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Associative Memory Realized by a Reconfigurable Memristive Hopfield

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Associative Memory Realized by a Reconfigurable Memristive Hopfield ARTICLE Received 30 Aug 2014 | Accepted 15 May 2015 | Published 25 Jun 2015 DOI: 10.1038/ncomms8522 Associative memory realized by a reconfigurable memristive Hopfield neural network S.G. Hu1,Y.Liu1, Z. Liu2, T.P. Chen3, J.J. Wang1,Q.Yu1, L.J. Deng1,Y.Yin4 & Sumio Hosaka4 Although synaptic behaviours of memristors have been widely demonstrated, implementa- tion of an even simple artificial neural network is still a great challenge. In this work, we demonstrate the associative memory on the basis of a memristive Hopfield network. Different patterns can be stored into the memristive Hopfield network by tuning the resistance of the memristors, and the pre-stored patterns can be successfully retrieved directly or through some associative intermediate states, being analogous to the associative memory behaviour. Both single-associative memory and multi-associative memories can be realized with the memristive Hopfield network. 1 State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, China. 2 School of Materials and Energy, Guangdong University of Technology, Guangzhou 510006, China. 3 School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore. 4 Graduate School of Engineering, Gunma University, 1-5-1Tenjin, Kiryu, Gunma 376-8515, Japan. Correspondence and requests for materials should be addressed to Y.L. (email: [email protected]) or T.P.C. (email:[email protected]). NATURE COMMUNICATIONS | 6:7522 | DOI: 10.1038/ncomms8522 | www.nature.com/naturecommunications 1 & 2015 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8522 he idea of building a cognitive system that can adapt like a c 1 103 the biological brain has existed for a long time . However, 200 nm Au ∼ μ G0: 25 S 10 nm Ni 0 building an artificial brain with the conventional digital 80 nm HfO 101 2 G T / 2 70 nm Ni computer based on von-Neumann paradigm is of great G –1 10 difficulty. Digital computers and biological brains process SiO 2 10–3 3 information in fundamentally different ways. Digital computers 10 ∼ μ G0: 5 S S4800 5.0 kV 6.1 mm × 100 k SE (U,LA0) 500 nm process information in sequence and are inflexible, precise and 0 101 G 3,4 / deterministic ; in contrast, biological brains process data in G b –1 parallel and are flexible, not precise, error-prone and good at 1.0 10 1,4 10–3 learning new matters . Obviously, to efficiently realize the 0.5 5 10 G : ∼1.4 μS 3 0 functionalities of biological brains, new computing architectures 0 10 0.0 G are required. In the past few decades, artificial neural networks / 101 G (ANNs) have received much attention, as they have a natural Current (mA) –0.5 10–1 10–3 capability for storing information and making it available –1.0 –3–2–10123 5 –2 –1 0 1 2 for use . In 1980s, Hopfield proposed a dynamic ANN Voltage (V) Voltage (V) called Hopfield network6–9. The Hopfield network has been 10 proved useful in content-addressable memories , and Figure 1 | The HfO2-based memristor. (a) Scanning electron microscopic combinatorial optimization problems, such as the travelling image of the cross-section of the memristor; (b) I–V characteristics of a salesman problem and the location allocation problem8,11. typical memristor measured for five repeated cycles of voltage sweeping Previous Hopfield network was realized by constructing with the compliance current of 1 mA; and (c) conductance (G) of the complementary metal–oxide–semiconductor circuits as the memristors with different initial conductance (G0) as a function of the pulse synapses at a cost of large chip area and power consumption10. voltage, with the pulse width fixed at 5 ms. In 1971, Chua predicted the fourth basic circuit element, namely, memristor12,13, which was later demonstrated in the laboratory by Williams et al. in 2008 (ref. 14). Subsequently, many for the negative voltage polarity, the current increases with the studies demonstrated that a memristor can be used as an voltage magnitude, but it decreases gradually when the voltage electronic synapse with its conductance representing the synaptic reaches B À 1V. weight15–25. Although synaptic operation of memristors has been Besides the voltage sweeping, voltage pulses can also be used to widely demonstrated, implementation of even a simple ANN is change the conductance of the memristor. Figure 1c shows the challenging. Encouragingly, some significant advances have been conductance change of the memristors with different initial reported recently. For example, ANN consisting of neurons and conductance (G0) for the pulse duration of 5 ms. Generally, a synapses has been constructed to realize the Pavlov’s dog positive or negative pulse voltage leads to an increase or decrease model26–28; Alibart et al. reported the realization of linear in the conductance, respectively. The conductance shows little pattern classification using a memristive network29; Park et al. change for small pulse voltage, but the change is large for a large realized neuromorphic speech systems using resistive random- pulse voltage (for example, þ 2 V for positive pulse voltage, access memory -based synapse30; and Eryilmaz et al. reported À 2 V for negative pulse voltage). The result indicates that brain-like associative learning using phase-change synaptic device the resistance of the memristor can be adjusted to the desired array31. Burr et al. demonstrated a neural network with 165K values with an appropriate voltage–pulse programming synapses implemented with phase-change devices32. scheme (see Supplementary Fig. 1). The conductive filament In this work, we have successfully constructed a Hopfield (CF) model can be used to explain the resistance change in the 33,34 network using HfO2 memristors and peripheral devices to realize HfO2-based resistive memristors . Considering the bipolar the associative memory that is capable of retrieving a piece of data nature of the memristor, the formation or rupture of some CF upon presentation of partial information from that piece of data. consisting of oxygen vacancies are responsible for the resistance The network can be reconfigured to realize various positive and change35. In the initialization process (that is, the forming negative synaptic weights. Both single-associative memory and process), CF are formed in the HfO2 thin film to connect the two multi-associative memories can be realized with the memristive electrodes, resulting in a low-resistance state. Subsequently, a Hopfield network (MHN). Associative memories via or not via negative (positive) voltage can lead to the gradual rupture intermediate states can be used to emulate humans’ ‘weak’ or (recovery) of CF, resulting in an increase (decrease) in the ‘strong’ memories, respectively. In addition, the proposed MHN resistance. The memristive switching from high-resistance state shows good robustness to device variation and variations in to low-resistance state could be attributed to CF formation at threshold voltage of the neurons. This study provides a possible the grain boundaries containing a high concentration of method for hardware implementation of artificial neuromorphic oxygen vacancies33. On the other hand, electric field could networks to emulate memorization. play an important role in switching from low-resistance state to high-resistance state34. It was suggested that electrical pulses lead to a progressive narrowing of the CF, and finally a gap is Results formed and the memristor switches to the high-resistance Memristor characterization. The memristor used in this work state33,34. has a metal/oxide/metal structure, as shown in Fig. 1a. After a forming process with high voltage, resistance of the memristor can be increased or decreased by voltage bias MHN implementation. Basic findings from the biological neuron depending on the voltage polarity. Figure 1b shows the I–V operation have enabled researchers to model the operations characteristics of five repeated cycles of voltage sweeping for a of artificial neurons36. A Hopfield network consists of a set of typical memristor. Each cycle of sweeping takes B10 s and the interconnected artificial neurons and synapses. In this work, a period of each applied voltage is 40 ms. For the positive voltage Hopfield network is constructed with nine synapses realized with polarity, the current increases very little with voltage at low vol- six memristors and three neurons. As shown in Fig. 2a, the B tages, but it rises rapidly when the voltage is increased to 1V; artificial neuron has three inputs and each input, Ni (i ¼ 1, 2 2 NATURE COMMUNICATIONS | 6:7522 | DOI: 10.1038/ncomms8522 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8522 ARTICLE 0 1 acN M11 M12 M13 1 @ A w1 the resistance matrix M ¼ M21 M22 M23 and the synaptic Inputs w w w Output 31 32 33 0 M31 M32 1M33 N2 w2 w11 w12 w13 w3 @ A w21 w22 w23 weight matrix W ¼ w21 w22 w23 , respectively. As the N3 w31 w32 w33 ¼ ¼ b Synapses Neuron w11 w12 w13 Hopfield network is symmetric, that is, M12 M21, M23 M32 and M13 ¼ M31, the network can be realized with only six I1 R S1 memristors as shown in Fig. 2d (see Supplementary Fig. 2 for the N1 – M B1 Output complete circuit schematic of the MHN). And all the discussions 1 I 2 1 2 3 R S + below are based on this optimized architecture. The threshold of N 2 2 B M 2 the artificial neurons (neurons 1, 2 and 3) are represented by the 2 I3 S threshold vector T ¼ (y y y ); and the states of the three R 3 w 1 2 3 N3 ij Synapse Neuron B3 neurons are represented by the state vector X ¼ (x x x ), where M3 1 2 3 x1, x2 and x3 are the states of neurons 1, 2 and 3, respectively.
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