Incorporating hierarchical structures like constituency trees has been shown to be effective for various natural language processing (NLP) tasks. However, it is evident that state-of-the-art (SOTA) sequence-based models like the Transformer struggle to encode such structures inherently. On the other hand, dedicated models like the Tree-LSTM, while explicitly modeling hierarchical structures, do not perform as efficiently as the Transformer. In this paper, we attempt to bridge this gap with "Hierarchical Accumulation" to encode parse tree structures into selfattention at constant time complexity. Our approach outperforms SOTA methods in four IWSLT translation tasks and the WMT'14 English-German translation task. It also yields improvements over Transformer and Tree-LSTM on three text classification tasks. We further demonstrate that using hierarchical priors can compensate for data shortage, and that our model prefers phrase-level attentions over token-level attentions.
This paper extends transformers by enabling them to incorporate hierarchical structures like constituency trees structured attention with hierarchical accumulation. In particular, they modified the architecture of transformers such that they can learn phrase-level attention scores, and use them in the final assigned task of text classification or language translation. 
They also explored a couple of variants of their proposed architecture: Hierarchical embeddings and Subnet masking which helped them outperform SOTA methods including Tree-LSTM (similar to this paper in principle, except that it was designed for LSTM-based models and not transformers). 
The paper is well written and well-augmented with supportive figures. Particularly, Figure1 was very helpful in understanding all the complexities of the proposed model. Further, the authors justify the utility of the proposed approach covering different aspects of evaluation including comparative studies with baselines, ablation studies, phrase vs token-level attentions, training-time analysis. 
A limitation of this work is high inference cost. As the results indicate, parsing trees from text is the most costly step in the entire framework, and consequently, the inference time of proposed model will still be much higher than transformers. Hence, this work might still not be applicable to low-latency constraint scenarios. 
Other Comments: 
1) I did not fully understand why it would be better to mask out the non descendants in subnet masking approach. Why shouldn't a phrase node seek attention from tokens outside its scope? Probably the answer lies in the the way these trees are constructed. Nevertheless, it would be useful to provide some intuition with examples to motivate subtree masking. 
2) In Equation(5), the subscripts "i-1" should be replaced with "i"? Otherwise it will be sensitive to ordering of non-terminal nodes in N, and also Figure 1 wouldn't make sense.