Paper:
State-of-the-art machine learning methods exhibit limited compositional generalization. At the same time, there is a lack of realistic benchmarks that comprehensively measure this ability, which makes it challenging to find and evaluate improvements. We introduce a novel method to systematically construct such benchmarks by maximizing compound divergence while guaranteeing a small atom divergence between train and test sets, and we quantitatively compare this method to other approaches for creating compositional generalization benchmarks. We present a large and realistic natural language question answering dataset that is constructed according to this method, and we use it to analyze the compositional generalization ability of three machine learning architectures. We find that they fail to generalize compositionally and that there is a surprisingly strong negative correlation between compound divergence and accuracy. We also demonstrate how our method can be used to create new compositionality benchmarks on top of the existing SCAN dataset, which confirms these findings.

Review:
This paper first introduces a method for quantifying to what extent a dataset split exhibits compound (or, alternatively, atom) divergence, where in particular atoms refer to basic structures used by examples in the datasets, and compounds result from compositional rule application to these atoms. The paper then proposes to evaluate learners on datasets with maximal compound divergence (but minimal atom divergence) between the train and test portions, as a way of testing whether a model exhibits compositional generalization, and suggests a greedy algorithm for forming datasets with this property. In particular, the authors introduce a large automatically generated semantic parsing dataset, which allows for the construction of datasets with these train/test split divergence properties. Finally, the authors evaluate three sequence-to-sequence style semantic parsers on the constructed datasets, and they find that they all generalize very poorly on datasets with maximal compound divergence, and that furthermore the compound divergence appears to be anticorrelated with accuracy.
This is an interesting and ambitious paper tackling an important problem. It is worth noting that the claim that it is the compound divergence that controls the difficulty of generalization (rather than something else, like length) is a substantive one, and the authors do provide evidence of this. At the same time, I think the authors could possibly do more to show that the trend in the plots in Figure 2 can't be explained by something else: for example, the authors could show that the length ratios remain constant as the compound divergence is varied.  I think it is also not necessarily clear how easily the notion of differing compound distributions generalizes to other types of tasks.
Presentation-wise, much of the paper is clear and well written, though I think the discussion of weighted frequency distributions of compounds (top of page 3) could be clarified further, and in particular an example subgraph of a rule application DAG should be highlighted here.