Paper:
We present methodology for using dynamic evaluation to improve neural sequence models. Models are adapted to recent history via a gradient descent based mechanism, causing them to assign higher probabilities to re-occurring sequential patterns. Dynamic evaluation outperforms existing adaptation approaches in our comparisons. Dynamic evaluation improves the state-of-the-art word-level perplexities on the Penn Treebank and WikiText-2 datasets to 51.1 and 44.3 respectively, and the state-of-the-art character-level cross-entropies on the text8 and Hutter Prize datasets to 1.19 bits/char and 1.08 bits/char respectively.

Review:
The authors provide an improved implementation of the idea of dynamic evaluation, where the update of the parameters used in the last time step proposed in (Mikolov et al. 2010) is replaced with a back-propagation through the last few time steps, and uses  RMSprop rather than vanilla SGD. The method is applied to word level and character level language modeling where it yields some gains in perplexity. The algorithm also appears able to perform domain adaptation, in a setting where a character-level language model trained mostly on English manages to quickly adapt to a Spanish test set. 
While the general idea is not novel, the implementation choices matter, and the authors provide one which appears to work well with recently proposed models. The character level experiments on the multiplicative LSTM make the most convincing point, providing a significant improvement over already good results on medium size data sets. Figure 2 also makes a strong case for the method's suitability for applications where domain adaptation is important.
The paper's weakest part is the word level language modeling section. Given the small size of the data sets considered, the results provided are of limited use, especially since the development set is used to fit the RMSprop hyper-parameters. How sensitive are the final results to this choice? Comparing dynamic evaluation to neural cache models is a good idea, given how both depend en medium-term history: (Grave et al. 2017) provide results on the larger text8 and wiki103, it would be useful to see results for dynamic evaluation at least on the former.
An indication of the actual additional evaluation time for word-level, char-level and sparse char-level dynamic evaluation would also be welcome.
Pros:
- Good new implementation of an existing idea
- Significant perplexity gains on character level language modeling
- Good at domain adaptation
Cons:
- Memory requirements of the method
- Word-level language modeling experiments need to be run on larger data sets
(Edit: the authors did respond satisfactorily to the original concern about the size of the word-level data set)