Cross-linguistically Small World Networks are Ubiquitous in Child-directed Speech Steven Moran, Danica Pajovi´ c, Sabine Stoll Department of Comparative Linguistics, University of Zurich Plattenstrasse 54, CH-8032 Zurich, Switzerland {steven.moran, danica.pajovic, sabine.stoll}@uzh.ch Abstract In this paper we use network theory to model graphs of child-directed speech from caregivers of children from nine typologically and morphologically diverse languages. With the resulting lexical adjacency graphs, we calculate the network statistics {N, E, <k>, L, C} and compare them against the standard baseline of the same parameters from randomly generated networks of the same size. We show that typologically and morphologically diverse languages all share small world properties in their child-directed speech. Our results add to the repertoire of universal distributional patterns found in the input to children cross-linguistically. We discuss briefly some implications for language acquisition research. Keywords: network theory, linguistics, corpus linguistics, child language acquisition 1. Overview Despite the remarkable diversity of linguistic structures in the world’s 7000 or so languages, children can acquire any language. This fact presents many questions, including im- portantly: what are the underlying cognitive mechanisms that enable children to acquire language? And are there universal patterns in the linguistic input to children that po- tentially bootstrap these mechanisms? Consider one salient difference among the world’s lan- guages (especially the under-studied ones): how words are constructed and how they relate to syntax. When analyzed in detail, it is rather difficult to define what a word is cross- linguistically (Hall et al., 2008). In some languages words represent what English speakers consider full phrases; in other languages the word and morpheme (smallest function bearing linguistic unit) are synonymous. Contrast two ut- terances from Indonesian (Gil and Tadmor, 2007) and Cree (Brittain, 2015): (1) O, Ei lagi minum susu. oh Ei more drink milk ‘Oh, Ei is drinking more milk.’ (Indonesian) (2) Chi-wˆ ap-iht-ˆ a-n ˆ a kˆ a-pushch-ishk-iw-ˆ a-t. 2-light-by.head-TR.INAN.NON3-2SG>0 Q PVB.CONJ- put.on-by.foot-STEM-TR.ANIM-3SG>4SG ‘You see? She was putting it on.’ (Cree) Indonesian is an example of a language with a fairly low degree of synthesis, whereas Cree belongs to one of the most genuinely polysynthetic language families of the world (and features both noun incorporation and polypartite stems). 1 Clearly the frequency in which children hear a par- ticular form is a function of synthesis combinatorics (Stoll et al., 2017). That is, in languages where morphology is in a closer one-to-one relationship between word and gram- matical function, these forms will occur more frequently in 1 Another example is verbal inflection: English typically has four forms, e.g. kick, kicks, kicked, kicking. But compare Chin- tang, a language spoken in rural Nepal. It has more than 4000 inflectional forms per verb (Stoll et al., 2017). the input. There will be greater transition probabilities in languages with more tokens than in morphologically-rich languages which have more types. Nevertheless, regardless of morphology, children from all languages learn to iden- tify words and to produce them. For a long time, Universal Grammar (UG) was the answer to such problems in language acquisition. In UG, lan- guage is the product of innate functions (Chomsky, 1957), where rules and parameters are hard-wired and the acquisi- tion process involves language-specific tuning of linguistic structures (Chomsky, 2000). Because the language acqui- sition device is posited as innate, models of UG are not necessarily data-driven, but instead theoretical and mainly focused on ‘Language’ as an abstract system – centered historically on the syntactic structure of English and a few other major languages. No matter what theoretical approach researchers adopt, they must explain how children identify patterns in their linguistic input and make use of these in productive gen- eralizations as observed in their linguistic output. Usage- based or constructivist approaches are functionalist in that they take into account the way that language is used and contexts in which linguistic elements appear. Increased access to richly annotated linguistic data and computing power, coupled with approaches particularly in corpus lin- guistics, have shown that there are discernible distributional and predictable patterns in the input to children. For exam- ple, grammatical knowledge can be learned from patterns in CDS (Gegov et al., 2011; Freudenthal et al., 2007; Red- ington et al., 1998; Cartwright and Brent, 1997). Distribu- tional patterns are also predictors of different grammatical categories to varying degrees, depending on the grammat- ical properties of the language (Mintz, 2003; Stoll et al., 2009; Stumper et al., 2011; Moran et al., In press). Gegov et al. (2011) call these invisible patterns, which they aim to discover using network theory to model language ac- quisition data. This line of inquiry is summarized by Vite- vitch (2008), Beckage et al. (2011) and Gegov et al. (2011). Networks have many properties that allow us to model, 4100