Learning Block Memories with Metric Networks

Authors: Mario Gonzalez, David Dominguez, Francisco B. Rodriguez

Abstract:

An attractor neural network on the small-world topology is studied. A learning pattern is presented to the network, then a stimulus carrying local information is applied to the neurons and the retrieval of block-like structure is investigated. A synaptic noise decreases the memory capability. The change of stability from local to global attractors is shown to depend on the long-range character of the network connectivity.

Keywords: Hebbian learning, image recognition, small world, spatial information.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327945

References:

[1] Patrick N. McGraw and Michael Menzinger, Topology and computational performance of attractor neural networks, Phys. Rev. E 68, 047102, 2003.
[2] Watts, D. J. and Strogatz, S. H., Collective dynamics of -small-world- networks, Nature, 393-6684, pages 440-442, 1998.
[3] R. Albert and A. Barabasi, Statistical mechanics of complex networks, Rev. Mod. Phys., 74-1, pages 47-97, 2002.
[4] D. R. Paula, A. D. Araujo, J. S. Andrade Jr., H.J. Herrmann and J. A. C. Gallas, Periodic neural activity induced by network complexity, Phys. Rev. E 74, 017102, 2006.
[5] D. J. Amit, Modelling Brain Function: The World of Attractor Neural Networks, Cambridge University Press, 1989.
[6] G. Morelli, G. Abramson and M. N. Kuperman, Associative memory on a small-world neural network, The European Physical Journal B 38-3, pages 495-500, 2004.
[7] T Nikoletopoulos, A. C. C. Coolen, I. Perez Castillo, N. S. Skantzos, J. P. L. Hatchett and B Wemmenhove, Replicated transfer matrix analysis of Ising spin models on small world lattices, J. Phys. A: Math. Gen. 37, pages 6455-64754, 2004.
[8] J. P. L. Hatchett, N. S. Skantzos, and T. Nikoletopoulos, Dynamic rewiring in small world networks, Phys. Rev. E 72, pages 066105, 2005.
[9] D. Dominguez, K. Koroutchev, E. Serrano and F. Rodriguez, Associative memory: information and topology, Research in Computing Science, Mexico, pages 39-48, 2006.
[10] D. Dominguez, Block information and topology in memory networks, CP887, Coop. Behavior in Neural Systems, Granada, pages 107-114, 2007.