On the Phase Transition of Hopfield Networks — Another Monte Carlo Study

Volk, Daniel

doi:10.1142/s0129183198000595

Cited by 11 publications

(5 citation statements)

References 6 publications

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“…Posterior computer simulations of larger Hopfield networks and its extrapolation to 1/N ! 0 resulted in a value of n c % 0.14 N (Volk 1998) which agrees with a theoretical value of n c ¼ 0.138 N obtained within a statistical physics mean-field approach (Amit et al 1987). This memory capacity can be increased assuming some conditions over the network topology and the stored patterns.…”

Section: Memory Capacitysupporting

confidence: 86%

Hopfield Network

Torres

2014

Encyclopedia of Computational Neuroscience

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Section: Memory Capacitysupporting

confidence: 86%

Hopfield Network

Torres

2014

Encyclopedia of Computational Neuroscience

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“…Posterior numerical simulations of larger Hopfield networks and its extrapolation to 1/N ! 0 resulted in a value of n c % 0.14 N (Volk 1998) which agrees with a theoretically value of n c = 0.138 N obtained within a statistical physics mean-field approach (Amit et al 1987). This memory capacity can be increased assuming some conditions over the network topology and the stored patterns.…”

Section: Memory Capacitysupporting

confidence: 85%

Hopfield Network

Torres¹

2019

Encyclopedia of Computational Neuroscience

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Attractor neural network; Binary neural network; Equilibrium neural network; Recurrent neural network Definition Hopfield model was originally introduced as the representation of a physical system, whose state in a given time is defined by a vector X(t) = {X 1 (t),.. .,X N (t)}, with a large number of locally stable states in its phase space, namely, X a , X b ,.. .., also called attractors. Starting from some initial condition within the basin of attraction of one of these minima, that is, X(0) = X a + D, the dynamics leads the system toward this minimum, that is, X(t ! 1) % X a. The model provides a rule

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“…For infinite range, m = N, the usual Hopfield model [12] gives an overlap Ψ close to 1 for P/N < 0.14 and a relatively small overlap Ψ ∼ 0.2 for P/N > 0.14, with a sharp jump at P/N = 0.14. Our simulations, in contrast, show a gradual deterioration as soon as more than one pattern is stored, but the value of Ψ is still of order 0.2 and distinctly larger than for the other (P − 1) patterns.…”

mentioning

confidence: 96%

Efficient Hopfield pattern recognition on a scale-free neural network

Stauffer

Aharony

Costa³

et al. 2003

The European Physical Journal B - Condensed Matter

113

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Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the "standard" Hopfield model, the N "neurons" are connected to each other via N 2 bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N 2 . The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q 3 . Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N . Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time.

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On the Phase Transition of Hopfield Networks — Another Monte Carlo Study

Cited by 11 publications

References 6 publications

Hopfield Network

Hopfield Network

Hopfield Network

Efficient Hopfield pattern recognition on a scale-free neural network

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