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Title:Optimization and Quantization in Gradient Symbol Systems: A Framework for Integrating the Continuous and the Discrete in Cognition
Authors:Paul Smolensky, Matthew Goldrick, Donald Mathis
Comment:Under review for a special issue of Cognitive Science honoring James L. McClelland, the recipient of the 2010 David E. Rumelhart Prize for Contributions to the Theoretical Foundations of Human Cognition.
Abstract:Mental representations have continuous as well as discrete, combinatorial aspects. For example, while predominantly discrete, phonological representations also vary continuously, as evidenced by instrumental studies of both grammatically-induced sound alternations and speech errors. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland & Rumelhart, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization-Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of discrete grammatical competence with both discrete and continuous patterns in language performance.
Type:Paper/tech report
Area/Keywords:Phonology,Computation,Formal Analysis,Psycholinguistics
Article:Version 1