Dynamic Cognitive Modeling
Peter beim Graben
Institut für deutsche Sprache und Linguistik
Humboldt-Universität zu Berlin

"Dynamic Cognitive Modeling" is a three tier top-down approach comprising the levels of (1) cognitive processes; (2) their state space representations; and (3) dynamical systems implementations that are guided by neuroscientific principles. These levels are passed through in a top-down fashion: (1) cognitive processes are described as algorithms sequentially operating on complex symbolic data structures that are decomposed using so-called filler/role bindings; (2) data structures are mapped onto points in abstract vector spaces using tensor product representations; (3) cognitive operations are implemented as dynamics of neural networks or neural/dynamic fields. The last step involves the solution of inverse problems, namely training the system's parameters to reproducing prescribed trajectories of cognitive operations in representation space.

The lecture will be structured as follows:
  • Introduction to linear algebra and calculus
  • Dynamical systems and neural networks
  • Dynamic automata: dynamic recognizers, fractal automata, nonlinear dynamical automata, and quantum automata
  • Language processing with neural networks: context-free and minimalist grammars
  • Dynamic field theory: functional representations, logics, and brain dynamics

Course materials

beim Graben, P. & Potthast, R. (2009). Inverse problems in dynamic cognitive modeling. Chaos: An Interdisciplinary Journal of Nonlinear Science, 19, 015103; and references therein.