U-shaped learning and frequency effects in a multi-layered perceptron: implications for child language acquisition

A three-layer back-propagation network is used to implement a pattern association task in which four types of mapping are learned. These mappings, which are considered analogous to those which characterize the relationship between the stem and past tense forms of English verbs, include arbitrary mappings, identity mappings, vowel changes, and additions of a suffix. The degree of correspondence between parallel distributed processing (PDP) models which learn mappings of this sort (e.g., Rumelhart & McClelland, 1986, 1987) and children's acquisition of inflectional morphology has recently been at issue in discussions of the applicability of PDP models to the study of human cognition and language (Pinker & Mehler, 1989; Bever, in press). In this paper, we explore the capacity of a network to learn these types of mappings, focusing on three major issues. First, we compare the performance of a single-layered perceptron similar to the one used by Rumelhart and McClelland with a multi-layered perceptron. The results suggest that it is unlikely that a single-layered perceptron is capable of finding an adequate solution to the problem of mapping stems and past tense forms in input configurations that are sufficiently analogous to English. Second, we explore the input conditions which determine learning in these networks. Several factors that characterize linguistic input are investigated: (a) the nature of the mapping performed by the network (arbitrary, suffixation, identity, and vowel change); (b) the competition effects that arise when the task demands simultaneous learning of distinct mapping types; (c) the role of the type and token frequency of verb stems; and (d) the influence of phonological subregularities in the irregular verbs. Each of these factors is shown to have selective consequences on both successful and erroneous performance in the network. Third, we outline several types of systems which could result in U-shaped acquisition, and discuss the ways in which learning in multi-layered networks can be seen to capture several characteristics of U-shaped learning in children. In general, these models provide information about the role of input in determining the kinds of errors that a network will produce, including the conditions under which rule-like behavior and U-shaped learning will and will not emerge. The results from all simulations are discussed in light of behavioral data on children's acquisition of the past tense and the validity of drawing conclusions about the acquisition of language from models of this sort.