing it from an existing source like WordNet. For instance, simply doing that gives no clear way to add other words not in wordnet into the taxonomy. This representation mapping doesn't really give any clear advantage beyond just looking up hyponymy relationships in wordnet when you need them.
Clarity:
 - Pro
   o The paper is in most respects clearly written and enjoyable to read.
 - Con
   o The mathematical style and precision has it's uses, but sometime it just seemed to make things harder to follow. Referring to things throughout as "Property k" – even though some of those properties were given names when first introduced – left me repeatedly flicking up and down through the PDF to refresh myself on what claim was being referred to without any apparent need....
Originality:
 - Pro
   o There is certainly originality of perspective. The authors make some cogent observations on how other prior work has been naive about adopted assumptions and as to what it has achieved (e.g., in the discussion at the start of section 5.1).
 - Con
   o There is not really significant originality of method. The logistic regression model is nothing but straightforward. (It is also highly problematic in learning a separate model for each word with a bunch of hyponyms. This both doesn't give a model that would generalize to novel words or ones with few hyponyms.) Mapping a tree to an interval is fairly trivial, and besides this is just a mapping of representations, it isn't learning a good representation as ML people (or ICLR people) would like. The idea that you can improve recall by using a co-product (disjunction) of intervals is cute, though, I admit. Nice.
Significance 
 - Con
   o I think this work would clearly need more development, and more cognizance of the goals of generalizable representation learning before it would make a significant contribution to the literature. 
Other:
 - p.1: Saying about WordNet etc., "these resources have a fundamentally symbolic representation, which can not be readily used as input to neural NLP models" seems misplaced when there is now a lot of work on producing neural graph embeddings (including node2vec, skip-graphs, deepwalk, etc.). Fundamentally, it is just a bad argument: It is no different to saying that words have a fundamentally symbolic representation which cannot be readily used as input to neural NLP models, but the premise of the whole paper is already that we know how to do that and it isn't hard through the use of word embeddings.
 - p.2: The idea of words and phrases living in subset (and disjointness etc.) relationships according to denotation is the central idea of Natural Logic approaches, and these might be cited here. There are various works, some more philosophical. A good place to start might be: https://nlp.stanford.edu/pubs/natlog-iwcs09.pdf
 - p.2: The notions of Property 1 and 2 are just "precision" and "recall", terms the paper also uses. Do we gain from introducing the names "Property 1" and "Property 2" for them? I also felt that I wouldn't have lost anything if Property 3 was just the idea that hyponymy is represented as vector subspace inclusion.
 - p.2: fn.2: True, but it seems fair to more note that cosine similarity is very standard as a word/document similarity measure, not for modeling hyponymy, for this reason.
 - p.4: Below the equation, shouldn't it be Q(w', w) [not both w'] and then Q(w', w) and not the reverse? If not, I'm misunderstanding.