On the Complexity and Typology of Inflectional Morphological Systems

On the Complexity and Typology of Inflectional Morphological Systems Ryan Cotterell and Christo Kirov and Mans Hulden and Jason Eisner Department of Computer Science, Johns Hopkins University Department of Linguistics, University of Colorado {ryan.cotterell,ckirov1,eisner}@jhu.edu, first.last@colorado.edu Abstract We quantify the linguistic complexity of dif- ferent languages’ morphological systems. We verify that there is a statistically significant empirical trade-off between paradigm size and irregularity: A language’s inflectional paradigms may be either large in size or highly irregular, but never both. We define a new measure of paradigm irregularity based on the conditional entropy of the surface realization of aparadigm— how hard it is to jointly predict all the word forms in a paradigm from the lemma. We estimate irregularity by training a predictive model. Our measurements are taken on large morphological paradigms from 36 typologi- cally diverse languages. 1 Introduction What makes an inflectional system ‘‘complex’’? Linguists have sometimes considered measur- ing this by the size of the inflectional paradigms (McWhorter, 2001). The number of distinct in- flected forms of each word indicates the number of morphosyntactic distinctions that the language makes on the surface. However, this gives only a partial picture of complexity (Sagot, 2013). Some inflectional systems are more irregular: It is harder to guess how the inflected forms of a word will be spelled or pronounced, given the base form. Ackerman and Malouf (2013) hypothesize that there is a limit to the irregu- larity of an inflectional system. We refine this hypothesis to propose that systems with many forms per paradigm have an even stricter limit on irregularity per distinct form. That is, the two dimensions interact: A system cannot be complex along both axes at once. In short, if a language demands that its speakers use a lot of distinct forms, those forms must be relatively predictable. In this work, we develop information-theoretic tools to operationalize this hypothesis about the complexity of inflectional systems. We model each inflectional system using a tree-structured directed graphical model whose factors are neural networks and whose structure (topology) must be learned along with the factors. We explain our approach to quantifying two aspects of inflectional complexity and, in one case, approximate our metric using a simple variational bound. This al- lows a data-driven approach by which we can mea- sure the morphological complexity of a given language in a clean manner that is more theory- agnostic than previous approaches. Our study evaluates 36 diverse languages, using collections of paradigms represented ortho- graphically. Thus, we are measuring the complex- ity of each written language. The corresponding spoken language would have different complexity, based on the corresponding phonological forms. Importantly, our method does not depend upon a linguistic analysis of words into constituent morphemes (e.g., hoping �→ hope+ing). We find support for the complexity trade-off hypothesis. Concretely, we show that the more unique forms an inflectional paradigm has, the more predictable the forms must be from one another—for example, forms in a predictable paradigm might all be related by a simple change of suffix. …

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