Paper:
Published as a conference paper at ICLR 2018 NEURAL LANGUAGE MODELING BY JOINTLY LEARNING SYNTAX AND LEXICON
We propose a neural language model capable of unsupervised syntactic structure induction. The model leverages the structure information to form better semantic representations and better language modeling. Standard recurrent neural networks are limited by their structure and fail to efficiently use syntactic information. On the other hand, tree-structured recursive networks usually require additional structural supervision at the cost of human expert annotation. In this paper, We propose a novel neural language model, called the Parsing-Reading-Predict Networks (PRPN), that can simultaneously induce the syntactic structure from unannotated sentences and leverage the inferred structure to learn a better language model. In our model, the gradient can be directly back-propagated from the language model loss into the neural parsing network. Experiments show that the proposed model can discover the underlying syntactic structure and achieve state-of-the-art performance on word/character-level language model tasks.

Review:
** UPDATE ** upgraded my score to 7 based on the new version of the paper.
The main contribution of this paper is to introduce a new recurrent neural network for language modeling, which incorporates a tree structure More precisely, the model learns constituency trees (without any supervision), to capture syntactic information. This information is then used to define skip connections in the language model, to capture longer dependencies between words. The update of the hidden state does not depend only on the previous hidden state, but also on the hidden states corresponding to the following words: all the previous words belonging to the smallest subtree containing the current word, such that the current word is not the left-most one. The authors propose to parametrize trees using "syntactic distances" between adjacent words (a scalar value for each pair of adjacent words w_t, w_{t+1}). Given these distances, it is possible to obtain the constituents and the corresponding gating activations for the skip connections. These different operations can be relaxed to differentiable operations, so that stochastic gradient descent can be used to learn the parameters. The model is evaluated on three language modeling benchmarks: character level PTB, word level PTB and word level text8. The induced constituency trees are also evaluated, for sentence of length 10 or less (which is the standard setting for unsupervised parsing).
Overall, I really like the main idea of the paper. The use of "syntactic distances" to parametrize the trees is clever, as they can easily be computed using only partial information up to time t. From these distances, it is also relatively straightforward to obtain which constituents (or subtrees) a word belongs to (and thus, the corresponding gating activations). Moreover, the operations can easily be relaxed to obtain a differentiable model, which can easily be trained using stochastic gradient descent.
The results reported on the language modeling experiments are strong. One minor comment here is that it would be nice to have an ablation analysis, as it is possible to obtain similarly strong results with simpler models (such as plain LSTM).
My main concern regarding the paper is that it is a bit hard to understand. In particular in section 4, the authors alternates between discrete and relaxed values: end of section 4.1, it is implied that alpha are in [0, 1], but in equation 6, alpha are in {0, 1}, then relaxed in equation 9 to [0, 1] again. I am also wondering whether it would make more sense to start by introducing the syntactic distances, then the alphas and finally the gates? I also found the section 5 to be quite confusing. While I get the	general idea, I am not sure what is the relation between hidden states h and m (section 5.1). Is there a mixup between h defined in equation 10 and h from section 5.1? I am aware that it is not straightforward to describe the proposed method, but believe it would be a much stronger paper if written more clearly.
To conclude, I really like the method proposed in this paper, and believe that the experimental results are quite strong.
My main concern	regarding the paper is its clarity: I will gladly increase my score if the authors can improve the writing.