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Dynamics of Neural Networks

Center for Cognitive Sciences Institute for Neurophysics University of Bremen

In my dissertation I investigated the dynamics of auto-associative neural networks. These are highly non-linear dynamical systems with large degrees of freedom. Instead of calculating thermodynamical properties, as it is usually done, in this thesis a dynamical theory of memory-recall was developed.

Specific results were:

  • Derivation of an approximate theory starting from an correct treatment of the exact theory. The approximate theory was able to describe correctly the dynamical recall of the stored memory-patterns, including the areas of attraction for the stored patterns, for deterministic and stochastic neuronal dynamics.
  • Discussion of various aspects of the dynamics of these networks; fully connected, sparse connected, areas of attraction, etc.
  • Investigations into the structure of the attractor space if multiple patterns are stored in the associative memory, dependence of the type of the neuronal update rule used.
  • An exact enumeration of all memory patters stable in a Hopfield-network which has learned only 7 patters: besides the seven learned patterns, 3.548.358 additional spurious states appear!
  • An network which has no spurious states - under certain circumstances.
Download a german version of the dissertation

You might want to check these publications:

  • Distribution of Internal Fields and Dynamics of Neural Networks, R. D. Henkel and M. Opper, Europhysics Lett. 11(5): 403-408.
  • Parallel Dynamics of the Neural Network with Pseudoinverse Coupling Matrix, R.D. Henkel and M. Opper, J. Phys. A: Math. Gen. 24: 2201-2218, 1991.

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