Paper:
We present a differentiable multi-prototype word representation model that disentangles senses of polysemous words and produces meaningful sense-specific embeddings without external resources. It jointly learns how to disambiguate senses given local context and how to represent senses using hard attention. Unlike previous multi-prototype models, our model approximates differentiable discrete sense selection via a modified Gumbel softmax. We also propose a novel human evaluation task that quantitatively measures (1) how meaningful the learned sense groups are to humans and (2) how well the model is able to disambiguate senses given a context sentence-an evaluation ignored by previous models. Our model not only discovers distinct, interpretable embeddings but is competitive against previous models on word similarity tasks.
Moreover, these evaluations ignore a key component of learning sense inventories: do they make sense to a human? Previous multisense embedding papers present nearest neighbors to claim their representations are interpretable and useful. Like topic models, these implicit interpretability claims need to be rigorously verified. In Section 6, we adapt techniqes for evaluating topic models (Chang et al., 2009) to measure whether learned sense groups are internally coherent and whether humans can consistently match a learned sense vector to a word in context. Just like topic models, word embedding models that win conventional evaluations do not always make sense to humans.
We present a simple method that not only correlates well with traditional word similarity evaluations (Section 5) but also discovers interpretable (measured by human evaluations) sense embeddings (Section 6). Our model extends the Skip-Gram Word2Vec model and simultaneously learns (1) automatic sense induction given local context and (2) sense-specific embeddings. To learn disentangled sense representations (i.e., avoid sense mixing), we approximate hard attention and preserve Figure 1: Network struture with an example of our GASI model which learns a set of global context embeddings C and a set of sense embeddings S differentiability via a scaled variant of the Gumbel Softmax function (Section 3.2). This modeling contribution-Scaled Gumbel Softmax-is critical for disambiguating senses.

Review:
The paper presents a method for deriving multi sense word embeddings. The key idea behind this method is to learn a sense embedding tensor using a skip-gram style training objective. The objective defines the probability of contexts marginalised over latent sense embeddings. The paper uses Gumbel-softmax reparametrization trick to approximate sampling from the discrete sense distributions. The method also uses a separate hyperparameter to help scale the dot product appropriately. 
Strengths:
1. The technique is a well-motivated solution for a hard problem that builds on the skip-gram model for learning word embeddings.
2. A new manual evaluation approach for comparing sense induction approaches.
3. The empirical advance while relatively modest appears to be significant since the technique seems to yield better results than multiple baselines across a range of tasks. 
Suggestions:
1. The number of senses is fixed to three. This is a bit arbitrary, even though it is following some precedence. I like the information in the appendix that shows how to handle cases when there are duplicate senses induced for words that dont have many senses. It would be useful to know how to handle the cases where a word can have more than three senses. Given that the authors have a way of pruning duplicate senses, it would have been interesting to try a few basic methods that select the number of senses per word dynamically. 
2. The evaluation includes word similarity task and crowdsourcing for sense intrusion and sense selection. These provide a measure of intrinsic quality of the sense based embeddings. However, as Li and Jurafsky (2015) point out, typically applications use more powerful models that use a wide context. It is not clear how these improvements to sense embeddings will translate in these settings. It would have been useful to have at least one or two end applications to illustrate this. 
3. Given that the empirical gains are not quite consistent, I would encourage the authors to specifically argue why this particular method should be favoured over other existing methods. The related work discussion merely highlights methodological differences. For example, the contrast with Lee and Chen (2017) seems to be only that of differentiability. Is the claim that differentiability is desirable because this allows for fine tuning in applications? If this is the case then it will be nice to have this verified. 
4. The lower bound on the log likelihood objective is good but what are we supposed to take away from it? Is it that there is an interpretation that allows us to get away with negative sampling? 
Overall I like the paper. It presents an application of the Gumbel-softmax trick for sense embeddings induction and shows some empirical evidence for the usefulness of this idea, including some manual evaluation. 
I think the evaluation could be strengthened with some end applications and much crisper arguments on why the method is preferable over other methods that achieve comparable performance.
References:
[Li and Jurafsky., EMNLP 2015] Do Multi-Sense Embeddings Improve Natural Language Understanding?