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
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
- 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.
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):
- Parallel Dynamics of the Neural Network with Pseudoinverse Coupling
Matrix, R.D. Henkel and M. Opper, J. Phys. A: Math. Gen. 24:
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