Paper:
Answering compositional questions that require multiple steps of reasoning against text is challenging, especially when they involve discrete, symbolic operations. Neural module networks (NMNs) learn to parse such questions as executable programs composed of learnable modules, performing well on synthetic visual QA domains. However, we find that it is challenging to learn these models for non-synthetic questions on open-domain text, where a model needs to deal with the diversity of natural language and perform a broader range of reasoning. We extend NMNs by: (a) introducing modules that reason over a paragraph of text, performing symbolic reasoning (such as arithmetic, sorting, counting) over numbers and dates in a probabilistic and differentiable manner; and (b) proposing an unsupervised auxiliary loss to help extract arguments associated with the events in text. Additionally, we show that a limited amount of heuristically-obtained question program and intermediate module output supervision provides sufficient inductive bias for accurate learning. Our proposed model significantly outperforms state-of-the-art models on a subset of the DROP dataset that poses a variety of reasoning challenges that are covered by our modules.

Review:
This works applies neural module network to reading comprehension that requires symbolic reasoning. There are two main contributions: (1) the authors designed a set of differentiable neural modules for different operations (for example, arithmetics, sorting, and counting) that is required to perform reasoning over a paragraph of text. These modules can be compositionally combined to perform complex reasoning. And the parameters of each module (which can be viewed as executor of each operation) are learned jointly with the parser that generates thee program composed of those modules. (2) To overcome the challenge of weak supervision, the authors proposed to use auxiliary loss (information extraction loss, parser supervision, intermediate output supervision). The model is evaluated on a subset of DROP, and outperforms the state-of-the-art models. Ablation studies supported the importance of the auxiliary losses.
Strength:
(1) The problem of applying symbolic reasoning over text is important and very challenging. This work has explored a promising direction that applies NMN, which achieved good results in VQA, to QA tasks that requires reasoning, specifically, a subset of the DROP dataset.
(2) The result, although preliminary, seems promising. The design of the modules seems intuitive and the introduction of auxiliary tasks to alleviate the problem of weak supervision is well motivated and works reasonably well. 
I am leaning towards rejection because:
(1) The main concern is that the paper, in its current form, seems incomplete. It is understandable that the type of datasets that requires reasoning is not very common nowadays, so only DROP is used for evaluation. However, the current evaluation is only on a subset of DROP, which seems unsatisfying.  
The paper argues that "Our model possesses diverse but limited reasoning capability; hence, we try to automatically extract questions in the scope of our model based on their first n-gram". However, results on the full dataset seems necessary for evaluating the potential of NMN approach over text. Even if the result is negative, it is still good to know the cause of the failure. For example, does the difficulty come from unstable training or does it come from insufficient coverage of the modules. 
(2) There are several modules introduced in the paper, but there isn't much analysis of them during the experiments. For example, what are some good and bad samples that uses each type of operations. 
(3) Since the modules are learned jointly with the parser, it is good to check whether the learned modules are indeed performing the intended operation instead of just adding more capacity to the model. For example, it might help to show a few examples that demonstrates the "compare-num-lt" is actually performing the comparisons. This can support the interpretability claim of the proposed model.  
Minor issues:
The complexities of some modules seem large. For example, "compare-num-lt" needs to enumerate all the pairs of numbers, which is quadratic. And the complexity of "find-max-num" depends on the choice of n, which could be large (although it is chosen to be 3 in this work). 
It is stated that "Our model performs significantly better than the baseline with less training data, showing the efficacy of explicitly modeling compositionality." However, the comparison with MTMSN using less training data seems a bit unfair since the proposed model is given more supervision (question parse supervision and intermediate module output supervision). Maybe a better argument is that by explicitly modeling compositionality, it is easier to add such extra supervisions than black box models like MTMSN. 
For "count", why is the attention scaled using values [1, 2, 5, 10] first?
In summary, I do like the main idea and the paper has merits, but it requires more evaluation and analysis to be accepted. I am willing to increase my score if more contents are added and I look forward to seeing it in a more complete form.
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Update after author response:
Thanks for the clarification and adding the content, I have updated my score accordingly. However, I still believe the impact of this paper will be much larger if the evaluation can be more complete, e.g., evaluating over the full DROP dataset or even include some other datasets. In the current form, it looks borderline. 
Selecting a subset (~22.7% of DROP dataset) based on the design of the proposed model ("heuristically chosen based on their first n-gram such that they are covered by our designed modules"), and compare to other models, which can actually handle a broader set of questions, only on the selected subset seems incomplete and raises concerns about how generally applicable the proposed model is. For example, since the proposed model is handling some types of questions better, it would be good to show that it can be combined with other models to get a better overall result.