Mathematical Analysis of Memristor CNN

In this chapter we present mathematical study of memristor systems. More precisely, we apply local activity theory in order to determine the edge of chaos regime in reaction-diffusion memristor cellular nanoscale networks (RD-MCNN) and in memristor hysteresis CNN (M-HCNN). First we give an overview of mathematical models of memristors, CNN and complexity. Then we consider the above mentioned two models and we develop constructive algorithm for determination of edge of chaos in them. Based on these algorithms numerical simulations are provided. Two applications of M-HCNN model in image processing are presented

Memristors

This Edited Volume Memristors - Circuits and Applications of Memristor Devices is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Engineering. The book comprises single chapters authored by various researchers and edited by an expert active in the physical sciences, engineering, and technology research areas. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on physical sciences, engineering, and technology,and open new possible research paths for further novel developments

Avalanches and the edge-of-chaos in neuromorphic nanowire networks

The brain's efficient information processing is enabled by the interplay between its neuro-synaptic elements and complex network structure. This work reports on the neuromorphic dynamics of nanowire networks (NWNs), a brain-inspired system with synapse-like memristive junctions embedded within a recurrent neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, thus satisfying criteria for criticality. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos. Dynamical states at the edge-of-chaos are found to optimise information processing for increasingly complex learning tasks. Overall, these results reveal a rich repertoire of emergent, collective dynamics in NWNs which may be harnessed in novel, brain-inspired computing approaches

A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into a non-linear dynamical system that maps low-dimensional inputs into a high-dimensional space. The model's rich dynamics, linear separability, and memory capacity then enable a simple linear readout to generate adequate responses for various applications. RC spans areas far beyond machine learning, since it has been shown that the complex dynamics can be realized in various physical hardware implementations and biological devices. This yields greater flexibility and shorter computation time. Moreover, the neuronal responses triggered by the model's dynamics shed light on understanding brain mechanisms that also exploit similar dynamical processes. While the literature on RC is vast and fragmented, here we conduct a unified review of RC's recent developments from machine learning to physics, biology, and neuroscience. We first review the early RC models, and then survey the state-of-the-art models and their applications. We further introduce studies on modeling the brain's mechanisms by RC. Finally, we offer new perspectives on RC development, including reservoir design, coding frameworks unification, physical RC implementations, and interaction between RC, cognitive neuroscience and evolution.Comment: 51 pages, 19 figures, IEEE Acces

Optimization of niobium oxide-based threshold switches for oscillator-based applications

In niobium oxide-based capacitors non-linear switching characteristics can be observed if the oxide properties are adjusted accordingly. Such non-linear threshold switching characteristics can be utilized in various non-linear circuit applications, which have the potential to pave the way for the application of new computing paradigms. Furthermore, the non-linearity also makes them an interesting candidate for the application as selector devices e.g. for non-volatile memory devices. To satisfy the requirements for those two areas of application, the threshold switching characteristics need to be adjusted to either obtain a maximized voltage extension of the negative differential resistance region in the quasi-static I-V characteristics, which enhances the non-linearity of the devices and results in improved robustness to device-to-device variability or to adapt the threshold voltage to a specific non-volatile memory cell. Those adaptations of the threshold switching characteristics were successfully achieved by deliberate modifications of the niobium oxide stack. Furthermore, the impact of the material stack on the dynamic behavior of the threshold switches in non-linear circuits as well as the impact of the electroforming routine on the threshold switching characteristics were analyzed. The optimized device stack was transferred from the micrometer-sized test structures to submicrometer-sized devices, which were packaged to enable easy integration in complex circuits. Based on those packaged threshold switching devices the behavior of single as well as of coupled relaxation oscillators was analyzed. Subsequently, the obtained results in combination with the measurement results for the statistic device-to-device variability were used as a basis to simulate the pattern formation in coupled relaxation oscillator networks as well as their performance in solving graph coloring problems. Furthermore, strategies to adapt the threshold voltage to the switching characteristics of a tantalum oxide-based non-volatile resistive switch and a non-volatile phase change cell, to enable their application as selector devices for the respective cells, were discussed.:Abstract I Zusammenfassung II List of Abbrevations VI List of Symbols VII 1 Motivation 1 2 Basics 5 2.1 Negative differential resistance and local activity in memristor devices 5 2.2 Threshold switches as selector devices 8 2.3 Switching effects observed in NbOx 13 2.3.1 Threshold switching caused by metal-insulator transition 13 2.3.2 Threshold switching caused by Frenkel-Poole conduction 18 2.3.3 Non-volatile resistive switching 32 3 Sample preparation 35 3.1 Deposition techniques 35 3.1.1 Evaporation 35 3.1.2 Sputtering 36 3.2 Micrometer-sized devices 36 3.3 Submicrometer-sized devices 37 3.3.1 Process flow 37 3.3.2 Reduction of the electrode resistance 39 3.3.3 Transfer from structuring via electron beam lithography to structuring via laser lithography 48 3.3.4 Packaging procedure 50 4 Investigation and optimization of the electrical device characteristic 51 4.1 Introduction 51 4.2 Measurement setup 52 4.3 Electroforming 53 4.3.1 Optimization of the electroforming process 53 4.3.2 Characterization of the formed filament 62 4.4 Dynamic device characteristics 67 4.4.1 Emergence and measurement of dynamic behavior 67 4.4.2 Impact of the dynamic device characteristics on quasi-static I-V characteristics 70 5 Optimization of the material stack 81 5.1 Introduction 81 5.2 Adjustment of the oxygen content in the bottom layer 82 5.3 Influence of the thickness of the oxygen-rich niobium oxide layer 92 5.4 Multilayer stacks 96 5.5 Device-to-device and Sample-to-sample variability 110 6 Applications of NbOx-based threshold switching devices 117 6.1 Introduction 117 6.2 Non-linear circuits 117 6.2.1 Coupled relaxation oscillators 117 6.2.2 Memristor Cellular Neural Network 121 6.2.3 Graph Coloring 127 6.3 Selector devices 132 7 Summary and Outlook 138 8 References 141 9 List of publications 154 10 Appendix 155 10.1 Parameter used for the LT Spice simulation of I-V curves for threshold switches with varying oxide thicknesses 155 10.2 Dependence of the oscillation frequency of the relaxation oscillator circuit on the capacitance and the applied source voltage 156 10.3 Calculation of the oscillation frequency of the relaxation oscillator circuit 157 10.4 Characteristics of the memristors and the cells utilized in the simulation of the memristor cellular neural network 164 10.5 Calculation of the impedance of the cell in the memristor cellular network 166 10.6 Example graphs from the 2nd DIMACS series 179 11 List of Figures 182 12 List of Tables 19

Simulation and implementation of novel deep learning hardware architectures for resource constrained devices

Corey Lammie designed mixed signal memristive-complementary metal–oxide–semiconductor (CMOS) and field programmable gate arrays (FPGA) hardware architectures, which were used to reduce the power and resource requirements of Deep Learning (DL) systems; both during inference and training. Disruptive design methodologies, such as those explored in this thesis, can be used to facilitate the design of next-generation DL systems

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Low Power Memory/Memristor Devices and Systems

This reprint focusses on achieving low-power computation using memristive devices. The topic was designed as a convenient reference point: it contains a mix of techniques starting from the fundamental manufacturing of memristive devices all the way to applications such as physically unclonable functions, and also covers perspectives on, e.g., in-memory computing, which is inextricably linked with emerging memory devices such as memristors. Finally, the reprint contains a few articles representing how other communities (from typical CMOS design to photonics) are fighting on their own fronts in the quest towards low-power computation, as a comparison with the memristor literature. We hope that readers will enjoy discovering the articles within

単層カーボンナノチューブ/ポルフィリン-ポリ酸ランダムネットワークを用いたマテリアルリザバー演算素子 —次世代機械知能への新規アプローチ

In a layman’s term, computation is defined as the execution of a given instruction through a programmable algorithm. History has it that starting from the simplest calculator to the sophisticated von Neumann machine, the above definition has been followed without a flaw. Logical operations for which a human takes a minute long to solve, is a matter of fraction of seconds for these gadgets. But contrastingly, when it comes to critical and analytical thinking that requires learning through observation like the human brain, these powerful machines falter and lag behind. Thus, inspired from the brain’s neural circuit, software models of neural networks (NN) integrated with high-speed supercomputers were developed as an alternative tool to implement machine intelligent tasks of function optimization, pattern, and voice recognition. But as device downscaling and transistor performance approaches the constant regime of Moore’s law due to high CMOS fabrication cost and large tunneling energy loss, training these algorithms over multiple hidden layers is turning out to be a grave concern for future applications. As a result, the interplay between faster performance and low computational power requirement for complex tasks deems highly disproportional. Therefore, alternative in terms of both NN models and conventional Neumann architecture needs to be addressed in today’s age for next-generation machine intelligence systems. Fortunately, through extensive research and studies, unconventional computing using a reservoir based neural network platform, called in-materio reservoir computing (RC) has come to the rescue. In-maerio RC uses physical, biological, chemical, cellular automata and other inanimate dynamical systems as a source of non-linear high dimensional spatio-temporal information processing unit to construct a specific target task. RC not only has a three-layer simplified neural architectural layer, but also imposes a cheap, fast, and simplified optimization of only the readout weights with machine intelligent regression algorithm to construct the supervised objective target via a weighted linear combination of the readouts. Thus, utilizing this idea, herein in this work we report such an in-materio RC with a dynamical random network of single walled carbon nanotube/porphyrin-polyoxometalate (SWNT/Por-POM) device. We begin with Chapter 1, which deals with the introduction covering the literature of ANN evolution and the shortcomings of von Neumann architecture and training models of these ANN, which leads us to adopt the in-materio RC architecture. We design the problem statement focused on extending the theoretical RC model of previously suggested SWNT/POM network to an experimental one and present the objective of fabricating a random network based on nanomaterials as they closely resemble the network structure of the brain. Finally, we conclude by stating the scope of this research work aiming towards validating the non-linear high dimensional reservoir property SWNT/Por-POM holds for it to explicitly demonstrate the RC benchmark tasks of optimization and classification. Chapter 2 describes the methodology including the chemical repository required for the facile synthesis of the material. The synthesis part is divided broadly into SWNT purification and then its dispersion with Por-POM to form the desired complex. It is then followed up with the microelectrode array fabrication and the consequent wet-transfer thin film deposition to give the ultimate reservoir architecture of input-output control read pads with SWNT/Por-POM reservoir. Finally we give a briefing of AFM, UV-Vis spectroscopy, FE-SEM characterization techniques of SWNT/Por-POM complex along with the electrical set-up interfaced with software algorithm to demonstrate the RC approach of in-materio machine intelligence. In Chapter 3, we study the current dynamics as a function of voltage and time and validate the non-linear information processing ability intrinsic to the device. The study reveals that the negative differential resistance (NDR) arising from redox nature of Por-POM results in oscillating random noise outputs giving rise to 1/f brain-like spatio-temporal information. We compute the memory capacity (MC) and prove that the device exhibits echo state property of fading memory, but remembers very little of the past information. The low MC and high non-linearity allowed us to choose mostly non-linear tasks of waveform generation, Boolean logic optimization and one-hot vector binary object classification as the RC benchmark. The Chapter 4 relates to the waveform generation task. Utilizing the high dimensional voltage readouts of varying amplitude, phase and higher harmonic frequencies, relative to input sine wave, a regression optimization was performed towards constructing cosine, triangular, square and sawtooth waves resulting in a high accuracy of around 95%. The task complexity of function optimization was further enhanced in Chapter 5 where two inputs were used to construct Boolean logic functions of OR, AND, XOR, NOR, NAND and XNOR. Similar to the waveform, accuracy over 95% could be achieved due to the presence of NDR nonlinearity. Furthermore, the device was also tested for classification problem in Chapter 6. Here we showed an off-line binary classification of four object toys; hedgehog, dog, block and bus, using the grasped tactile information of these objects as inputs obtained from the Toyota Human Support Robot. A one-ridge regression analysis to fit the hot vector supervised target was used to optimize the output weights for predicting the correct outcome. All the objects were successfully classified owing to the 1/f information processing factor. Lastly, we conclude the section in Chapter 7 with the future scope of extending the idea to fabricate a 3-D model of the same material as it opens up opportunity for higher memory capacity fruitful for future benchmark tasks of time-series prediction. Overall, our research marks a step stone in utilizing SWNT/Por-POM as the in-materio RC for the very first time thereby making it a desirable candidate for next-generation machine intelligence.九州工業大学博士学位論文 学位記番号：生工博甲第425号 学位授与年月日：令和3年12月27日1 Introduction and Literature review|2 Methodology|3 Reservoir dynamics emerging from an incidental structure of single-walled carbon nanotube/porphyrin-polyoxometalate complex|4 Fourier transform waveforms via in-materio reservoir computing from single-walled carbon nanotube/porphyrin-polyoxometalate complex|5 Room temperature demonstration of in-materio reservoir computing for optimizing Boolean function with single-walled carbon nanotube/porphyrin-polyoxometalate composite|6 Binary object classification with tactile sensory input information of via single-walled carbon nanotube/porphyrin-polyoxometalate network as in-materio reservoir computing|7 Future scope and Conclusion九州工業大学令和3年