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Inverse problems in dynamic cognitive modeling

Beim Graben, P. and Potthast, R. (2009) Inverse problems in dynamic cognitive modeling. Chaos, 19 (1). p. 21. ISSN 1089-7682

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To link to this article DOI: 10.1063/1.3097067

Abstract/Summary

Inverse problems for dynamical system models of cognitive processes comprise the determination of synaptic weight matrices or kernel functions for neural networks or neural/dynamic field models, respectively. We introduce dynamic cognitive modeling as a three tier top-down approach where cognitive processes are first described as algorithms that operate on complex symbolic data structures. Second, symbolic expressions and operations are represented by states and transformations in abstract vector spaces. Third, prescribed trajectories through representation space are implemented in neurodynamical systems. We discuss the Amari equation for a neural/dynamic field theory as a special case and show that the kernel construction problem is particularly ill-posed. We suggest a Tikhonov-Hebbian learning method as regularization technique and demonstrate its validity and robustness for basic examples of cognitive computations.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Life Sciences > School of Psychology and Clinical Language Sciences
ID Code:14156
Uncontrolled Keywords:cognition, inverse problems, neural nets, nonlinear dynamical systems, GEOMETRIC VISUAL HALLUCINATIONS, RECURRENT NEURAL-NETWORKS, COMPLEX, BRAIN NETWORKS, FIELD-THEORY, SPATIOTEMPORAL DYNAMICS, TEMPORAL, TRAJECTORIES, SMOLENSKY SOLUTION, PATTERN-FORMATION, HUMAN EEG, SYSTEMS
Publisher:American Institute of Physics

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