Paper:
We present Neural Phrase-to-Phrase Machine Translation (NP 2 MT), a phrasebased translation model that uses a novel phrase-attention mechanism to discover relevant input (source) segments to generate output (target) phrases. We propose an efficient dynamic programming algorithm to marginalize over all possible segments at training time and use a greedy algorithm or beam search for decoding. We also show how to incorporate a memory module derived from an external phrase dictionary to NP 2 MT to improve decoding. Experiment results demonstrate that NP 2 MT outperforms the best neural phrase-based translation model (Huang  et al., 2018)  both in terms of model performance and speed, and is comparable to a state-of-the-art Transformer-based machine translation system (Vaswani et al., 2017).

Review:
This paper presents a phrase-based encoder-decoder model for machine translation. The encoder considers all possible phrases (i.e. word sequences) up to a certain length and compute phrase representations using bidirectional LSTMs from contextual word embeddings computed with another bidirectional LSTM layer. The decoder also considers possible segmentations and computes contextual representations for the previously generated segments. Each word in the current segment is generated by a Transformer model by attending to all phrases in the source sentence. The authors present a dynamic programming method for considering all possible segmentations in decoding. They also present a method for incorporating a phrase-to-phrase dictionary built by Moses into the decoding process.
I like the idea of phrase-to-phrase translation and the relatively simple architecture proposed in the paper. At the moment, however, I am not quite sure how practical their approach is. One reason is the experimental setting. Both of the datasets used in the experiments are quite small and it is not clear how the proposed model performs when several millions of sentence pairs are available for training. 
Another reason is that the computational cost of the proposed model is not really clear. The authors state that it is much more efficient than NPMT but it is not clear how it compares to the standard Transformer approach. It seems to me that the computational cost of their model is highly dependent on the value of P (maximum length of phrases). 
At first, I thought the decoder was implemented with LSTMs, but I realized that it was actually implemented with a Transformer by reading the appendix. I think this should be explained in the main body of the paper. I am also wondering how the authors’ model compares to a standard seq-to-seq model whose decoder is implemented with a Transformer.
The equation in section 2.2 seems to suggest that the model prefers segmentations with small numbers of segments. I am wondering if there is any negative effect on the translation quality.
Here are some minor comments:
p.2 valid of -> valid
p.4 lookup -> look up?
p.4 forr -> for
p.4 indict -> indicate?
p.5 Table 1 -> Table 1