Introduction
Compositional mechanisms are widely believed to be the basis for human language production and comprehension (Baroni, 2020 ) . These mechanisms involve the combination of simpler parts to form complex concepts, where valid combinations are licensed by a recursive grammar (Kratzer and Heim, 1998 ; Partee et al., 1984 ) . However, domain general neural architectures often fail to generalize to new, unseen data in a compositional manner, revealing a failure in inferring the data-generating grammar (Kim and Linzen, 2020 ; Lake and Baroni, 2018 ; Wu et al., 2023 ) . This failure hinders these models from closely approximating the productivity and systematicity of human language.

Consider the task of automatic morphological inflection, where models must learn the underlying rules of a language's morphoysyntax to produce the inflectional variants for any lexeme from a large lexicon. The task is challenging: the models must efficiently induce the rules with only a small human-annotated dataset. Indeed, a recent analysis by Goldman et al. ( 2022 ) demonstrates that even state-of-the-art, task-specific automatic inflection models fall short of a compositional solution: they perform well in random train-test splits, but struggle in compositional ones where they must inflect lexemes that were unseen at training time.

Nevertheless, there is reason for optimism. Several works have shown that automatic inflection models come much closer to a compositional solution when the human-annotated dataset is complimented by a synthetic data-augmentation procedure (Liu and Hulden, 2022 ; Silfverberg et al., 2017 ; Anastasopoulos and Neubig, 2019 ; Lane and Bird, 2020 ; Samir and Silfverberg, 2022 ) , where morphological affixes are identified and attached to synthetic lexemes distinct from those in the training dataset (Fig. 2 ). However, little is understood about this prominent data augmentation method and the extent to which it can improve compositional generalization in neural word inflection. In this work, we seek to reveal the implicit assumptions about morpheme distributions made by this rule-based augmentation scheme, and analyze the effect of these assumptions on learning of cross-linguistically prevalent morphological patterns.

To this end, our work presents the first theoretical explanation for the effectiveness of compositional data augmentation in morphological inflection. Through an information-theoretic analysis (Section 3 ), we show that this method eliminates ``spurious correlations'' (Gardner et al., 2021 ) between the word's constituent morphemes, specifically between the stem (e.g., walk ) and the inflectional affix (e.g., -ed ). By removing these correlations, the training data distribution becomes aligned with concatenative morphology, where a word can be broken down into two independent substructures: the stem (identifying the lexeme) and the inflectional affixes (specifying grammatical function). This finding sheds light on why the method is widely attested to improve compositional generalization (Liu and Hulden, 2022 ) , as concatenative morphological distributions are cross-linguistically prevalent (Haspelmath and Sims, 2013 ) .

We go on to show, however, that the augmentation method tends towards removing all correlations between stems and affixes, whether spurious or not. Unfortunately, this crude representation of concatenative morphology, while reasonable in broad strokes, is violated in virtually all languages to varying degrees by long-distance phonological phenomena like vowel harmony and reduplication. Thus, our analysis demonstrates that while the method induces a useful approximation to concatenative morphology, there is still ample room for improvement in better handling of allomorphy and phonological alternations.

Building on our theoretical analysis, we investigate whether it is possible to improve the sample-efficiency with which the data augmentation method induces probabilistic independence between stems and affixes. Specifically, we investigate whether we can use a small subset of the synthetic data to add to our training dataset. We find that selecting a subset that incorporates both high predictive uncertainty and high diversity (see Fig. 1 ) is significantly more efficient in removing correlations between stems and affixes, providing an improvement in sample-efficiency for languages where the morphological system is largely concatenative. At the same time, in accordance with our theoretical analysis, this selection strategy impairs performance for languages where phonological alternations are common.

Our work contributes to a comprehensive understanding of a prominent data augmentation method from both a theoretical (Section 3 ) and practical standpoint (Section 4 ). Through our systematic analysis, we aim to inspire further research in the analysis and evaluation of existing compositional data augmentation methods (reviewed in Section 6 ), as well as the development of novel augmentation methods that can better capture cross-linguistic diversity in morphological patterns.