Hopfield Network with Interneuronal Connections Based on Memristor Bridges
A scheme for the Hopfield associative memory hardware implementation with interneuronal connections through bridges using memristors is proposed. The Hopfield associative memory is realized as a network of coupled phase oscillators. It is shown how to use
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Abstract. A scheme for the Hopfield associative memory hardware implementation with interneuronal connections through bridges using memristors is proposed. The Hopfield associative memory is realized as a network of coupled phase oscillators. It is shown how to use the CMOS transistor switches to control the memristance (memristor resistance) value. Keywords: Memristor matrix LTSPICE
Memristance Bridge Hopfield network Weight
1 Introduction Memristor was predicted theoretically in 1971 by Chua [1]. First physical memristor implementation in 2008 was demonstrated by a laboratory from Hewlett Packard as a thin film structure TiO2 [2]. In Russia the first TiO2 memristor was obtained in 2012 by the Tyumen State University [3]. The memristor has many advantages such as non-volatile storage media, low power consumption, high density integration and excellent scalability. The unique ability to retain traces of the device excitation makes it an ideal candidate for the implementation of electronic synapses in neural networks [4]. The memristor-based Hopfield networks are intensively investigated now [5, 6]. In this article we propose a new version of the memristor-based Hopfield associative memory implemented as a network of coupled phase oscillators [7]. Such network has only error-free retrieval states.
2 Memristor A memristor behaves like a synapse: it “remembers” the total electric charge passed through it [8]. The memristor-based memory can reach its very high integration degree of 100 Gbits/cm2, several times higher than that based on the flash memory technology [9]. These unique properties make the memristor a promising device for creating massively parallel neuromorphic systems [10–12].
© Springer International Publishing Switzerland 2016 L. Cheng et al. (Eds.): ISNN 2016, LNCS 9719, pp. 196–203, 2016. DOI: 10.1007/978-3-319-40663-3_23
Hopfield Network with Interneuronal Connections
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A memristance (the memristor resistance) (Fig. 1) can be represented [13] as MðpÞ ¼ p Ron þ ð1 pÞ Roff ;
ð1Þ
where 0 p 1 is the doping front position relative to the total film thickness h of TiO2, Ron is the memristor minimum resistance, Roff is the memristor maximum resistance. Setting the memristor to the desired level of memristance Md depends on the ratio between Md and the initial memristance value M0 . For model (1), the memristance adjustment is made by applying a constant voltage V [ Vth for M0 [ Md or a voltage V\ Vth for M0 \Md to the memristor due some time [14]
s¼
8 > < > :
M02 Md2 2kðVVth Þ ; M02 Md2 2kðV þ Vth Þ ;
V [ Vth ;
ð2Þ
V\ Vth ;
R
where k ¼ lv hoff2 ðRoff Ron Þ. Here lv is the average ion mobility, h is the total memristor film thickness, VðtÞ is the current voltage value on the memristor, Vth is the threshold voltage.
Fig. 1. The memristor structure: D – the low resistance region, U – the high resistance region, p 2 ½0; 1 is the doping front position relative to the total film thickness h of TiO2
3 Weighting Input Signals by Bridge Circuits Both positive and negative weighi
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