Paper:
Hash Embeddings for Efficient Word Representations
We present hash embeddings, an efficient method for representing words in a continuous vector form. A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing trick). In hash embeddings each token is represented by k d-dimensional embeddings vectors and one k dimensional weight vector. The final d dimensional representation of the token is the product of the two. Rather than fitting the embedding vectors for each token these are selected by the hashing trick from a shared pool of B embedding vectors. Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions of tokens. When using a hash embedding there is no need to create a dictionary before training nor to perform any kind of vocabulary pruning after training. We show that models trained using hash embeddings exhibit at least the same level of performance as models trained using regular embeddings across a wide range of tasks. Furthermore, the number of parameters needed by such an embedding is only a fraction of what is required by a regular embedding. Since standard embeddings and embeddings constructed using the hashing trick are actually just special cases of a hash embedding, hash embeddings can be considered an extension and improvement over the existing regular embedding types.

Review:
This work describes an extension of the standard word hashing trick for embedding representation by using a weighted combination of several vectors indexed by different hash functions to represent each word. This can be done using a predefined dictionary or during online training. The approach has the benefit of being easy to understand and implement and greatly reduces the number of embedding parameters.
The results are generally good and the approach is quite elegant. Additionally, the hash embeddings seem to act as an effective regularizer. However, table 2 would benefit from describing the final selected vocabulary sizes as well as the parameter reduction provided by the hash embedding. Table 3 is also missing a joint state of the art model for the DBPedia dataset [1].
Line 255 makes the claim that the ensemble would train in the same amount of time as the single large model. However, this would only be true if each model in the ensemble had an architecture with fewer weights (that were not embedding weights). From the description, it seems that the number of non-embedding weights in each network in the ensemble is the same as that in the large model so that training time would be significantly larger for the ensemble.
Table 3 highlights the top 3 best models, however, a clearer comparison might be to split the table into embedding only approaches vs RNN/CNN approaches. It would also be interesting to see these embeddings used in the more context-sensitive RNN/CNN models.
Minor comments:
L9: Typo: million(s)
L39: to(o) much
L148: This sentence is awkwardly rewritten.
L207: What is patience?
L235: Typo: table table
Table 4: Were these obtained through summing the importance weights? What were the order of the highest/lowest weights?
[1] Miyato, Takeru, Andrew M. Dai, and Ian Goodfellow. "Virtual adversarial training for semi-supervised text classification." ICLR 2017.