Retrieval dynamics of associative memory of the Hopfield type

Nishimori, Hidetoshi; Ozeki, Tomohiko

doi:10.1088/0305-4470/26/4/013

Cited by 56 publications

(28 citation statements)

References 14 publications

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“…It has been confirmed with numerical simulations that the assumption is valid as long as the network succeeds in retrieval [28]. Under the above assumptions, we study the properties of this network by applying the methods of statistical neurodynamics [29][30][31][32].…”

Section: Theoretical Analysismentioning

confidence: 73%

Abrupt and Arbitrary Profile Formation in Silicon Using a Low-Kinetic-Energy Ion Bombardment Process

Shindo¹,

Hirayama²,

Ohmi³

1995

Jpn. J. Appl. Phys.

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We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean activity level and in the timing of spikes. Applying the methods of statistical neurodynamics to our model, we investigate theoretically the model's associative memory capability by evaluating its maximum storage capacities and deriving its basins of attraction. It is shown that, as in the Hopfield model, the storage capacity diverges as the activity level decreases. We consider various practically and theoretically important cases. For example, it is revealed that a dynamically adjusted threshold mechanism enhances the retrieval ability of the associative memory. It is also found that, under suitable conditions, the network can recall patterns even in the case that patterns with different activity levels are stored at the same time. In addition, we examine the robustness with respect to damage of the synaptic connections. The validity of these theoretical results is confirmed by reasonable agreement with numerical simulations.

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Section: Theoretical Analysismentioning

confidence: 73%

Abrupt and Arbitrary Profile Formation in Silicon Using a Low-Kinetic-Energy Ion Bombardment Process

Shindo¹,

Hirayama²,

Ohmi³

1995

Jpn. J. Appl. Phys.

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“…It was analyzed by many researchers since the 1980s (see, for instance, [10,35,48]). It was analyzed by many researchers since the 1980s (see, for instance, [10,35,48]).…”

Section: Network Of Autoassociative Memorymentioning

confidence: 99%

“…The macrodynamical system derived in [10] can be written in the form The extension of the statistical macrodynamical approach [10] to finite tempera ture dynamics was performed in [48].…”

Section: Macrodynamical System For the Retrieval Processmentioning

confidence: 99%

2. Neural and oscillatory networks of associative memory

Kuzmina¹,

Manykin²,

Grichuk³

2013

Oscillatory Neural Networks

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Design of artificial neural network models with simple architectures of connections is a necessary step to the elucidation of basic principles of parallel information pro cessing. It allows us to understand the capabilities and limitations of these network models and obtain well-established mathematical results.Various neural network models of correlation-type associative memory have been developed since 1972. The first models were proposed in [12,29,46]. There is a number of different types of associative memory networks, among which are cross-correlation associative memory networks (or networks of heteroassociative memory), autocorrela tion associative memory networks, sequence recalling associative memory networks, bilateral associative memory (BAM) networks and others. In this section, we present the most important results of a qualitative analysis of the main properties of associa tive memory networks: their memory storage capacity and dynamical behavior.

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“…In models with symmetry in the synapses, the correlations among the elements of the crosstalk noise cannot be ignored. The numerical simulations show that the Gaussian assumption is only approximately valid when a successful recovery process takes place [13]. In Ref.…”

Section: Introductionmentioning

confidence: 97%

Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

Reynaga

2009

Physica A: Statistical Mechanics and its Applications

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Retrieval dynamics of associative memory of the Hopfield type

Cited by 56 publications

References 14 publications

Abrupt and Arbitrary Profile Formation in Silicon Using a Low-Kinetic-Energy Ion Bombardment Process

Abrupt and Arbitrary Profile Formation in Silicon Using a Low-Kinetic-Energy Ion Bombardment Process

2. Neural and oscillatory networks of associative memory

Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

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