In my dissertation I investigated the dynamics of autoassociative neural
networks. These are highly nonlinear dynamical systems with large degrees
of freedom. Instead of calculating thermodynamical properties, as it is
usually done, in this thesis a dynamical theory of memoryrecall
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 memorypatterns, 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 Hopfieldnetwork
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.
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):
403408.
 Parallel Dynamics of the Neural Network with Pseudoinverse Coupling
Matrix, R.D. Henkel and M. Opper, J. Phys. A: Math. Gen. 24:
22012218, 1991.
© 19942003  all rights reserved.
