A Dynamical Connectionist Account of Conceptual Change

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A Dynamical Connectionist Account of Conceptual Change Athanassios Raftopoulos (raftop@ucy.ac.cy), Andreas Demetriou (ademet@ucy.ac.cy) Department of Educational Sciences, University of Cyprus P.O. Box 20537, 1678 Nicosia, Cyprus. Abstract Conceptual change can be accounted for at various levels of explanation. The cognitive level (Marr’s computational level), the representational (Marr’s “algorithmic”), and the implementational level. In this paper, we offer a dynamical account of types of conceptual change at the representational level. Our aim is to show that some classes of neural models can implement the types of change that we have proposed elsewhere. First we briefly describe at the cognitive level certain types of change that purport to account for some of the kinds of conceptual change. Then we lay forth the framework of dynamical connectionism; we discuss the representational level realizations of the cognitive level and claim that these can be depicted as points in the system’s activational landscape. We offer, third, a dynamical account of some types change and we claim that conceptual change can be modeled as a process of modification, appearance of new and disappearance of attractors and/or basins of attraction that shape the system’s landscape. Finally, we discuss the kinds of mechanisms at the representational level that could produce the types of change observed at the cognitive level, as modeled by means of dynamic connectionism. Introduction Conceptual change can be accounted for at various levels of explanation. Following Marr (1980), one can distinguish between three levels: the computational, the algorithmic, and the implementational level of explanation of cognitive systems. We prefer the term “cognitive” to “computational”, and the term “representational” to “algorithmic”, since there are accounts of cognition that deny the algorithmic nature of mental operations. At the cognitive level, one can discuss cognitive operations that apply to information-processing content (such as addition and subtraction), operations that apply to structures as wholes, such as differentiation or coalescence (Carey, 1985; Chi, 1992), or, conceptual combination, generalization and abduction, and hypothesis formation (Thagard, 1992). This level addresses the issue of the functions computed by the information processing system. At the representational level one can examine the algorithmic processes that realize conceptual change at the cognitive level by transforming representations, such as Newell and Simon’s (1972) “problem behavior graph” in production systems. In the connectionist paradigm one can study the processes of the emergence of new attractors, and repositioning of points realizing representational states in high-dimensional state spaces (Horgan and Tienson, 1996), or the changes in the connection weights and network structure (Elman et al., 1996; Schultz et. al., 1995; Plunkett & Sinha, 1992). In this paper, we will discuss a theory of different types of cognitive change and their implementation at the representation level. Our aim is to show how certain classes of neural networks could implement some of the types of change that the authors have proposed (Demetriou and Raftopoulos, 1999). First, we will summarize these types of change. In the second part we will sketch the framework for the dynamics of change, relying on the dynamical interpretation of connectionist networks to explore possible means of modeling the stipulated types. In the third part we offer a dynamical account of some types change and we claim that conceptual change can be modeled as a process of modification, appearance of new and disappearance of attractors and/or basins of attraction that shape the system’s landscape. Finally, we discuss the kinds of mechanisms at the representational level that could produce the types of cognitive change. To that end we will employ neural networks whose behavior can be viewed as falling under one or the other of our kinds of change, and describe the behavior that neural networks should exhibit if they are to implement type of change. Types of Change Demetriou and Raftopoulos (1999) previously published a theory of conceptual change that addresses the issue of how a learning system makes the transition from one state to another. The theory provides a detailed analysis of the types of change that are observed both in cognitive development and during learning. The types of change are summarized in Figure 1.