Statistical Mechanics of an Oscillator Associative Memory with Scattered Natural Frequencies

Aonishi, Toru; Kurata, K.; Okada, Masato

doi:10.1103/physrevlett.82.2800

Cited by 49 publications

(34 citation statements)

References 16 publications

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“…The other one is the replica theory, which has been used to analyze the equilibrium states in Model 1 [9]. However, the replica theory cannot be applied to a system where the free energy cannot be defined (e.g., a model with a nonmonotonic output function [10] or an oscillator associative memory model [11]), while the SCSNA can treat these systems without the energy function. Since previous studies with the SCSNA have mainly focused on systems with uniformly distributed patterns, the SCSNA cannot be directly applied to Model 1.…”

Section: A Generalized Scsnamentioning

confidence: 99%

Bistability of mixed states in a neural network storing hierarchical patterns

Toya

Fukushima

Kabashima

et al. 2000

J. Phys. A: Math. Gen.

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We discuss the properties of equilibrium states in an autoassociative memory model storing hierarchically correlated patterns (hereafter, hierarchical patterns). We will show that symmetric mixed states (hereafter, mixed states) are bi-stable on the associative memory model storing the hierarchical patterns in a region of the ferromagnetic phase. This means that the first-order transition occurs in this ferromagnetic phase. We treat these contents with a statistical mechanical method (SCSNA) and by computer simulation. Finally, we discuss a physiological implication of this model. Sugase et al. analyzed the time-course of the information carried by the firing of face-responsive neurons in the inferior temporal cortex [1]. We also discuss the relation between the theoretical results and the physiological experiments of Sugase et al.

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Section: A Generalized Scsnamentioning

confidence: 99%

Bistability of mixed states in a neural network storing hierarchical patterns

Toya

Fukushima

Kabashima

et al. 2000

J. Phys. A: Math. Gen.

Self Cite

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“…Recently, based on the above cited theory of Sakaguchi and Kuramoto, Aonishi et al proposed a systematic method to treat the macroscopic properties of associative memory with distributed natural frequencies. 23) They studied how the overlap is influenced by the variance of the frequency distribution and the loading rate α (= p/N ). Their theory contains both the theories of Kuramoto and Sakaguchi and of Cook.…”

Section: §1 Introductionmentioning

confidence: 99%

Oscillation of the Overlap Parameter in a Phase Coupled Model

Kawaguchi

2002

Progress of Theoretical Physics

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A phase coupled oscillator neural network for associative memory is studied. The natural frequency is assumed to be distributed among several types. We use an overlap parameter in order to measure the ability of the retrieval system. When there are higher frequency neurons with sufficiently large population fraction, the system cannot converge to an equilibrium state, and the overlap oscillates. This periodic oscillation is destabilized to quasi-periodic or chaotic oscillation through the period-doubling route as the range of the natural frequency increases. In this research, we numerically investigate the oscillation of the overlap. We find that the population whose frequency is distributed around zero remains a non-zero fixed value of the overlap. On the other hand, the other groups with higher frequencies contribute to the oscillatory components. The mean value of the oscillatory overlap determined using the modified SCSNA well agrees in case of periodic oscillation with small amplitude. However, it is difficult to evaluate this value for the quasi-periodic and chaotic oscillation, as the overlap obtained with the time average is time dependent. We discuss the dependences of the overlap oscillation and its phase diagram on the natural frequency distributions, and refer to the limitations of the existing theories for the equilibrium state. §1. IntroductionSystems with large numbers of elements often exhibit coherent motions. 1) In the case that each element has different characteristics, it seems to be impossible to have such collective behavior. However, we often observe collective phenomena under specific conditions with certain types of interactions. To understand the mechanism of such collective motion is very important and attractive so that many researchers has devoted to it. 2), 3)Although the brain is one such complicated system, it behaves coherently. In order to understand real brain functions, it is important to study the macroscopic properties of assemblies of many neurons. In mammalian brains, there are different types of neurons, which cooperate with each other to perform complex functions. It is known that some groups of neurons fire with synchronized timing. They code information and transmit signals through the temporal timing of their firing. 4)-10) It is difficult to directly describe such a complex system in detail. As a good simplification of such a complex system, we regard each neuron as a harmonic oscillator with a phase variable. So far, there have been many studies of phase coupled oscillator models, and some kinds of associative memory models have been proposed. 11)-15) In a system of a large number of neurons, the system can retrieve embedded patterns * ) Present address:

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“…For instance, an oscillatory neural network is a class of coupled phase oscillators, in which each oscillator is regarded as a spiking neuron in a periodic firing state. The dynamical and statistical properties of the oscillatory neural networks have been investigated in detail as a model of associative memory [2], [3].…”

Section: Introductionmentioning

confidence: 99%

CMOS pulse-modulation circuit implementation of phase-locked loop neural networks

Atuti

Nakada

Matsukawa

2008

2008 IEEE International Symposium on Circuits and Systems (ISCAS)

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In this paper, we have applied the pulse-modulation circuit technique to implement phase-locked loop (PLL) neural networks proposed by Hoppensteadt and Izhikevich. The PLL neural network is an oscillatory neural network as a model of associative memory, and it is represented as coupled phase oscillators with periodic phase variables and periodic nonlinear interactions. In our circuit implementation, the phase variables and their summation and subtraction are represented by pulsewidth modulation (PWM) signals. The interactions are realized by using nonlinear current waveform sampled with pulse-phase modulation (PPM) signals converted from the PWM signals. We have designed an element circuit and simulated two coupled such circuits with SPICE using the TSMC 0.25 μm device parameters. The results demonstrate that the element circuits synchronized with in-and anti-phase depending on coupling strength at different operation frequencies. The element circuit has an advantage in extracting phase difference between the circuits. This will facilitate implementing of learning by arbitrary spike-timing dependent plasticity (STDP) rules using the phase difference.

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Statistical Mechanics of an Oscillator Associative Memory with Scattered Natural Frequencies

Cited by 49 publications

References 16 publications

Bistability of mixed states in a neural network storing hierarchical patterns

Bistability of mixed states in a neural network storing hierarchical patterns

Oscillation of the Overlap Parameter in a Phase Coupled Model

CMOS pulse-modulation circuit implementation of phase-locked loop neural networks

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