Cross-Situational Learning: A Mathematical Approach

Joint attention and language evolution

“…In this study, we will assume that all agents have three joint attentional skills based on those proposed by Carpenter et al to reduce the context size. Based on previous studies (Smith et al, 2006), we predict that each mechanism has a positive effect on the rate with which lexicons are acquired in the population. The question is which skill yields better performances and whether there are optimal combinations of mechanisms those agents can use.…”

“…Despite Quine's referential indeterminacy, it has been shown mathematically that cross-situational learning is very robust against context size (i.e., the ratio between context size and lexicon size can be very high), though the time it takes to learn a lexicon increases super linear with increasing context sizes (Smith et al, 2006). However, these results were achieved with idealised assumptions concerning the input to the learner, in particular it was assumed that 1. there is a strict one-to-one mapping between word and meaning in the input lexicon, 2. the input for the learner is consistent and comes from one source, such that each utterance always cooccurs with the intended meaning (or feature) and 3. the input is presented to the learner with a uniform distribution.…”

“…We assume that joint attentional skills are used to reduce the uncertainty with which the meanings of words can be inferred and that the different skills contribute differently in reducing this uncertainty. Assuming a cross-situational learner (Siskind, 1996), we know that the more uncertainties there are in the learning situations, the longer it takes to learn a set of word-meaning mappings (Smith, Smith, Blythe & Vogt, 2006). Although the ordering of emergence in attentional skills may be accounted for by different factors (e.g., complexity of the required skill), we will assume that those skills that contribute most to language development are most likely to have evolved first.…”

“…The speed with which agents can learn an idealised language using cross-situational learning is proportional to the complexity of the situation in which the agents communicate (Smith et al 2006). Although under ideal circumstances cross-situational learning works well, a reduction of complexity in learning situations is required in more complex worlds (e.g., Vogt & Coumans, 2003).…”

Learning Meaning Before Syntax

“…Cross-situational learning has been investigated by [21,22,24], among others. For each encountered word w, we consider all utterances u i containing w and their corresponding situations S i , and form the intersection of the sets of predicates occurring in these S i .…”