Measuring Morphological Fusion Using Partial Information Decomposition (2022)

Abstract: Morphological systems across languages vary when it comes to the relation between form and meaning. In some languages, a single meaning feature corresponds to a single morpheme, whereas in other languages, multiple meaning features are bundled together into one morpheme. The two types of languages have been called agglutinative and fusional, respectively, but this distinction does not capture the graded nature of the phenomenon. We provide a mathematically precise way of characterizing morphological systems using partial information decomposition, a framework for decomposing mutual information into three components: unique, redundant, and synergistic information. We show that highly fusional languages are characterized by high levels of synergy.

## introduction languages are, to a large extent, systematic; there are predictable patterns in the way that meanings are mapped to forms. however, languages differ when it comes to the nature of the relation between meaning and form. this variability is particularly apparent in the domain of morphology, and underlies the distinction between so-called agglutinative and fusional languages @xcite . the two types of languages differ in the extent to which multiple units of meaning are expressed by a single morpheme. in this paper, a unit of meaning simply refers to a semantic (or grammatical) feature such as plural or accusative. highly agglutinative languages have words that are built up of clearly separable morphemes, each of which corresponds to an individual unit of meaning. the relationship between meaning and form in these languages is thus highly systematic. on the other hand, highly fusional languages fuse together multiple units of meaning into a single affix that cannot be decomposed in any in the agglutinative versus fusional distinction captures a core intuition about the different ways meaning can correspond to morphological form, but the distinction is binary and therefore does not characterize the graded nature of the phenomenon @xcite -that is, the fact that different languages (and, indeed, specific domains within a language) show varying degrees of fusion. in this paper, we take an information-theoretic approach to quantifying systematicity in meaning-form relations across morphological systems. the core insight we draw upon is that meanings can contribute information about a linguistic form in three different ways. first, a unit of meaning can provide information about the form that no other unit of meaning provides. this is called unique information. second, a unit of meaning can provide the exact same information about the form that another unit of meaning provides. this is called redundant information. third, a unit of meaning can, in combination with some other unit of meaning, jointly provide information that is not provided by either on its own. this is called synergistic information. going on these definitions, we expect fusional languages to have a higher relative amount of synergy than agglutinative languages. we argue that these three kinds of information in morphological systems correspond precisely to existing notions of unique, redundant, and synergistic information in the information theory literature. in particular, the partial information decomposition (pid) framework, introduced by @xcite , decomposes the mutual information between a target variable and two (or more) source variables into unique, redundant, and synergistic information. this decomposition of mutual information into three components makes up the information profile of a system. when we take form to be the target variable and the individual meaning features to be the source variables, the information profile gives the amount of information conveyed individually, concurrently, or jointly, by units of the meaning about form. crucially, two systems can have equal mutual information between meaning and form, but different information profiles, corresponding to different degrees of morphological fusion. therefore, pid offers a mathematically precise way of placing morphological systems along an agglutinative-to-fusional spectrum. in summary, our contributions are as follows. we use the pid framework to develop a novel measure of the systematicity of meaning-form mappings in morphological systems. to validate our method, we first carry out two simulations using artificial languages for which we can control the degree of morphological fusion. we show that languages possessing a low relative amount of synergistic information are the most systematic. finally, we apply the decomposition to morphological systems in 22 real languages, successfully recapitulating existing linguistic categorizations in a graded way. ## methods we compute pid between meaning and form of noun paradigms in suffixing languages from uni-morph (sylak-glassman, 2016), which contains annotated morphological data for 167 languages using a universal schema. an example paradigm is in ## experiments we first validate that @xcite 's pid measure captures the phenomenon we are interested in by running the measure on noun paradigms in two sets of artificial languages. after validating the measure, we then apply the pid framework to noun paradigms in 22 real languages, showing that the proportion of synergy characterizes the degree of fusion in a linguistic system. ## discussion our results suggest that pid does indeed capture the spectrum between agglutinative and fusional. we also find that there is more unique information overall than redundant or synergistic information, which points to an overall high level of systematicity in morphology. redundant information makes up the smallest proportion of information overall, suggesting that morphological systems are not particularly redundant. this raises the question of whether other domains in language show similar levels of redundancy, and how the low amount of redundancy should be accounted for. while pid seems to be able to capture morphological fusion, it is important to note that the agglutinative/fusional classification system is very coarse-when we apply a single label to each language, we miss fine-grained distinctions such as the fact that different domains within a language can have different degrees of fusion. for this reason, we believe that when evaluating any measure of fusion, it is best to examine the actual paradigms. let us consider a paradigm from latin, shown in ## related work there is a growing literature on informationtheoretic approaches to problems in morphology and syntax. one line of work looks at the trade-off between the surprisal of a linguistic form and the closely related to our work is @xcite , which proposes a measure of informational fusion in morphology, based on @xcite 's definition of morphological irregularity. let ℓ be a lexeme, σ a semantic feature combination, and w a surface form. informational fusion is defined as: informational fusion is a measure of the surprisal of a surface form given the rest of the paradigm. unlike the pid approach, which involves segmenting the suffix and finding the information profile of each subpart, informational fusion is computed with respect to un-segmented forms, and does not make reference to individual morphemes. pid gives us a way of investigating the exact question we are interested in-to what extent do units of the meaning individually or jointly contribute information about individual units of the form? we use pid to get at the fine-grained distinctions between information profiles, an approach that we believe can be extended to study compositionality more generally. ## conclusion we have proposed a novel way of characterizing morphological systems cross-linguistically, using partial information decomposition. pid allows us to decompose the mutual information between meaning and form into three distinct components: unique, redundant, and synergistic information. we argued that the relative amount of synergistic information provides a mathematically precise and intuitive measure of the degree of fusion in a morphological system. we carried out a study on noun paradigms, demonstrating the promise of this approach in this specific domain. our study applies pid at the level of morphemes, and suggests extensions to word-and sentence-level domains, potentially leading to a more general theory of compositionality. we see pid as an exciting tool for investigating the information profile of any system in which meaning features are expressed by linguistic forms.