Efficient Hopfield pattern recognition on a scale-free neural network

Stauffer, Dietrich; Aharony, Ammon; Costa, Luciano da F.; Adler, John

doi:10.1140/epjb/e2003-00114-7

Cited by 113 publications

(70 citation statements)

References 10 publications

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“…For the functional networks of the human brain with ␥ Ӎ 2.1 (32), this implies that the storage capacity grows as N ␣ with ␣ Ӎ 0.73. These mean field predictions should be accessible to simulation studies that have been restricted, so far, to the special case ␥ ϭ 3 Ͼ 5͞2 (35).…”

Section: [14]mentioning

confidence: 99%

Dynamic pattern evolution on scale-free networks

Zhou

Lipowsky

2005

Proc. Natl. Acad. Sci. U.S.A.

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A general class of dynamic models on scale-free networks is studied by analytical methods and computer simulations. Each network consists of N vertices and is characterized by its degree distribution, P(k), which represents the probability that a randomly chosen vertex is connected to k nearest neighbors. Each vertex can attain two internal states described by binary variables or Ising-like spins that evolve in time according to local majority rules. Scalefree networks, for which the degree distribution has a power law tail P(k) ϳ k ؊␥ , are shown to exhibit qualitatively different dynamic behavior for ␥ < 5͞2 and ␥ > 5͞2, shedding light on the empirical observation that many real-world networks are scale-free with 2 < ␥ < 5͞2. For 2 < ␥ < 5͞2, strongly disordered patterns decay within a finite decay time even in the limit of infinite networks. For ␥ > 5͞2, on the other hand, this decay time diverges as ln(N) with the network size N. An analogous distinction is found for a variety of more complex models including Hopfield models for associative memory networks. In the latter case, the storage capacity is found, within mean field theory, to be independent of N in the limit of large N for ␥ > 5͞2 but to grow as N ␣ with ␣ ‫؍‬ (5 ؊ 2␥)͞(␥ ؊ 1) for 2 < ␥ < 5͞2.random network ͉ Boolean dynamics ͉ cellular automata ͉ associative memory

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Section: [14]mentioning

confidence: 99%

Dynamic pattern evolution on scale-free networks

Zhou

Lipowsky

2005

Proc. Natl. Acad. Sci. U.S.A.

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“…Indeed, there are many examples of dynamics on complex networks, in which nodes are interacting each other and a macroscopically functional behavior emerges. Examples of these networks with dynamics are neural networks in a brain [8], Hopfield models in complex networks [9,10,11], protein folding [12], and combinatoric optimization problems [13].…”

Section: Introductionmentioning

confidence: 99%

Statistical-mechanical iterative algorithms on complex networks

2005

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The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in Barabási and Albert networks, but does not influence that in Erdös and Rényi networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barabási-Albert's scale-free networks.

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“…One of the practical applications of such an artificial neural network can be found in the Hopfield model [17], which is used frequently in the pattern recognition. Very recently, there have been studies of the Hopfield model of neurons put on the structure of complex networks [18,19], with major focus on how the topology, the degree distribution in particular, of a network affects the computational performance of the Hopfield model. Also in the neuroscience, recent investigations have revealed the close interrelationship between the brain activity and the underlying neuroanatomy [13].…”

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confidence: 99%

Performance of networks of artificial neurons: The role of clustering

Kim

2004

Phys. Rev. E

123

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The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barabási-Albert network, and the neuronal network of the C. elegans. Through the use of a systematic way of controlling the clustering coefficient, with the degree of each neuron kept unchanged, we find that the networks with the lower clustering exhibit much better performance. The results are discussed in the practical viewpoint of application, and the biological implications are also suggested.

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Efficient Hopfield pattern recognition on a scale-free neural network

Cited by 113 publications

References 10 publications

Dynamic pattern evolution on scale-free networks

Dynamic pattern evolution on scale-free networks

Statistical-mechanical iterative algorithms on complex networks

Performance of networks of artificial neurons: The role of clustering

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