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7 - Effects of network structure on associative memory

from Part II - The use of artificial neural networks to elucidate the nature of perceptual processes in animals

Published online by Cambridge University Press:  05 July 2011

By
Hiraku Oshima  and
Takashi Odagaki
Edited by
Colin R. Tosh  and
Graeme D. Ruxton
Hiraku Oshima
Affiliation:
Kyushu University
Takashi Odagaki
Affiliation:
Kyushu University
Colin R. Tosh
Affiliation:
University of Leeds
Graeme D. Ruxton
Affiliation:
University of Glasgow
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Summary

Introduction

The brain has various functions such as memory, learning, awareness, thinking and so on. These functions are produced by the activity of neurons that are connected to each other in the brain. There are many models to reproduce the memory of the brain, and the Hopfield model is one of the most studied (Hopfield, 1982). The Hopfield model was proposed to reproduce associative memory, and it has been studied extensively by physicists because this model is similar to the Ising model of spin glasses. This model was studied circumstantially, for example, the storage capacity was analysed by the replica method (Amit, 1989; Hertz et al., 1991). However, in these studies, the neural networks are completely connected, i.e. each neuron is connected to all other neurons. It was not clear how the properties of the model depend on the connections of neurons until recently (Tosh & Ruxton, 2006a, 2006b).

In recent years the study of complex networks has been paid much attention. A network consists of nodes and links. A node is a site or point on the network such as a neuron; the nodes are connected by links such as an axon or synapse of a neuron. Several characteristic network structures have been proposed, and the small-world and the scale-free networks have been studied heavily in recent years. Small-world networks have the properties that the characteristic path length is very short, and simultaneously the clustering coefficient is large (Watts & Strogatz, 1998).

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Modelling Perception with Artificial Neural Networks , pp. 134 - 148
Publisher: Cambridge University Press
Print publication year: 2010

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References

Albert, R. & Barabási, A. L. 2002. Statistical mechanics of complex networks. Rev Mod Phys 74, 47–97.CrossRefGoogle Scholar
Amit, D. J. 1989. Modeling Brain Function: The World of Attractor Neural Networks. Cambridge University Press.
Barabási, A. L. & Albert, R. 1999. Emergence of scaling in random networks. Science 286, 509–512.Google ScholarPubMed
Barabási, A. L., Albert, R. & Jeong, H. 1999. Mean-field theory for scale-free random networks. Physica A 272, 173–187.CrossRefGoogle Scholar
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. 2006. Complex networks: structure and dynamics. Phys Rep 424, 175–308.CrossRefGoogle Scholar
Bohland, J. W. & Minai, A. A. 2001. Efficient associative memory using small-world architecture. Neurocomputing 38–40, 489–496.CrossRefGoogle Scholar
Dorogovtsev, S. N., Mendes, J. F. F. & Samukhin, A. N. 2000. Structure of growing networks with preferential linking. Phys Rev Lett 85, 4633–4636.CrossRefGoogle ScholarPubMed
Eguíluz, V. M., Chialvo, D. R., Cecchi, G. A., Baliki, M. & Apkarian, A. V. 2005. Scale-free brain functional networks. Phys Rev Lett 94, 018102.CrossRefGoogle ScholarPubMed
Forrest, B. M. & Wallace, D. J. 1991. Storage capacity and learning in Ising–Spin neural networks. In Models of Neural Networks (ed. Domany, E., Hemmen, J. L. & Schulten, K.), pp. 121–148. Springer-Verlag.Google Scholar
Hertz, J., Krogh, A. & Palmer, R. G. 1991. Introduction to the Theory of Neural Computation. Addison-Wesley Publishing Co.Google Scholar
Hopfield, J. J. 1982. Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79, 2554–2558.CrossRefGoogle ScholarPubMed
Kim, B. J. 2004. Performance of networks of artificial neurons: the role of clustering. Phys Rev E 69, 045101.CrossRefGoogle ScholarPubMed
Lu, J., He, J., Cao, J. & Gao, Z. 2006. Topology influences performance in the associative memory neural networks. Phys Lett A 354, 335–343.CrossRefGoogle Scholar
McCulloch, W. S. & Pitts, W. 1990. A logical calculus of the ideas imminent in nervous activity. Bull Math Biol 52, 99–115.CrossRefGoogle Scholar
McGraw, P. N. & Menzinger, M. 2003. Topology and computational performance of attractor neural networks. Phys Rev E 68, 047102.CrossRefGoogle ScholarPubMed
Morelli, L. G., Abramson, G. & Kuperman, M. N. 2004. Associative memory on a small-world neural network. Eur Phys J B 38, 495–500.CrossRefGoogle Scholar
Newman, M. E. J. 2003. The structure and function of complex networks. SIAM Rev 45, 167–256.CrossRefGoogle Scholar
Oshima, H. & Odagaki, T. 2007. Storage capacity and retrieval time of small-world neural networks. Phys Rev E 76, 036114.CrossRefGoogle ScholarPubMed
Oshio, K., Iwasaki, Y., Morita, S.et al. 2003. Database of Synaptic Connectivity of C. elegans for Computation. Technical Report of CCeP, Keio Future No. 3. Keio University. http://www.bio.keio.ac.jp/ccep/
Stauffer, D., Aharony, A., Costa, L. D. & Adler, J. 2003. Efficient Hopfield pattern recognition on a scale-free neural network. Eur Phys J B 32, 395–399.CrossRefGoogle Scholar
Strogatz, S. H. 2003. Sync: The Emerging Science of Spontaneous Order. Hyperion.Google Scholar
Tosh, C. R. & Ruxton, G. D. 2006a. Artificial neural network properties associated with wiring patterns in the visual projections of vertebrates and arthropods. Am Natl 168, E38–E52.CrossRefGoogle ScholarPubMed
Tosh, C. R. & Ruxton, G. D. 2006b. Introduction. The use of artificial neural networks to study perception in animals. Phil Trans R Soc B 362, 337–338.CrossRefGoogle Scholar
Watts, D. J. & Strogatz, S. H. 1998. Collective dynamics of ‘small-world’ networks. Nature 393, 440–442.CrossRefGoogle ScholarPubMed

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