Mathematical Modeling of Learning from an Inconsistent Source: A Nonlinear Approach

Continuing the discussion of how children can modify and regularize linguistic inputs from adults, we present a new interpretation of existing algorithms to model and investigate the process of a learner learning from an inconsistent source. On the basis of this approach is a (possibly nonlinear) function (the update function) that relates the current state of the learner with an increment that it receives upon processing the source's input, in a sequence of updates. The model can be considered a nonlinear generalization of the classic Bush-Mosteller algorithm. Our model allows us to analyze and present a theoretical explanation of a frequency boosting property, whereby the learner surpasses the fluency of the source by increasing the frequency of the most common input. We derive analytical expressions for the frequency of the learner, and also identify a class of update functions that exhibit frequency boosting. Applications to the Feature-Label-Order effect in learning are presented.