Iterated learning in populations of Bayesian agents

Iterated learning in populations of Bayesian agents Kenny Smith (kenny.smith@northumbria.ac.uk) Cognition and Communication Research Centre, Division of Psychology, Northumbria University Northumberland Building,Northumberland Road,Newcastle-upon-Tyne, NE1 8ST,UK Abstract languages during their transmission. The classic example of this second constraint is the mismatch between the infinite ex- pressivity of languages and the finite set of data from which such languages must be learned. This transmission bottleneck favours languages which can be recreated from a subset via generalisation. Recursive compositionality is one such gen- eralisation (e.g. Kirby, 2002; Brighton, 2002), and therefore represents an adaptation by language in response to pressure arising from transmission factors external to the human mind. While this evolutionary process requires certain learner biases (e.g. ability to generalise), it does not arise as a consequence of these learning biases alone, but is modulated by the trans- mission bottleneck (Brighton, Smith, & Kirby, 2005). This suggests that the biases of language learners can’t simply be read off from typological distributions. However, this transmission-mediated view of the relation- ship between learning biases and typology has recently been thrown into doubt by some modelling work in the Bayesian framework. As discussed below, Griffiths and Kalish (2007) show that iterated learning in populations of Bayesian learn- ers produces outcomes which are solely determined by the biases of language learners: in other words, in the linguis- tic case, the relationship between learning bias and language typology might be a transparent one after all. It is shown here that a variant of Griffiths & Kalish’s model (where each learner selects a single grammar after observing data produced by multiple individuals, rather than a single in- dividual) leads to a blurring of the relationship between prior biases of learners and outcomes of cultural evolution: popu- lations of Bayesian agents converge on distributions of lan- guages which are dependent on both the biases of language learners and transmission factors (such as the diversity of models a learner is exposed to). Previous analytic results (Griffiths & Kalish, 2007) show that repeated learning and transmission of languages in populations of Bayesian learners results in distributions of languages which directly reflect the biases of learners. This result potentially has profound implications for our understanding of the link between the human language learning apparatus and the dis- tribution of languages in the world. It is shown here that a variation on these models (such that learners learn from the linguistic behaviour of multiple individuals, rather than a sin- gle individual) changes this transparent relationship between learning bias and typology. This suggests that inferring learn- ing bias from typology (or population behaviour from labora- tory diffusion chains) is potentially unsafe. Keywords: language learning; iterated learning; Bayesian learning; cultural evolution; language universals Introduction What is the relationship between the biases of language learn- ers and the observed distribution of languages in the world? Under the standard generative account (e.g. Chomsky, 1965), a direct mapping is assumed between the mental apparatus of language learners and language structure. In the strongest possible form (e.g. Baker, 2001), the claim is that we can read off the structure of the language faculty from the typological distribution of languages in the world. A second account which posits a similarly close match be- tween the biases of language learners and the structure of lan- guage arises from considerations of cultural evolution (Chris- tiansen & Chater, 2008). Rather than language structure being strongly constrained by a highly restrictive domain- specific learning apparatus, the idea is that languages have adapted over repeated episodes of learning and production in response to much weaker (and possibly domain-general) constraints arising from the biases of language learners. This process is sometimes called iterated learning: the outcome of learning at one generation provides the input to learning at the next. While typologically unattested languages might be both possible and even learnable, the languages we see in the world will typically be selected from the restricted set of highly learnable languages: languages which are hard to learn will tend to change, and those which are easy to learn will be preserved, eventually yielding languages which are uniformly well-fitted to the biases of language learners. We have previ- ously termed this evolutionary pressure cultural selection for learnability (Brighton, Kirby, & Smith, 2005). Are learner biases the only factor shaping the distribu- tion of languages in the world? It has been argued (see e.g. Kirby, 2002; Zuidema, 2003; Brighton, Kirby, & Smith, 2005; Kirby, Dowman, & Griffiths, 2007) that, at a minimum, language must be seen as a compromise between two fac- tors: the biases of learners, and other constraints acting on Summary of iterated learning results for Bayesian learners Bayesian learners select a hypothesis h according to its pos- terior probability in light of some data d: P(h|d) = P(d|h)P(h) ∑ h P(d|h)P(h) P(d|h) gives the likelihood of data d being produced un- der hypothesis h, and P(h) gives the prior probability of each hypothesis. For models of iterated learning of language, the set of hypotheses are interpreted as the set of possible gram- mars, data are sets of utterances from which learners must induce a language, and the prior probability distribution over grammars arises from the bias (domain-specific or domain- general, innate or learned) of learners.