1
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Kim G, In JH, Lee Y, Rhee H, Park W, Song H, Park J, Jeon JB, Brown TD, Talin AA, Kumar S, Kim KM. Mott neurons with dual thermal dynamics for spatiotemporal computing. NATURE MATERIALS 2024; 23:1237-1244. [PMID: 38890486 DOI: 10.1038/s41563-024-01913-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 05/05/2024] [Indexed: 06/20/2024]
Abstract
Heat dissipation is a natural consequence of operating any electronic system. In nearly all computing systems, such heat is usually minimized by design and cooling. Here, we show that the temporal dynamics of internally produced heat in electronic devices can be engineered to both encode information within a single device and process information across multiple devices. In our demonstration, electronic NbOx Mott neurons, integrated on a flexible organic substrate, exhibit 18 biomimetic neuronal behaviours and frequency-based nociception within a single component by exploiting both the thermal dynamics of the Mott transition and the dynamical thermal interactions with the organic substrate. Further, multiple interconnected Mott neurons spatiotemporally communicate purely via heat, which we use for graph optimization by consuming over 106 times less energy when compared with the best digital processors. Thus, exploiting natural thermal processes in computing can lead to functionally dense, energy-efficient and radically novel mixed-physics computing primitives.
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Affiliation(s)
- Gwangmin Kim
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Jae Hyun In
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Younghyun Lee
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Hakseung Rhee
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Woojoon Park
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Hanchan Song
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Juseong Park
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Jae Bum Jeon
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | | | - A Alec Talin
- Sandia National Laboratories, Livermore, CA, USA
| | - Suhas Kumar
- Sandia National Laboratories, Livermore, CA, USA.
| | - Kyung Min Kim
- Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea.
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2
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Delacour C, Carapezzi S, Abernot M, Todri-Sanial A. Energy-Performance Assessment of Oscillatory Neural Networks Based on VO 2 Devices for Future Edge AI Computing. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024; 35:10045-10058. [PMID: 37022082 DOI: 10.1109/tnnls.2023.3238473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Oscillatory neural network (ONN) is an emerging neuromorphic architecture composed of oscillators that implement neurons and are coupled by synapses. ONNs exhibit rich dynamics and associative properties, which can be used to solve problems in the analog domain according to the paradigm let physics compute. For example, compact oscillators made of VO2 material are good candidates for building low-power ONN architectures dedicated to AI applications at the edge, like pattern recognition. However, little is known about the ONN scalability and its performance when implemented in hardware. Before deploying ONN, it is necessary to assess its computation time, energy consumption, performance, and accuracy for a given application. Here, we consider a VO2-oscillator as an ONN building block and perform circuit-level simulations to evaluate the ONN performances at the architecture level. Notably, we investigate how the ONN computation time, energy, and memory capacity scale with the number of oscillators. It appears that the ONN energy grows linearly when scaling up the network, making it suitable for large-scale integration at the edge. Furthermore, we investigate the design knobs for minimizing the ONN energy. Assisted by technology computer-aided design (TCAD) simulations, we report on scaling down the dimensions of VO2 devices in crossbar (CB) geometry to decrease the oscillator voltage and energy. We benchmark ONN versus state-of-the-art architectures and observe that the ONN paradigm is a competitive energy-efficient solution for scaled VO2 devices oscillating above 100 MHz. Finally, we present how ONN can efficiently detect edges in images captured on low-power edge devices and compare the results with Sobel and Canny edge detectors.
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3
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Nath SK, Das SK, Nandi SK, Xi C, Marquez CV, Rúa A, Uenuma M, Wang Z, Zhang S, Zhu RJ, Eshraghian J, Sun X, Lu T, Bian Y, Syed N, Pan W, Wang H, Lei W, Fu L, Faraone L, Liu Y, Elliman RG. Optically Tunable Electrical Oscillations in Oxide-Based Memristors for Neuromorphic Computing. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2400904. [PMID: 38516720 DOI: 10.1002/adma.202400904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 03/18/2024] [Indexed: 03/23/2024]
Abstract
The application of hardware-based neural networks can be enhanced by integrating sensory neurons and synapses that enable direct input from external stimuli. This work reports direct optical control of an oscillatory neuron based on volatile threshold switching in V3O5. The devices exhibit electroforming-free operation with switching parameters that can be tuned by optical illumination. Using temperature-dependent electrical measurements, conductive atomic force microscopy (C-AFM), in situ thermal imaging, and lumped element modelling, it is shown that the changes in switching parameters, including threshold and hold voltages, arise from overall conductivity increase of the oxide film due to the contribution of both photoconductive and bolometric characteristics of V3O5, which eventually affects the oscillation dynamics. Furthermore, V3O5 is identified as a new bolometric material with a temperature coefficient of resistance (TCR) as high as -4.6% K-1 at 423 K. The utility of these devices is illustrated by demonstrating in-sensor reservoir computing with reduced computational effort and an optical encoding layer for spiking neural network (SNN), respectively, using a simulated array of devices.
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Affiliation(s)
- Shimul Kanti Nath
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
- Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
- School of Photovoltaic and Renewable Energy Engineering, University of New South Wales (UNSW Sydney), Kensington, NSW, 2052, Australia
| | - Sujan Kumar Das
- Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
- Department of Physics, Jahangirnagar Univeristy, Savar, Dhaka, 1342, Bangladesh
| | - Sanjoy Kumar Nandi
- Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
| | - Chen Xi
- Department of Electrical and Electronic Engineering, the University of Hong Kong, Pok Fu Lam Rd, Hong Kong Island, Hong Kong
| | | | - Armando Rúa
- Department of Physics, University of Puerto Rico, Mayaguez, PR, 00681, USA
| | - Mutsunori Uenuma
- Information Device Science Laboratory, Nara Institute of Science and Technology (NAIST), Nara, 630-0192, Japan
| | - Zhongrui Wang
- Department of Electrical and Electronic Engineering, the University of Hong Kong, Pok Fu Lam Rd, Hong Kong Island, Hong Kong
| | - Songqing Zhang
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
| | - Rui-Jie Zhu
- Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, 95064, USA
| | - Jason Eshraghian
- Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, 95064, USA
| | - Xiao Sun
- John de Laeter Centre, Curtin University, Perth, WA, 6102, Australia
| | - Teng Lu
- Research School of Chemistry, The Australian National University, Canberra, ACT, 2601, Australia
| | - Yue Bian
- Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
- Australian Research Council Centre of Excellence for Transformative Meta-Optical Systems, Canberra, ACT, 2601, Australia
| | - Nitu Syed
- Australian Research Council Centre of Excellence for Transformative Meta-Optical Systems, School of Physics, University of Melbourne, Melbourne, Victoria, 3010, Australia
| | - Wenwu Pan
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
- Australian Research Council Centre of Excellence for Transformative Meta-Optical Systems, Perth, WA, 6009, Australia
| | - Han Wang
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
| | - Wen Lei
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
| | - Lan Fu
- Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
- Australian Research Council Centre of Excellence for Transformative Meta-Optical Systems, Canberra, ACT, 2601, Australia
| | - Lorenzo Faraone
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
- Australian Research Council Centre of Excellence for Transformative Meta-Optical Systems, Perth, WA, 6009, Australia
| | - Yun Liu
- Research School of Chemistry, The Australian National University, Canberra, ACT, 2601, Australia
| | - Robert G Elliman
- Department of Electronic Materials Engineering, Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
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4
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Maher O, Jiménez M, Delacour C, Harnack N, Núñez J, Avedillo MJ, Linares-Barranco B, Todri-Sanial A, Indiveri G, Karg S. A CMOS-compatible oscillation-based VO 2 Ising machine solver. Nat Commun 2024; 15:3334. [PMID: 38637549 PMCID: PMC11026484 DOI: 10.1038/s41467-024-47642-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 04/09/2024] [Indexed: 04/20/2024] Open
Abstract
Phase-encoded oscillating neural networks offer compelling advantages over metal-oxide-semiconductor-based technology for tackling complex optimization problems, with promising potential for ultralow power consumption and exceptionally rapid computational performance. In this work, we investigate the ability of these networks to solve optimization problems belonging to the nondeterministic polynomial time complexity class using nanoscale vanadium-dioxide-based oscillators integrated onto a Silicon platform. Specifically, we demonstrate how the dynamic behavior of coupled vanadium dioxide devices can effectively solve combinatorial optimization problems, including Graph Coloring, Max-cut, and Max-3SAT problems. The electrical mappings of these problems are derived from the equivalent Ising Hamiltonian formulation to design circuits with up to nine crossbar vanadium dioxide oscillators. Using sub-harmonic injection locking techniques, we binarize the solution space provided by the oscillators and demonstrate that graphs with high connection density (η > 0.4) converge more easily towards the optimal solution due to the small spectral radius of the problem's equivalent adjacency matrix. Our findings indicate that these systems achieve stability within 25 oscillation cycles and exhibit power efficiency and potential for scaling that surpasses available commercial options and other technologies under study. These results pave the way for accelerated parallel computing enabled by large-scale networks of interconnected oscillators.
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Affiliation(s)
- Olivier Maher
- IBM Research Europe - Zurich, Säumerstrasse 4, 8803 Rüschlikon, Zürich, Switzerland.
- Institute of Neuroinformatics, University of Zürich and ETH Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
| | - Manuel Jiménez
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC, Universidad de Sevilla), Av. Américo Vespucio 28, 41092, Sevilla, Spain
| | | | - Nele Harnack
- IBM Research Europe - Zurich, Säumerstrasse 4, 8803 Rüschlikon, Zürich, Switzerland
| | - Juan Núñez
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC, Universidad de Sevilla), Av. Américo Vespucio 28, 41092, Sevilla, Spain
| | - María J Avedillo
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC, Universidad de Sevilla), Av. Américo Vespucio 28, 41092, Sevilla, Spain
| | - Bernabé Linares-Barranco
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC, Universidad de Sevilla), Av. Américo Vespucio 28, 41092, Sevilla, Spain
| | - Aida Todri-Sanial
- LIRMM, University of Montpellier, 56227, Montpellier, France
- Eindhoven University of Technology, Electrical Engineering Department, 5612AZ, Eindhoven, Netherlands
| | - Giacomo Indiveri
- Institute of Neuroinformatics, University of Zürich and ETH Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Siegfried Karg
- IBM Research Europe - Zurich, Säumerstrasse 4, 8803 Rüschlikon, Zürich, Switzerland.
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5
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Jeon JW, Park B, Jang YH, Lee SH, Jeon S, Han J, Ryoo SK, Kim KD, Shim SK, Cheong S, Choi W, Jeon G, Kim S, Yoo C, Han JK, Hwang CS. Vertically Stackable Ovonic Threshold Switch Oscillator Using Atomic Layer Deposited Ge 0.6Se 0.4 Film for High-Density Artificial Neural Networks. ACS APPLIED MATERIALS & INTERFACES 2024. [PMID: 38491936 DOI: 10.1021/acsami.3c18625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/18/2024]
Abstract
Nanodevice oscillators (nano-oscillators) have received considerable attention to implement in neuromorphic computing as hardware because they can significantly improve the device integration density and energy efficiency compared to complementary metal oxide semiconductor circuit-based oscillators. This work demonstrates vertically stackable nano-oscillators using an ovonic threshold switch (OTS) for high-density neuromorphic hardware. A vertically stackable Ge0.6Se0.4 OTS-oscillator (VOTS-OSC) is fabricated with a vertical crossbar array structure by growing Ge0.6Se0.4 film conformally on a contact hole structure using atomic layer deposition. The VOTS-OSC can be vertically integrated onto peripheral circuits without causing thermal damage because the fabrication temperature is <400 °C. The fabricated device exhibits oscillation characteristics, which can serve as leaky integrate-and-fire neurons in spiking neural networks (SNNs) and coupled oscillators in oscillatory neural networks (ONNs). For practical applications, pattern recognition and vertex coloring are demonstrated with SNNs and ONNs, respectively, using semiempirical simulations. This structure increases the oscillator integration density significantly, enabling complex tasks with a large number of oscillators. Moreover, it can enhance the computational speed of neural networks due to its rapid switching speed.
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Affiliation(s)
- Jeong Woo Jeon
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Byongwoo Park
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Yoon Ho Jang
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Soo Hyung Lee
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Sangmin Jeon
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Janguk Han
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Seung Kyu Ryoo
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Kyung Do Kim
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Sung Keun Shim
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Sunwoo Cheong
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Wonho Choi
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Gwangsik Jeon
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Sungjin Kim
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Chanyoung Yoo
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States
| | - Joon-Kyu Han
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
| | - Cheol Seong Hwang
- Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Gwanak-ro 1, Daehagdong, Gwanak-gu, Seoul 08826, Republic of Korea
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6
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Yun SY, Han JK, Choi YK. A Nanoscale Bistable Resistor for an Oscillatory Neural Network. NANO LETTERS 2024; 24:2751-2757. [PMID: 38259042 DOI: 10.1021/acs.nanolett.3c04539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2024]
Abstract
Coupled oscillators construct an oscillatory neural network (ONN) by mimicking the interactions among neurons in the human brain. This work demonstrates a fully CMOS-based oscillator consisting of a bistable resistor (biristor), which shares a structure identical with that of a metal-oxide-semiconductor field-effect transistor, except for the use of a gate electrode. The biristor-based oscillator (birillator) generates oscillating voltage signals in the form of spikes due to a single transistor latch phenomenon. When two birillators are connected with a coupling capacitor, they become synchronized with a phase difference of 180°. These coupled oscillation characteristics are experimentally investigated for an ONN. As practical applications of the ONN with coupled birillators, edge detection and vertex coloring are conducted by encoding information into phase differences between them. The proposed fully CMOS-based birillators are advantageous for low power consumption, high CMOS compatibility, and a compact footprint area.
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Affiliation(s)
- Seong-Yun Yun
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
| | - Joon-Kyu Han
- System Semiconductor Engineering and Department of Electronic Engineering, Sogang University, 35 Baekbeom-ro, Mapo-gu, Seoul 04107, Republic of Korea
| | - Yang-Kyu Choi
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
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7
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Rudner T, Porod W, Csaba G. Design of oscillatory neural networks by machine learning. Front Neurosci 2024; 18:1307525. [PMID: 38500486 PMCID: PMC10944938 DOI: 10.3389/fnins.2024.1307525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2023] [Accepted: 02/12/2024] [Indexed: 03/20/2024] Open
Abstract
We demonstrate the utility of machine learning algorithms for the design of oscillatory neural networks (ONNs). After constructing a circuit model of the oscillators in a machine-learning-enabled simulator and performing Backpropagation through time (BPTT) for determining the coupling resistances between the ring oscillators, we demonstrate the design of associative memories and multi-layered ONN classifiers. The machine-learning-designed ONNs show superior performance compared to other design methods (such as Hebbian learning), and they also enable significant simplifications in the circuit topology. We also demonstrate the design of multi-layered ONNs that show superior performance compared to single-layer ones. We argue that machine learning can be a valuable tool to unlock the true computing potential of ONNs hardware.
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Affiliation(s)
- Tamás Rudner
- Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary
| | - Wolfgang Porod
- Department of Electrical Engineering, University of Notre Dame (NDnano), Notre Dame, IN, United States
| | - Gyorgy Csaba
- Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary
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8
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Jiménez M, Núñez J, Shamsi J, Linares-Barranco B, Avedillo MJ. Experimental demonstration of coupled differential oscillator networks for versatile applications. Front Neurosci 2023; 17:1294954. [PMID: 38111840 PMCID: PMC10725936 DOI: 10.3389/fnins.2023.1294954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/10/2023] [Indexed: 12/20/2023] Open
Abstract
Oscillatory neural networks (ONNs) exhibit a high potential for energy-efficient computing. In ONNs, neurons are implemented with oscillators and synapses with resistive and/or capacitive coupling between pairs of oscillators. Computing is carried out on the basis of the rich, complex, non-linear synchronization dynamics of a system of coupled oscillators. The exploited synchronization phenomena in ONNs are an example of fully parallel collective computing. A fast system's convergence to stable states, which correspond to the desired processed information, enables an energy-efficient solution if small area and low-power oscillators are used, specifically when they are built on the basis of the hysteresis exhibited by phase-transition materials such as VO2. In recent years, there have been numerous studies on ONNs using VO2. Most of them report simulation results. Although in some cases experimental results are also shown, they do not implement the design techniques that other works on electrical simulations report that allow to improve the behavior of the ONNs. Experimental validation of these approaches is necessary. Therefore, in this study, we describe an ONN realized in a commercial CMOS technology in which the oscillators are built using a circuit that we have developed to emulate the VO2 device. The purpose is to be able to study in-depth the synchronization dynamics of relaxation oscillators similar to those that can be performed with VO2 devices. The fabricated circuit is very flexible. It allows programming the synapses to implement different ONNs, calibrating the frequency of the oscillators, or controlling their initialization. It uses differential oscillators and resistive synapses, equivalent to the use of memristors. In this article, the designed and fabricated circuits are described in detail, and experimental results are shown. Specifically, its satisfactory operation as an associative memory is demonstrated. The experiments carried out allow us to conclude that the ONN must be operated according to the type of computational task to be solved, and guidelines are extracted in this regard.
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Affiliation(s)
- Manuel Jiménez
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC/Universidad de Sevilla), Seville, Spain
| | - Juan Núñez
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC/Universidad de Sevilla), Seville, Spain
| | - Jafar Shamsi
- Department of Cell Biology and Anatomy, University of Calgary, Calgary, AB, Canada
| | - Bernabé Linares-Barranco
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC/Universidad de Sevilla), Seville, Spain
| | - María J. Avedillo
- Instituto de Microelectrónica de Sevilla, IMSE-CNM (CSIC/Universidad de Sevilla), Seville, Spain
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9
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Liu H, Qin Y, Chen HY, Wu J, Ma J, Du Z, Wang N, Zou J, Lin S, Zhang X, Zhang Y, Wang H. Artificial Neuronal Devices Based on Emerging Materials: Neuronal Dynamics and Applications. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2205047. [PMID: 36609920 DOI: 10.1002/adma.202205047] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Artificial neuronal devices are critical building blocks of neuromorphic computing systems and currently the subject of intense research motivated by application needs from new computing technology and more realistic brain emulation. Researchers have proposed a range of device concepts that can mimic neuronal dynamics and functions. Although the switching physics and device structures of these artificial neurons are largely different, their behaviors can be described by several neuron models in a more unified manner. In this paper, the reports of artificial neuronal devices based on emerging volatile switching materials are reviewed from the perspective of the demonstrated neuron models, with a focus on the neuronal functions implemented in these devices and the exploitation of these functions for computational and sensing applications. Furthermore, the neuroscience inspirations and engineering methods to enrich the neuronal dynamics that remain to be implemented in artificial neuronal devices and networks toward realizing the full functionalities of biological neurons are discussed.
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Affiliation(s)
- Hefei Liu
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Yuan Qin
- Center for Power Electronics Systems, Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24060, USA
| | - Hung-Yu Chen
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Jiangbin Wu
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Jiahui Ma
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Zhonghao Du
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Nan Wang
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA, 90089, USA
| | - Jingyi Zou
- Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
| | - Sen Lin
- Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
| | - Xu Zhang
- Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
| | - Yuhao Zhang
- Center for Power Electronics Systems, Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24060, USA
| | - Han Wang
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA, 90089, USA
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10
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Albertsson DI, Rusu A. Highly reconfigurable oscillator-based Ising Machine through quasiperiodic modulation of coupling strength. Sci Rep 2023; 13:4005. [PMID: 36899045 PMCID: PMC10006240 DOI: 10.1038/s41598-023-31155-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 03/06/2023] [Indexed: 03/12/2023] Open
Abstract
Ising Machines (IMs) have the potential to outperform conventional Von-Neuman architectures in notoriously difficult optimization problems. Various IM implementations have been proposed based on quantum, optical, digital and analog CMOS, as well as emerging technologies. Networks of coupled electronic oscillators have recently been shown to exhibit characteristics required for implementing IMs. However, for this approach to successfully solve complex optimization problems, a highly reconfigurable implementation is needed. In this work, the possibility of implementing highly reconfigurable oscillator-based IMs is explored. An implementation based on quasiperiodically modulated coupling strength through a common medium is proposed and its potential is demonstrated through numerical simulations. Moreover, a proof-of-concept implementation based on CMOS coupled ring oscillators is proposed and its functionality is demonstrated. Simulation results show that our proposed architecture can consistently find the Max-Cut solution and demonstrate the potential to greatly simplify the physical implementation of highly reconfigurable oscillator-based IMs.
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Affiliation(s)
- Dagur I Albertsson
- Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Electrum 229, 164 40, Kista, Sweden.
| | - Ana Rusu
- Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Electrum 229, 164 40, Kista, Sweden
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11
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Das SK, Nandi SK, Marquez CV, Rúa A, Uenuma M, Puyoo E, Nath SK, Albertini D, Baboux N, Lu T, Liu Y, Haeger T, Heiderhoff R, Riedl T, Ratcliff T, Elliman RG. Physical Origin of Negative Differential Resistance in V 3 O 5 and Its Application as a Solid-State Oscillator. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2208477. [PMID: 36461165 DOI: 10.1002/adma.202208477] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 11/28/2022] [Indexed: 06/17/2023]
Abstract
Oxides that exhibit an insulator-metal transition can be used to fabricate energy-efficient relaxation oscillators for use in hardware-based neural networks but there are very few oxides with transition temperatures above room temperature. Here the structural, electrical, and thermal properties of V3 O5 thin films and their application as the functional oxide in metal/oxide/metal relaxation oscillators are reported. The V3 O5 devices show electroforming-free volatile threshold switching and negative differential resistance (NDR) with stable (<3% variation) cycle-to-cycle operation. The physical mechanisms underpinning these characteristics are investigated using a combination of electrical measurements, in situ thermal imaging, and device modeling. This shows that conduction is confined to a narrow filamentary path due to self-confinement of the current distribution and that the NDR response is initiated at temperatures well below the insulator-metal transition temperature where it is dominated by the temperature-dependent conductivity of the insulating phase. Finally, the dynamics of individual and coupled V3 O5 -based relaxation oscillators is reported, showing that capacitively coupled devices exhibit rich non-linear dynamics, including frequency and phase synchronization. These results establish V3 O5 as a new functional material for volatile threshold switching and advance the development of robust solid-state neurons for neuromorphic computing.
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Affiliation(s)
- Sujan Kumar Das
- Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
- Department of Physics, Jahangirnagar University, Dhaka, 1342, Bangladesh
| | - Sanjoy Kumar Nandi
- Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
| | | | - Armando Rúa
- Department of Physics, University of Puerto Rico, Mayaguez, PR, 00681, USA
| | - Mutsunori Uenuma
- Information Device Science Laboratory, Nara Institute of Science and Technology (NAIST), Nara, 630-0192, Japan
| | - Etienne Puyoo
- Université Lyon, INSA Lyon, CNRS, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, Villeurbanne, 69621, France
| | - Shimul Kanti Nath
- Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
- Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA, 6009, Australia
| | - David Albertini
- Université Lyon, INSA Lyon, CNRS, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, Villeurbanne, 69621, France
| | - Nicolas Baboux
- Université Lyon, INSA Lyon, CNRS, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, Villeurbanne, 69621, France
| | - Teng Lu
- Research School of Chemistry, The Australian National University, Canberra, ACT, 2601, Australia
| | - Yun Liu
- Research School of Chemistry, The Australian National University, Canberra, ACT, 2601, Australia
| | - Tobias Haeger
- Institute of Electronic Devices, Wuppertal Center for Smart Materials & Systems, University of Wuppertal, Rainer-Gruenter-Strasse 21, 42119, Wuppertal, Germany
| | - Ralf Heiderhoff
- Institute of Electronic Devices, Wuppertal Center for Smart Materials & Systems, University of Wuppertal, Rainer-Gruenter-Strasse 21, 42119, Wuppertal, Germany
| | - Thomas Riedl
- Institute of Electronic Devices, Wuppertal Center for Smart Materials & Systems, University of Wuppertal, Rainer-Gruenter-Strasse 21, 42119, Wuppertal, Germany
| | - Thomas Ratcliff
- Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
| | - Robert Glen Elliman
- Research School of Physics, The Australian National University, Canberra, ACT, 2601, Australia
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12
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CMOS-compatible ising machines built using bistable latches coupled through ferroelectric transistor arrays. Sci Rep 2023; 13:1515. [PMID: 36707539 PMCID: PMC9883258 DOI: 10.1038/s41598-023-28217-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 01/16/2023] [Indexed: 01/28/2023] Open
Abstract
Realizing compact and scalable Ising machines that are compatible with CMOS-process technology is crucial to the effectiveness and practicality of using such hardware platforms for accelerating computationally intractable problems. Besides the need for realizing compact Ising spins, the implementation of the coupling network, which describes the spin interaction, is also a potential bottleneck in the scalability of such platforms. Therefore, in this work, we propose an Ising machine platform that exploits the novel behavior of compact bi-stable CMOS-latches (cross-coupled inverters) as classical Ising spins interacting through highly scalable and CMOS-process compatible ferroelectric-HfO2-based Ferroelectric FETs (FeFETs) which act as coupling elements. We experimentally demonstrate the prototype building blocks of this system, and evaluate the scaling behavior of the system using simulations. Our work not only provides a pathway to realizing CMOS-compatible designs but also to overcoming their scaling challenges.
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13
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Lee D, Kwak M, Lee J, Woo J, Hwang H. Linear Frequency Modulation of NbO2-Based Nanoscale Oscillator With Li-Based Electrochemical Random Access Memory for Compact Coupled Oscillatory Neural Network. Front Neurosci 2022; 16:939687. [PMID: 35844222 PMCID: PMC9280362 DOI: 10.3389/fnins.2022.939687] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 06/03/2022] [Indexed: 11/29/2022] Open
Abstract
Oscillatory neural network (ONN)-based classification of clustered data relies on frequency synchronization to injected signals representing input data, showing a more efficient structure than a conventional deep neural network. A frequency tunable oscillator is a core component of the network, requiring energy-efficient, and area-scalable characteristics for large-scale hardware implementation. From a hardware viewpoint, insulator-metal transition (IMT) device-based oscillators are attractive owing to their simple structure and low power consumption. Furthermore, by introducing non-volatile analog memory, non-volatile frequency programmability can be obtained. However, the required device characteristics of the oscillator for high performance of coupled oscillator have not been identified. In this article, we investigated the effect of device parameters of IMT oscillator with non-volatile analog memory on coupled oscillators network for classification of clustered data. We confirmed that linear conductance response with identical pulses is crucial to accurate training. In addition, considering dispersed clustered inputs, a wide synchronization window achieved by controlling the hold voltage of the IMT shows resilient classification. As an oscillator that satisfies the requirements, we evaluated the NbO2-based IMT oscillator with non-volatile Li-based electrochemical random access memory (Li-ECRAM). Finally, we demonstrated a coupled oscillator network for classifying spoken vowels, achieving an accuracy of 85%, higher than that of a ring oscillator-based system. Our results show that an NbO2-based oscillator with Li-ECRAM has the potential for an area-scalable and energy-efficient network with high performance.
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Affiliation(s)
- Donguk Lee
- Department of Materials Science and Engineering, Center of Single Atom-based Semiconductor Device, Pohang University of Science and Technology, Pohang, South Korea
| | - Myonghoon Kwak
- Department of Materials Science and Engineering, Center of Single Atom-based Semiconductor Device, Pohang University of Science and Technology, Pohang, South Korea
| | - Jongwon Lee
- Department of Materials Science and Engineering, Center of Single Atom-based Semiconductor Device, Pohang University of Science and Technology, Pohang, South Korea
| | - Jiyong Woo
- School of Electronics Engineering, Kyungpook National University, Dague, South Korea
| | - Hyunsang Hwang
- Department of Materials Science and Engineering, Center of Single Atom-based Semiconductor Device, Pohang University of Science and Technology, Pohang, South Korea
- *Correspondence: Hyunsang Hwang,
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14
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Graph Coloring via Locally-Active Memristor Oscillatory Networks. JOURNAL OF LOW POWER ELECTRONICS AND APPLICATIONS 2022. [DOI: 10.3390/jlpea12020022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This manuscript provides a comprehensive tutorial on the operating principles of a bio-inspired Cellular Nonlinear Network, leveraging the local activity of NbOx memristors to apply a spike-based computing paradigm, which is expected to deliver such a separation between the steady-state phases of its capacitively-coupled oscillators, relative to a reference cell, as to unveal the classification of the nodes of the associated graphs into the least number of groups, according to the rules of a non-deterministic polynomial-hard combinatorial optimization problem, known as vertex coloring. Besides providing the theoretical foundations of the bio-inspired signal-processing paradigm, implemented by the proposed Memristor Oscillatory Network, and presenting pedagogical examples, illustrating how the phase dynamics of the memristive computing engine enables to solve the graph coloring problem, the paper further presents strategies to compensate for an imbalance in the number of couplings per oscillator, to counteract the intrinsic variability observed in the electrical behaviours of memristor samples from the same batch, and to prevent the impasse appearing when the array attains a steady-state corresponding to a local minimum of the optimization goal. The proposed Memristor Cellular Nonlinear Network, endowed with ad hoc circuitry for the implementation of these control strategies, is found to classify the vertices of a wide set of graphs in a number of color groups lower than the cardinality of the set of colors identified by traditional either software or hardware competitor systems. Given that, under nominal operating conditions, a biological system, such as the brain, is naturally capable to optimise energy consumption in problem-solving activities, the capability of locally-active memristor nanotechnologies to enable the circuit implementation of bio-inspired signal processing paradigms is expected to pave the way toward electronics with higher time and energy efficiency than state-of-the-art purely-CMOS hardware.
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15
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Zahedinejad M, Fulara H, Khymyn R, Houshang A, Dvornik M, Fukami S, Kanai S, Ohno H, Åkerman J. Memristive control of mutual spin Hall nano-oscillator synchronization for neuromorphic computing. NATURE MATERIALS 2022; 21:81-87. [PMID: 34845363 DOI: 10.1038/s41563-021-01153-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Accepted: 10/07/2021] [Indexed: 06/13/2023]
Abstract
Synchronization of large spin Hall nano-oscillator (SHNO) arrays is an appealing approach toward ultrafast non-conventional computing. However, interfacing to the array, tuning its individual oscillators and providing built-in memory units remain substantial challenges. Here, we address these challenges using memristive gating of W/CoFeB/MgO/AlOx-based SHNOs. In its high resistance state, the memristor modulates the perpendicular magnetic anisotropy at the CoFeB/MgO interface by the applied electric field. In its low resistance state the memristor adds or subtracts current to the SHNO drive. Both electric field and current control affect the SHNO auto-oscillation mode and frequency, allowing us to reversibly turn on/off mutual synchronization in chains of four SHNOs. We also demonstrate that two individually controlled memristors can be used to tune a four-SHNO chain into differently synchronized states. Memristor gating is therefore an efficient approach to input, tune and store the state of SHNO arrays for non-conventional computing models.
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Affiliation(s)
- Mohammad Zahedinejad
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- NanOsc AB, Kista, Sweden
| | - Himanshu Fulara
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- Department of Physics, Indian Institute of Technology Roorkee, Roorkee, India
| | - Roman Khymyn
- Physics Department, University of Gothenburg, Gothenburg, Sweden
| | - Afshin Houshang
- Physics Department, University of Gothenburg, Gothenburg, Sweden
| | | | - Shunsuke Fukami
- Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
- Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan
- Center for Spintronics Research Network, Tohoku University, Sendai, Japan
- Center for Innovative Integrated Electronic Systems, Tohoku University, Sendai, Japan
- WPI-Advanced Institute for Materials Research, Tohoku University, Sendai, Japan
| | - Shun Kanai
- Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
- Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan
- Center for Spintronics Research Network, Tohoku University, Sendai, Japan
- Division for the Establishment of Frontier Sciences, Tohoku University, Sendai, Japan
| | - Hideo Ohno
- Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
- Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan
- Center for Spintronics Research Network, Tohoku University, Sendai, Japan
- Center for Innovative Integrated Electronic Systems, Tohoku University, Sendai, Japan
- WPI-Advanced Institute for Materials Research, Tohoku University, Sendai, Japan
| | - Johan Åkerman
- Physics Department, University of Gothenburg, Gothenburg, Sweden.
- NanOsc AB, Kista, Sweden.
- Material and Nanophysics, School of Engineering Sciences, KTH Royal Institute of Technology, Kista, Sweden.
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16
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Delacour C, Todri-Sanial A. Mapping Hebbian Learning Rules to Coupling Resistances for Oscillatory Neural Networks. Front Neurosci 2021; 15:694549. [PMID: 34819831 PMCID: PMC8606813 DOI: 10.3389/fnins.2021.694549] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 10/14/2021] [Indexed: 11/25/2022] Open
Abstract
Oscillatory Neural Network (ONN) is an emerging neuromorphic architecture with oscillators representing neurons and information encoded in oscillator's phase relations. In an ONN, oscillators are coupled with electrical elements to define the network's weights and achieve massive parallel computation. As the weights preserve the network functionality, mapping weights to coupling elements plays a crucial role in ONN performance. In this work, we investigate relaxation oscillators based on VO2 material, and we propose a methodology to map Hebbian coefficients to ONN coupling resistances, allowing a large-scale ONN design. We develop an analytical framework to map weight coefficients into coupling resistor values to analyze ONN architecture performance. We report on an ONN with 60 fully-connected oscillators that perform pattern recognition as a Hopfield Neural Network.
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Affiliation(s)
- Corentin Delacour
- Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, Département de Microélectronique, Université de Montpellier, CNRS, Montpellier, France
| | - Aida Todri-Sanial
- Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, Département de Microélectronique, Université de Montpellier, CNRS, Montpellier, France
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17
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Yang K, Joshua Yang J, Huang R, Yang Y. Nonlinearity in Memristors for Neuromorphic Dynamic Systems. SMALL SCIENCE 2021. [DOI: 10.1002/smsc.202100049] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Affiliation(s)
- Ke Yang
- Department of Micro/nanoelectronics Peking University Beijing 100871 China
| | - J. Joshua Yang
- Electrical and Computer Engineering Department University of Southern California Los Angeles CA 90089 USA
| | - Ru Huang
- Department of Micro/nanoelectronics Peking University Beijing 100871 China
- Center for Brain Inspired Chips Institute for Artificial Intelligence Peking University Beijing 100871 China
- Center for Brain Inspired Intelligence Chinese Institute for Brain Research (CIBR) Beijing 102206 China
| | - Yuchao Yang
- Department of Micro/nanoelectronics Peking University Beijing 100871 China
- Center for Brain Inspired Chips Institute for Artificial Intelligence Peking University Beijing 100871 China
- Center for Brain Inspired Intelligence Chinese Institute for Brain Research (CIBR) Beijing 102206 China
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18
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Núñez J, Avedillo MJ, Jiménez M, Quintana JM, Todri-Sanial A, Corti E, Karg S, Linares-Barranco B. Oscillatory Neural Networks Using VO 2 Based Phase Encoded Logic. Front Neurosci 2021; 15:655823. [PMID: 33935638 PMCID: PMC8085264 DOI: 10.3389/fnins.2021.655823] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/25/2021] [Indexed: 02/03/2023] Open
Abstract
Nano-oscillators based on phase-transition materials are being explored for the implementation of different non-conventional computing paradigms. In particular, vanadium dioxide (VO2) devices are used to design autonomous non-linear oscillators from which oscillatory neural networks (ONNs) can be developed. In this work, we propose a new architecture for ONNs in which sub-harmonic injection locking (SHIL) is exploited to ensure that the phase information encoded in each neuron can only take two values. In this sense, the implementation of ONNs from neurons that inherently encode information with two-phase values has advantages in terms of robustness and tolerance to variability present in VO2 devices. Unlike conventional interconnection schemes, in which the sign of the weights is coded in the value of the resistances, in our proposal the negative (positive) weights are coded using static inverting (non-inverting) logic at the output of the oscillator. The operation of the proposed architecture is shown for pattern recognition applications.
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Affiliation(s)
- Juan Núñez
- Instituto de Microelectrónica de Sevilla (IMSE-CNM), CSIC and Universidad de Sevilla, Seville, Spain
| | - María J Avedillo
- Instituto de Microelectrónica de Sevilla (IMSE-CNM), CSIC and Universidad de Sevilla, Seville, Spain
| | - Manuel Jiménez
- Instituto de Microelectrónica de Sevilla (IMSE-CNM), CSIC and Universidad de Sevilla, Seville, Spain
| | - José M Quintana
- Instituto de Microelectrónica de Sevilla (IMSE-CNM), CSIC and Universidad de Sevilla, Seville, Spain
| | - Aida Todri-Sanial
- Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM), University of Montpellier, Montpellier, France
| | - Elisabetta Corti
- Department of Science and Technology, IBM Research - Zurich, Rüschlikon, Switzerland
| | - Siegfried Karg
- Department of Science and Technology, IBM Research - Zurich, Rüschlikon, Switzerland
| | - Bernabé Linares-Barranco
- Instituto de Microelectrónica de Sevilla (IMSE-CNM), CSIC and Universidad de Sevilla, Seville, Spain
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19
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Higher-order and long-range synchronization effects for classification and computing in oscillator-based spiking neural networks. Neural Comput Appl 2021. [DOI: 10.1007/s00521-020-05177-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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20
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Vaidya J, Bashar MK, Shukla N. Using noise to augment synchronization among oscillators. Sci Rep 2021; 11:4462. [PMID: 33627725 PMCID: PMC7904917 DOI: 10.1038/s41598-021-83806-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 02/08/2021] [Indexed: 11/09/2022] Open
Abstract
Noise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators-relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms.
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Affiliation(s)
- Jaykumar Vaidya
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Mohammad Khairul Bashar
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Nikhil Shukla
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA.
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21
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Kumar S, Williams RS, Wang Z. Third-order nanocircuit elements for neuromorphic engineering. Nature 2020; 585:518-523. [PMID: 32968256 DOI: 10.1038/s41586-020-2735-5] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 08/03/2020] [Indexed: 11/09/2022]
Abstract
Current hardware approaches to biomimetic or neuromorphic artificial intelligence rely on elaborate transistor circuits to simulate biological functions. However, these can instead be more faithfully emulated by higher-order circuit elements that naturally express neuromorphic nonlinear dynamics1-4. Generating neuromorphic action potentials in a circuit element theoretically requires a minimum of third-order complexity (for example, three dynamical electrophysical processes)5, but there have been few examples of second-order neuromorphic elements, and no previous demonstration of any isolated third-order element6-8. Using both experiments and modelling, here we show how multiple electrophysical processes-including Mott transition dynamics-form a nanoscale third-order circuit element. We demonstrate simple transistorless networks of third-order elements that perform Boolean operations and find analogue solutions to a computationally hard graph-partitioning problem. This work paves a way towards very compact and densely functional neuromorphic computing primitives, and energy-efficient validation of neuroscientific models.
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22
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Mallick A, Bashar MK, Truesdell DS, Calhoun BH, Joshi S, Shukla N. Using synchronized oscillators to compute the maximum independent set. Nat Commun 2020; 11:4689. [PMID: 32943644 PMCID: PMC7499257 DOI: 10.1038/s41467-020-18445-1] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Accepted: 08/20/2020] [Indexed: 12/03/2022] Open
Abstract
Not all computing problems are created equal. The inherent complexity of processing certain classes of problems using digital computers has inspired the exploration of alternate computing paradigms. Coupled oscillators exhibiting rich spatio-temporal dynamics have been proposed for solving hard optimization problems. However, the physical implementation of such systems has been constrained to small prototypes. Consequently, the computational properties of this paradigm remain inadequately explored. Here, we demonstrate an integrated circuit of thirty oscillators with highly reconfigurable coupling to compute optimal/near-optimal solutions to the archetypally hard Maximum Independent Set problem with over 90% accuracy. This platform uniquely enables us to characterize the dynamical and computational properties of this hardware approach. We show that the Maximum Independent Set is more challenging to compute in sparser graphs than in denser ones. Finally, using simulations we evaluate the scalability of the proposed approach. Our work marks an important step towards enabling application-specific analog computing platforms to solve computationally hard problems. Designing efficient analog dynamical systems for solving hard optimization problems remains a challenge. Here, the authors demonstrate a dynamical system of thirty oscillators with reconfigurable coupling to compute optimal/near-optimal solutions to the hard Maximum Independent Set problem with over 90% accuracy.
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Affiliation(s)
- Antik Mallick
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Mohammad Khairul Bashar
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Daniel S Truesdell
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Benton H Calhoun
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA
| | - Siddharth Joshi
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Nikhil Shukla
- Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA.
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23
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Sebastian A, Le Gallo M, Khaddam-Aljameh R, Eleftheriou E. Memory devices and applications for in-memory computing. NATURE NANOTECHNOLOGY 2020; 15:529-544. [PMID: 32231270 DOI: 10.1038/s41565-020-0655-z] [Citation(s) in RCA: 298] [Impact Index Per Article: 74.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Accepted: 02/10/2020] [Indexed: 05/02/2023]
Abstract
Traditional von Neumann computing systems involve separate processing and memory units. However, data movement is costly in terms of time and energy and this problem is aggravated by the recent explosive growth in highly data-centric applications related to artificial intelligence. This calls for a radical departure from the traditional systems and one such non-von Neumann computational approach is in-memory computing. Hereby certain computational tasks are performed in place in the memory itself by exploiting the physical attributes of the memory devices. Both charge-based and resistance-based memory devices are being explored for in-memory computing. In this Review, we provide a broad overview of the key computational primitives enabled by these memory devices as well as their applications spanning scientific computing, signal processing, optimization, machine learning, deep learning and stochastic computing.
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24
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Crnkić A, Povh J, Jaćimović V, Levnajić Z. Collective dynamics of phase-repulsive oscillators solves graph coloring problem. CHAOS (WOODBURY, N.Y.) 2020; 30:033128. [PMID: 32237769 DOI: 10.1063/1.5127794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2019] [Accepted: 02/20/2020] [Indexed: 06/11/2023]
Abstract
We show how to couple phase-oscillators on a graph so that collective dynamics "searches" for the coloring of that graph as it relaxes toward the dynamical equilibrium. This translates a combinatorial optimization problem (graph coloring) into a functional optimization problem (finding and evaluating the global minimum of dynamical non-equilibrium potential, done by the natural system's evolution). Using a sample of graphs, we show that our method can serve as a viable alternative to the traditional combinatorial algorithms. Moreover, we show that, with the same computational cost, our method efficiently solves the harder problem of improper coloring of weighed graphs.
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Affiliation(s)
- Aladin Crnkić
- Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina
| | - Janez Povh
- Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva cesta 6, 1000 Ljubljana, Slovenia
| | - Vladimir Jaćimović
- Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica, Montenegro
| | - Zoran Levnajić
- Complex Systems and Data Science Lab, Faculty of Information Studies in Novo Mesto, Ljubljanska cesta 31A, 8000 Novo Mesto, Slovenia
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Zahedinejad M, Awad AA, Muralidhar S, Khymyn R, Fulara H, Mazraati H, Dvornik M, Åkerman J. Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing. NATURE NANOTECHNOLOGY 2020; 15:47-52. [PMID: 31873287 DOI: 10.1038/s41565-019-0593-9] [Citation(s) in RCA: 51] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Accepted: 11/08/2019] [Indexed: 06/10/2023]
Abstract
In spin Hall nano-oscillators (SHNOs), pure spin currents drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and may mutually synchronize. Here, we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 × 2 to 8 × 8 nano-constrictions, observed both electrically and using micro-Brillouin light scattering microscopy. On short time scales, where the auto-oscillation linewidth [Formula: see text] is governed by white noise, the signal quality factor, [Formula: see text], increases linearly with the number of mutually synchronized nano-constrictions (N), reaching 170,000 in the largest arrays. We also show that SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps as can be used for neuromorphic vowel recognition. Our demonstrations may hence enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and ultra-fast neuromorphic computing.
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Affiliation(s)
- Mohammad Zahedinejad
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- NanOsc AB, Kista, Sweden
| | - Ahmad A Awad
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- NanOsc AB, Kista, Sweden
| | | | - Roman Khymyn
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- NanOsc AB, Kista, Sweden
| | - Himanshu Fulara
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- NanOsc AB, Kista, Sweden
| | - Hamid Mazraati
- NanOsc AB, Kista, Sweden
- Material and Nanophysics, School of Engineering Sciences, KTH Royal Institute of Technology, Kista, Sweden
| | - Mykola Dvornik
- Physics Department, University of Gothenburg, Gothenburg, Sweden
- NanOsc AB, Kista, Sweden
| | - Johan Åkerman
- Physics Department, University of Gothenburg, Gothenburg, Sweden.
- NanOsc AB, Kista, Sweden.
- Material and Nanophysics, School of Engineering Sciences, KTH Royal Institute of Technology, Kista, Sweden.
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Fang Y, Wang Z, Gomez J, Datta S, Khan AI, Raychowdhury A. A Swarm Optimization Solver Based on Ferroelectric Spiking Neural Networks. Front Neurosci 2019; 13:855. [PMID: 31456659 PMCID: PMC6700359 DOI: 10.3389/fnins.2019.00855] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Accepted: 07/30/2019] [Indexed: 11/13/2022] Open
Abstract
As computational models inspired by the biological neural system, spiking neural networks (SNN) continue to demonstrate great potential in the landscape of artificial intelligence, particularly in tasks such as recognition, inference, and learning. While SNN focuses on achieving high-level intelligence of individual creatures, Swarm Intelligence (SI) is another type of bio-inspired models that mimic the collective intelligence of biological swarms, i.e., bird flocks, fish school and ant colonies. SI algorithms provide efficient and practical solutions to many difficult optimization problems through multi-agent metaheuristic search. Bridging these two distinct subfields of artificial intelligence has the potential to harness collective behavior and learning ability of biological systems. In this work, we explore the feasibility of connecting these two models by implementing a generalized SI model on SNN. In the proposed computing paradigm, we use SNNs to represent agents in the swarm and encode problem solutions with the spike firing rate and with spike timing. The coupled neurons communicate and modulate each other's action potentials through event-driven spikes and synchronize their dynamics around the states of optimal solutions. We demonstrate that such an SI-SNN model is capable of efficiently solving optimization problems, such as parameter optimization of continuous functions and a ubiquitous combinatorial optimization problem, namely, the traveling salesman problem with near-optimal solutions. Furthermore, we demonstrate an efficient implementation of such neural dynamics on an emerging hardware platform, namely ferroelectric field-effect transistor (FeFET) based spiking neurons. Such an emerging in-silico neuron is composed of a compact 1T-1FeFET structure with both excitatory and inhibitory inputs. We show that the designed neuromorphic system can serve as an optimization solver with high-performance and high energy-efficiency.
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Affiliation(s)
- Yan Fang
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, United States
| | - Zheng Wang
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, United States
| | - Jorge Gomez
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, United States
| | - Suman Datta
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, United States
| | - Asif I Khan
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, United States
| | - Arijit Raychowdhury
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, United States
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Dutta S, Parihar A, Khanna A, Gomez J, Chakraborty W, Jerry M, Grisafe B, Raychowdhury A, Datta S. Programmable coupled oscillators for synchronized locomotion. Nat Commun 2019; 10:3299. [PMID: 31341167 PMCID: PMC6656780 DOI: 10.1038/s41467-019-11198-6] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Accepted: 06/21/2019] [Indexed: 01/25/2023] Open
Abstract
The striking similarity between biological locomotion gaits and the evolution of phase patterns in coupled oscillatory network can be traced to the role of central pattern generator located in the spinal cord. Bio-inspired robotics aim at harnessing this control approach for generation of rhythmic patterns for synchronized limb movement. Here, we utilize the phenomenon of synchronization and emergent spatiotemporal pattern from the interaction among coupled oscillators to generate a range of locomotion gait patterns. We experimentally demonstrate a central pattern generator network using capacitively coupled Vanadium Dioxide nano-oscillators. The coupled oscillators exhibit stable limit-cycle oscillations and tunable natural frequencies for real-time programmability of phase-pattern. The ultra-compact 1 Transistor-1 Resistor implementation of oscillator and bidirectional capacitive coupling allow small footprint area and low operating power. Compared to biomimetic CMOS based neuron and synapse models, our design simplifies on-chip implementation and real-time tunability by reducing the number of control parameters. Designing alternative paradigms for bio-inspired analog computing that harnesses collective dynamics remains a challenge. Here, the authors exploit the synchronization dynamics of coupled vanadium dioxide-based insulator-to-metal phase-transition nano-oscillators for adaptive locomotion control.
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Affiliation(s)
- Sourav Dutta
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA.
| | - Abhinav Parihar
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
| | - Abhishek Khanna
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Jorge Gomez
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Wriddhi Chakraborty
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Matthew Jerry
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Benjamin Grisafe
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Arijit Raychowdhury
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
| | - Suman Datta
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
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Hamerly R, Inagaki T, McMahon PL, Venturelli D, Marandi A, Onodera T, Ng E, Langrock C, Inaba K, Honjo T, Enbutsu K, Umeki T, Kasahara R, Utsunomiya S, Kako S, Kawarabayashi KI, Byer RL, Fejer MM, Mabuchi H, Englund D, Rieffel E, Takesue H, Yamamoto Y. Experimental investigation of performance differences between coherent Ising machines and a quantum annealer. SCIENCE ADVANCES 2019; 5:eaau0823. [PMID: 31139743 PMCID: PMC6534389 DOI: 10.1126/sciadv.aau0823] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 04/17/2019] [Indexed: 05/05/2023]
Abstract
Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.
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Affiliation(s)
- Ryan Hamerly
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 50 Vassar Street, Cambridge, MA 02139, USA
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
- Corresponding author. (R.H.); (T.I.); (P.L.M.)
| | - Takahiro Inagaki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- Corresponding author. (R.H.); (T.I.); (P.L.M.)
| | - Peter L. McMahon
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA
- Corresponding author. (R.H.); (T.I.); (P.L.M.)
| | - Davide Venturelli
- NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL), Mail Stop 269-1, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science (RIACS), 615 National Avenue, Mountain View, CA 94035, USA
| | - Alireza Marandi
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- California Institute of Technology, Pasadena, CA 91125, USA
| | - Tatsuhiro Onodera
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Edwin Ng
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Carsten Langrock
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Kensuke Inaba
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Toshimori Honjo
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Koji Enbutsu
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Takeshi Umeki
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Ryoichi Kasahara
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Shoko Utsunomiya
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
| | - Satoshi Kako
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
| | - Ken-ichi Kawarabayashi
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
| | - Robert L. Byer
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Martin M. Fejer
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Hideo Mabuchi
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Dirk Englund
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 50 Vassar Street, Cambridge, MA 02139, USA
| | - Eleanor Rieffel
- NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL), Mail Stop 269-1, Moffett Field, CA 94035, USA
| | - Hiroki Takesue
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Yoshihisa Yamamoto
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- ImPACT Program, Japan Science and Technology Agency, Gobancho 7, Chiyoda-ku, Tokyo 102-0076, Japan
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Abstract
We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an internal parameter. We provide an brief historical introduction, as well as an overview over the physical mechanism that lead to memristive behavior. This review is meant to guide nonpractitioners in the field of memristive circuits and their connection to machine learning and neural computation.
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30
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Molnár B, Molnár F, Varga M, Toroczkai Z, Ercsey-Ravasz M. A continuous-time MaxSAT solver with high analog performance. Nat Commun 2018; 9:4864. [PMID: 30451849 PMCID: PMC6242876 DOI: 10.1038/s41467-018-07327-2] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2018] [Accepted: 10/26/2018] [Indexed: 11/25/2022] Open
Abstract
Many real-life optimization problems can be formulated in Boolean logic as MaxSAT, a class of problems where the task is finding Boolean assignments to variables satisfying the maximum number of logical constraints. Since MaxSAT is NP-hard, no algorithm is known to efficiently solve these problems. Here we present a continuous-time analog solver for MaxSAT and show that the scaling of the escape rate, an invariant of the solver’s dynamics, can predict the maximum number of satisfiable constraints, often well before finding the optimal assignment. Simulating the solver, we illustrate its performance on MaxSAT competition problems, then apply it to two-color Ramsey number R(m, m) problems. Although it finds colorings without monochromatic 5-cliques of complete graphs on N ≤ 42 vertices, the best coloring for N = 43 has two monochromatic 5-cliques, supporting the conjecture that R(5, 5) = 43. This approach shows the potential of continuous-time analog dynamical systems as algorithms for discrete optimization. Continuous-time computation paradigm could represent a viable alternative to the standard digital one when dealing with certain classes of problems. Here, the authors propose a generalised version of a continuous-time solver and simulate its performances in solving MaxSAT and two-colour Ramsey problems.
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Affiliation(s)
- Botond Molnár
- Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania.,Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania.,Transylvanian Institute of Neuroscience, Cluj-Napoca, 400157, Romania
| | - Ferenc Molnár
- Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Melinda Varga
- Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA.,Center for Vascular Biology Research and Department of Medicine, Beth Israel Deaconess Medical Center, Boston, MA, 02215, USA
| | - Zoltán Toroczkai
- Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA.
| | - Mária Ercsey-Ravasz
- Faculty of Physics, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania. .,Transylvanian Institute of Neuroscience, Cluj-Napoca, 400157, Romania. .,Romanian Institute of Science and Technology, Cluj-Napoca, 400487, Romania.
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