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.
[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.
[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.
@article{"International Journal of Information, Control and Computer Sciences:49372", author = "Mario Gonzalez and David Dominguez and Francisco B. Rodriguez", title = "Learning Block Memories with Metric Networks", 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.", volume = "2", number = "1", pages = "1-4", }
