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.
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Research Article| March 31 2009
Inverse problems in dynamic cognitive modeling
Peter beim Graben;
Peter beim Graben, Roland Potthast; Inverse problems in dynamic cognitive modeling. Chaos 1 March 2009; 19 (1): 015103. https://doi.org/10.1063/1.3097067
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