Explorations of fitness landscapes of a Hopfield associative memory with random and evolutionary walks

We apply evolutionary computations to the Hopfield's neural network model of associative memory. In the model, some of the appropriate configurations of the synaptic weights give the network a function of associative memory. One of our goals is to obtain the distribution of these optimal configurations as the global optima in the synaptic weight space as well as the information of local optima created together. In other words, our aim is to know a geometry of fitness landscapes defined on weight space. As a step toward this goal, we concentrate in this paper mainly on the local optima. Hence, we use a walk by the Gaussian mutation to explore the fitness landscape, rather than more effective evolutionary walks, expecting its high probability to be trapped at the local optima.

[1]  A. Bray,et al.  Metastable states in spin glasses with short-ranged interactions , 1981 .

[2]  E. Capaldi,et al.  The organization of behavior. , 1992, Journal of applied behavior analysis.

[3]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Akira Imada,et al.  Random Perturbations to Hebbian Synapses of Associative Memory Using a Genetic Algorithm , 1997, IWANN.

[5]  John Maynard Smith,et al.  Natural Selection and the Concept of a Protein Space , 1970, Nature.

[6]  Tatsuya Uezu,et al.  The Phase Space of Interactions and the Hebb Rule in the Neural Network Models , 1996 .

[7]  E. Gardner,et al.  Metastable states of a spin glass chain at 0 temperature , 1986 .

[8]  Leon N. Cooper,et al.  A possible organization of animal memory and learning , 1973 .

[9]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[10]  J. Maynard Smith.  Natural Selection and the Concept of a Protein Space , 1970 .

[11]  P. Schuster,et al.  A computer model of evolutionary optimization. , 1987, Biophysical chemistry.

[12]  János Komlós,et al.  Convergence results in an associative memory model , 1988, Neural Networks.

[13]  S. Kauffman,et al.  Towards a general theory of adaptive walks on rugged landscapes. , 1987, Journal of theoretical biology.

[14]  A. Perelson,et al.  Evolutionary walks on rugged landscapes , 1991 .

[15]  Akira Imada,et al.  Evolution of Hopfield Model of Associative Memory by the Breeder Genetic Algorithm , 1997, ICGA.

[16]  A. Bray,et al.  Metastable states in spin glasses , 1980 .