Information Processing by Nonlinear Phase Dynamics in Locally Connected Arrays

📝 Abstract

Research toward powerful information processing systems that circumvent the interconnect bottleneck by exploiting the nonlinear evolution of multiple phase dynamics in locally connected arrays is discussed. We focus on a scheme in which logic states are defined by the electrical phase of a dynamic process and information processing is realized through interactions between the elements in the array. Simulation results are given for networks comprised of neuron-like integrate-and-fire elements, which could potentially be implemented by ultra-small tunnel junctions, molecules and other types of nanoscale elements. This approach could lead to powerful information processing systems due to massive parallelism in simple, highly scalable nano-architectures. The rational for this approach, its advantages, simulation results, critical issues, and future research directions are discussed.

💡 Analysis

Research toward powerful information processing systems that circumvent the interconnect bottleneck by exploiting the nonlinear evolution of multiple phase dynamics in locally connected arrays is discussed. We focus on a scheme in which logic states are defined by the electrical phase of a dynamic process and information processing is realized through interactions between the elements in the array. Simulation results are given for networks comprised of neuron-like integrate-and-fire elements, which could potentially be implemented by ultra-small tunnel junctions, molecules and other types of nanoscale elements. This approach could lead to powerful information processing systems due to massive parallelism in simple, highly scalable nano-architectures. The rational for this approach, its advantages, simulation results, critical issues, and future research directions are discussed.

📄 Content

1 Information Processing by Nonlinear Phase Dynamics
in Locally Connected Arrays Richard A. Kiehl
Department of Electrical and Computer Engineering,
University of Minnesota, Minneapolis, Minn.* Introduction This article describes research toward powerful information processing systems that circumvent the interconnect bottleneck by exploiting the nonlinear evolution of multiple phase dynamics in locally connected arrays. We focus on a scheme in which logic states are defined by the electrical phase of a dynamic physical process, such as electron tunneling in ultra-small junctions or molecules. This process produces impulsive “neuron-like” waveforms that are coupled to nearest neighbors in a 2D (or possibly 3D) array. Input data can be represented by the distribution of dc bias level, initial charge, or coupling strength across the array. Information processing is realized through the nonlinear dynamics produced by interactions between the elements in the array, rather than through Boolean operations.
The dynamics give rise to an evolution of complex two-dimensional patterns in the phase-state across the array and represent a computation on the input data. Examples are given for a network comprised of neuron-like integrate-and-fire elements, which could potentially be implemented by Coulomb blockade in ultra-small junctions or molecules, or by other types of nanoscale elements. A simple two- dimensional network with uniform electrostatic coupling between each element and its four nearest neighbors, which could be implemented by capacitive coupling between closely spaced elements, is considered. The results demonstrate the generation of complex patterns and repeating sequences of patterns and the capability for performing some simple image processing tasks. Specific design of the 2D coupling distribution within the array is expected to lead to capabilities for performing higher-level image processing tasks and, possibly, to more general information processing functions. This approach could lead to powerful information processing systems due to massive parallelism in simple, highly scalable architectures compatible with the nanoscale. In this paper, we discuss the rational for this approach, its advantages, simulation results, critical issues, and future research directions.
Background The frequency and phase of a signal is commonly used to represent information in communication systems, in large part because of the robustness of frequency- and phase-modulation to noise.
Biological systems, which are full of noise, also encode information by using frequency and phase, in this case the frequency and phase of a spike train generated by neurons.[1]

The use of the electrical phase of an oscillator as the basis of a logic gate was first proposed independently by von Neumann[2] and by Goto[3] in the 1950’s. These early proposals were based on
parametric excitations, where pumping by an ac signal at ωp results in a negative resistance at ωp/2. In a suitable circuit, the negative resistance results in oscillations at ωp/2 that are phase locked to the pump at one of two possible phases, each of which is used to represent a logic state. Since the signals representing the logic states are 180 degrees out of phase, a 3-input majority-logic gate is produced by the phase-dependent cancellation among the three summed inputs. A clear summary of von Neumann’s patent and computing concept was given by Wigington[4].

*Present address: School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 2 The spike trains generated by neurons are believed to be used for both communication and information processing in biological systems. Biological systems provide the ultimate “existence proof” for the possibility of realizing powerful information processing systems with neuron-like devices. Reverse engineering of biological systems to understand their “hardware” and “software” has been a motivation in the field of neural networks for many years and covers a wide variety of disciplines. While much is still unknown, some features of the general operation of these systems have been found. It is well known that neurons can behave as biological oscillators due to their integrate-and-fire response, in which the inputs are integrated and a spike to be generated each time a threshold is exceeded. A particularly important finding is that, in some parts of mammalian cortex, information processing appears to be based on nonlinear dynamics in spatially distributed networks.[5]

The development of information processing systems based on the use of nonlinear dynamics in locally connected networks, as opposed to what are generally called “neural networks”, is a prime motivation for the research described in this paper. Tunneling Phase Logic Schemes for performing logic or information processing based on the e

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