On the validity of simulating stagewise development by means of PDP networks: Application of catastrophe analysis and an experimental test of rule-like network performance

Abstract

INTRODUCTIONAuthors, in both the area of experimental research and the area of computer simulation in developmental psychology, have considered neural networks (including connectionist PDP networks) as important process models ofWe would like to thank Han van der Maas, Anny Bosman, and the reviewers for their helpful comments on this article.Correspondence and requests for reprints should be sent to Maartje Raijmakers, Department of Psychology, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands, E-mail: op_raijmakers@macmaiI.psy.uva.nl. 101 102 RAIJMAKERS, VAN KOTEN, AND MOLENAARcognitive development (Bates & Elman, 1993; Grossberg, 1980; McClelland, 1989; Plunkett & Sinha, 1992;Siegler, 1989). Contrary to the relatively fixed architectures of the symbol manipulating production systems commonly employed in cognitive science, neural networks develop their knowledge base in adaptive interaction with the environment. In this respect, neural networks are compatible with epigenetical theory, according to which such interactions are the prime source of the emergence of more powerful cognitive structures (cf. Molenaar, 1986b). PDP networks, introduced by McClelland, Rumelhart, and the PDP research group (1986), constitute a distinct subset of neural network models. They are thought to be capable of both acquiring symbolic systems up to the level of natural language and modeling specific developmental phenomena like the accommodation process, which lies at the heart of Piaget's theory of developmental change (McClelland & Jenkins, 1991, p. 69). The applicability of those models to developmental processes is mainly studied by comparing their performance with empirical data, pertaining to, for example, English verb morphology, concept formation and vocabulary growth, and stagewise cognitive development (Plunkett & Sinha, 1992).In this article, we will take a closer look at the latter application: the simulation of stagewise cognitive development. McClelland and others (e.g., McClelland & Jenkins, 1991) have drawn two main conclusions from their study of a PDP network that learns the balance scale task. First, the learning behaviour can be described as the acquisition of increasingly complex rules. This conclusion is based on an application of Siegler's (1981) rule-assessment methodology, in which observed response patterns are classified as being generated by one of four distinct rules. Second, the acquisition of more complex rules by the network appears to proceed in a stagewise manner. That is, the performance of the network is for a while consistent with a particular arule and then suddenly shifts to another rule.However, questions have been raised about the evidence on which these conclusions are based. The four increasingly complex rules in Siegler's (1981) scheme constitute a measurement scale with discrete values. Hence, an application of this scheme to the learning behaviour of the network implies that the observed response patterns, which can vary continuously along multiple dimens...

Children balance theories and evidence in exploration, explanation, and learning.

“…For this purpose, we focus the current investigation on children's beliefs about balance relationships. We chose this domain both because children's beliefs about balance have been well established by prior research (e.g., Karmiloff-Smith & Inhelder, 1974;Case, 1985;Halford et al, 2002;Jansen & van der Maas, 2002;McClelland, 1989;McClelland, 1995;Normandeau, Larivee, Roulin, & Longeot, 1989;Shultz & Takane, 2007;Siegler, 1976;Siegler & Chen, 1998;Siegler & Chen, 2002;Pine & Messer, 2000;Raijmakers, van Koten, & Molenaar, 1996) and because balancing blocks are natural and accessible stimuli for exploratory play.…”

“…These studies have typically focused on transitions in children's use of rules and strategies in balance scale tasks (e.g. Case, 1985;Halford, Andrews, Dalton, Boag, & Zielinski, 2002;Jansen & van der Maas, 2002;Normandeau et al, 1989;Siegler, 1976;Siegler & Chen, 1998;Siegler & Chen, 2002;Pine & Messer, 2000;Raijmakers et al, 1996). Consistent with the Karmiloff-Smith and Inhelder (1974) study, such research 1 Because we used the Karmiloff-Smith and Inhelder (1974) study as a starting point, we adopt their practice of referring to the children's beliefs about balance relations as "theories".…”

Rule transition on the balance scale task: a case study in belief change

“…Jansen and van der Maas (1997) demonstrated that the behavior of McClelland's (1989) connectionist model could not be classified into rules. Moreover, Raijmakers, van Koten, and Molenaar (1996) showed that this model fails to show qualitative transitions between the rules. In contrast, the cascade-correlation network does show rule-like behavior (Quinlan, van der Maas, Jansen, Booij, & Rendell, in press).…”

“…Rules I, II, and the addition-rule were recognized in the classes, but the model also performed according to rules that were never found in human performance. The results of latent class analysis did suggest qualitative transitions between several rules, but a proper test of the data (as was done for McClelland's model by Raijmakers et al, 1996) has not yet been performed for the cascade correlation network.…”

Modeling developmental transitions on the balance scale task

“…The model therefore fails to show homogeneity within item types. Furthermore, Raijmakers, Van Koten, and Molenaar (1996) showed that the model fails to show qualitative transitions between the Rules.…”