Regularization behavior in a non-linguistic domain

Regularization behavior in a non-linguistic domain Vanessa Ferdinand (v.a.ferdinand@sms.ed.ac.uk), Bill Thompson (bill@ling.ed.ac.uk), Simon Kirby (simon@ling.ed.ac.uk), Kenny Smith (kenny@ling.ed.ac.uk) Language Evolution and Computation Research Unit School of Philosophy, Psychology & Language Sciences, University of Edinburgh Dugald Stewart Building, 3 Charles Street, Edinburgh, EH8 9AD, UK Abstract variables. Participants with lower capacity overproduced the most common variant, whereas participants with higher ca- pacity did not. Regularization is also modulated by the num- ber of variables in a task; adults regularized slightly more when predicting which of three lights will flash next than when predicting for two lights (Gardner, 1957). In this paper, we explore the effect of tracking single versus multiple frequencies on the regularization behavior of adults in a non-linguistic task. We show that participants probabil- ity match when tracking a single frequency, but regularize when tracking six frequencies concurrently. Because con- current frequency learning is a prominent aspect of language learning (Saffran, Alin & Newport, 1996), and also elicits regularization in a non-linguistic task, this is consistent with a domain-general account of the observed regularization bias in language, possibly attributable to limited working memory. Language learners tend to regularize unpredictable variation and some claim that is due to a language-specific regularization bias. We investigate the role of task difficulty on regularization behavior in a non-linguistic frequency learning task and show that adults regularize variable input when tracking multiple fre- quencies concurrently, but reliably reproduce the variation they have observed when tracking one frequency. These results sug- gest that regularization behavior may be due to domain-general factors, such as memory limitations. Keywords: frequency learning; regularization; probability matching; Bayesian models; Introduction Languages contain very little unpredictable variation (Cham- bers et al., 2003) and language learners tend to regularize the inconsistent input they encounter (Reali & Griffiths, 2009; Hudson Kam & Newport, 2009, Smith & Wonnacott, 2010). For example, English contains two forms of the indefinite ar- ticle a and an, but a deterministic rule (based on the initial phoneme of the following noun) governs the use of these two variants. Why are languages regular, and what drives learn- ers to eliminate free variation in language? Some have sug- gested that we come to the task of language learning with the expectation that languages are regular and that this expecta- tion takes the form of a language-specific innate bias (Bicker- ton, 1984; DeGraaff, 1999; Lumsden, 1999; Becker & Veen- stra, 2003). Others claim that linguistic regularization can be explained by domain-general learning mechanisms, such as the effects of memory limitations on the type of variation that learners produce (Hudson Kam & Newport, 2005, 2009; Hudson Kam & Chang, 2009). Hudson Kam and Newport (2005, 2009) have shown that children tend to regularize free variation, whereas adults maintain it by probability matching, and attribute this difference to children having lower work- ing memory capacity than adults. Newport (1990) demon- strated that children have more of a limited ability to learn from inconsistent input and Hudson Kam and Chang (2009) showed that adults probability matched more when word re- trieval was made easier and regularized more when it was difficult, further corroborating their claim that memory limi- tations can lead to regularization, although see Perfors (2012) for an account of restricted memory encoding that does not lead to regularization. A similar effect of memory limitations can be found in a non-linguistic tasks. In a study with adults, Kareev et al. (1997) reported an effect of individual differences in work- ing memory capacity (as determined by a digit-span test) on participants’ perception of the correlation of two probabilistic Frequency learning experiment Participants 381 participants were recruited via Amazon’s Mechanical Turk crowdsourcing platform and completed our experiment online. 37 participants were excluded on the ba- sis of the following criteria: failing a color vision test (2), self-reporting the use of a pen or pencil during the task (14), not reporting their sex or age (2), or having previously partic- ipated in any of our experiments, as determined by their user ID with MTurk (19). More participants were recruited than necessary with the expectation that many would be excluded by these criteria. Once the predetermined number of partic- ipants per condition was met, data from the last participants was excluded, totaling 24 participants across all conditions and tasks. All excluded participants received the full mone- tary reward for the task. The average monetary reward per participant, converted to an hourly rate, was $2.64. Of the final 320 participants, 184 are female, and the mean age is 36 (min = 18, max = 69), with a standard deviation of 12 years. Materials The experiment was coded up as a java applet that ran in the participant’s web browser in a 600x800-pixel field. Photographs of 6 different containers (a box, pouch, jar, bowl, bucket, and basket) and graphically generated images of marbles in 12 different colors (blue, orange, brown, grey, black, yellow, red, teal, olive, pink, purple, and lime) served as stimuli. One-item task This experiment consisted of a training phase in which participants observed a series of 10 marble draws from a bag, and a testing phase in which participants were asked to produce another several likely draws from the