Recurrent oscillatory networks of associative memory with Hebbian learning algorithm

• Main Authors: Kuzmina, M., Manykin, E., Surina, I.
• Format: Conference Proceeding
• Language: English
• Subjects: Associative memory; Biological system modeling; Clocks; Hebbian theory; Limit-cycles; Neural networks; Oscillators; Recurrent neural networks; Symmetric matrices; Synchronization
• DOI: 10.1109/ISNINC.1995.480864

Recurrent networks of associative memory of coupled limit-cycle oscillators in synchronization regime can be designed. Complex-valued Hermitian matrices are proved to be the proper class of matrices for specification of modifiable symmetrical couplings. The expressions for both weighted Hebbian and pseudo-inverse matrices of connections, representing the natural generalizations of those for Hopfield neural networks, are obtained. In the case of strong interaction between the oscillators a set of slightly perturbed eigenvectors of the matrix of connections belongs to the set of the network memory vectors. The locations of these memory vectors in the phase space can be calculated using a perturbation method on appropriate small parameter. Retrieval characteristics of oscillatory networks in the case of strong interaction coincide with those of "clock" neural networks (the networks of magnetic spins on a plane with continuous state space). Results of direct study of the set of fixed points of oscillatory network dynamics for the networks of various architectures are presented.