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Register a new userProbabilistic Memristive Networks: Application of a Master Equation to Networks of Binary ReRAM cells
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The possibility of using non-deterministic circuit components has been gaining significant attention in recent years. The modeling and simulation of their circuits require novel approaches, as now the state of a circuit at an arbitrary moment in time cannot be precisely predicted. Generally, these circuits should be described in terms of probabilities, the circuit variables should be calculated on average, and correlation functions should be used to explore interrelations among the variables. In this paper, we use, for the first time, a master equation to analyze the networks composed of probabilistic binary memristors. Analytical solutions of the master equation for the case of identical memristors connected in-series and in-parallel are found. Our analytical results are supplemented by results of numerical simulations that extend our findings beyond the case of identical memristors. The approach proposed in this paper facilitates the development of probabilistic/stochastic electronic circuits and advance their real-world applications.
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Efficient simulation of probabilistic memristors and their networks requires novel modeling approaches. One major departure from the conventional memristor modeling is based on a master equation for the occupation probabilities of network states [arXiv:2003.11011 (2020)]. In the present article, we show how to implement such master equations in SPICE - a general-purpose circuit simulation program. In the case studies, we simulate the dynamics of ac-driven probabilistic binary and multi-state memristors, and dc-driven networks of probabilistic binary and multi-state memristors. Our SPICE results are in perfect agreement with known analytical solutions. Examples of LTspice codes are included.
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing, non-equilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between non-equilibrium and classical equilibrium networks.
The analog nature of computing in Memristive crossbars poses significant issues due to various non-idealities such as: parasitic resistances, non-linear I-V characteristics of the device etc. The non-idealities can have a detrimental impact on the functionality i.e. computational accuracy of crossbars. Past works have explored modeling the non-idealities using analytical techniques. However, several non-idealities have data dependent behavior. This can not be captured using analytical (non data-dependent) models thereby, limiting their suitability in predicting application accuracy. To address this, we propose a Generalized Approach to Emulating Non-Ideality in Memristive Crossbars using Neural Networks (GENIEx), which accurately captures the data-dependent nature of non-idealities. We perform extensive HSPICE simulations of crossbars with different voltage and conductance combinations. Following that, we train a neural network to learn the transfer characteristics of the non-ideal crossbar. Next, we build a functional simulator which includes key architectural facets such as textit{tiling}, and textit{bit-slicing} to analyze the impact of non-idealities on the classification accuracy of large-scale neural networks. We show that GENIEx achieves textit{low} root mean square errors (RMSE) of $0.25$ and $0.7$ for low and high voltages, respectively, compared to HSPICE. Additionally, the GENIEx errors are $7times$ and $12.8times$ better than an analytical model which can only capture the linear non-idealities. Further, using the functional simulator and GENIEx, we demonstrate that an analytical model can overestimate the degradation in classification accuracy by $ge 10%$ on CIFAR-100 and $3.7%$ on ImageNet datasets compared to GENIEx.
We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is considered in detail. Some analytical solutions are found. Our work offers a novel analytical/numerical tool for modeling complex stochastic networks, which may find a broad range of applications.
Acting as artificial synapses, two-terminal memristive devices are considered fundamental building blocks for the realization of artificial neural networks. Organized into large arrays with a top-down approach, memristive devices in conventional crossbar architecture demonstrated the implementation of brain-inspired computing for supervised and unsupervised learning. Alternative way using unconventional systems consisting of many interacting nano-parts have been proposed for the realization of biologically plausible architectures where the emergent behavior arises from a complexity similar to that of biological neural circuits. However, these systems were unable to demonstrate bio-realistic implementation of synaptic functionalities with spatio-temporal processing of input signals similarly to our brain. Here we report on emergent synaptic behavior of biologically inspired nanoarchitecture based on self-assembled and highly interconnected nanowire (NW) networks realized with a bottom up approach. The operation principle of this system is based on the mutual electrochemical interaction among memristive NWs and NW junctions composing the network and regulating its connectivity depending on the input stimuli. The functional connectivity of the system was shown to be responsible for heterosynaptic plasticity that was experimentally demonstrated and modelled in a multiterminal configuration, where the formation of a synaptic pathway between two neuron terminals is responsible for a variation in synaptic strength also at non-stimulated terminals. These results highlight the ability of nanowire memristive architectures for building brain-inspired intelligent systems based on complex networks able to physically compute the information arising from multi-terminal inputs.
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