Oscillator-Based Computing
Oscillator-based computing (OBC) is a field of study that explores the use of coupled oscillators as computational devices.[1]. The concept, while not new, has gained significant attention in recent years as part of the search for "beyond Moore" electronic devices. This interest is largely driven by biological observations, particularly the operation of neural systems and mammalian brains, which appear to function based on oscillatory signals. This article provides a comprehensive review of OBC, focusing on the physics of (mostly nanoscale) oscillatory systems and their characteristics that may enable effective computing.
Introduction
Oscillator-based computing (OBC) is a computational approach that leverages the complex dynamics of interacting oscillators. These oscillators have been a topic of study in physics and mathematics for a long time and have been widely used as a model system for various biological processes. Recently, coupled oscillators have been investigated as a potentially practical way of performing computation, especially as building blocks of artificial intelligence (AI) hardware.
The concept of computation is most often approached from Turing's definition of machine-based computing[2]. However, for understanding computing as a physical process, it is often useful to view computing as a simulation procedure. In this simulation, a complex system is modeled in analogy with a more controllable, tunable, or accessible physical system. This concept is the basis of "analog computing," where electrical analogs are built to model a harder-to-access physical system.
In a traditional computing device, information is represented by the phase and/or frequency of oscillatory signals in addition to, or instead of, the signal levels. This approach, however, can be argued to waste the information carried by the timing of the signals. Using phase and frequency as a carrier may allow for a richer representation of information. A key characteristic of OBCs is that information is primarily represented by frequencies and phases of oscillatory signals, while the signal amplitude may or may not play a role.
Biological Inspiration and Neuromorphic Computing
The design of OBC is largely inspired by biological observations. Neuromorphic computing devices are often imagined as interconnected units of elementary processors, which are loosely referred to as neurons. The interaction of these units drives them into a collective state, and this state carries the results of a computation.
The artificial neurons should obey certain requirements in order to perform computation—typically, they are multi-input devices, which compute a superposition of their inputs and then output a nonlinear function of this sum. While such an operation is conceptually simple, it is not at all easy to find physically realizable low-power, robust, reproducibly behaving elements that could serve as building blocks of the neurons.
Many types of oscillators exist that can straightforwardly realize neuron functions. Most physical oscillators show a suitable nonlinear phase and frequency response if they are perturbed by incoming oscillatory signals[3]. For example, two interacting oscillators will run at exactly the same frequency if the difference in their free-running frequencies is below a certain threshold value. In addition to being good nonlinear units, oscillators are also ubiquitous in the physical world, making them attractive for realizing computing systems.
Definition of Oscillator-based Computing
The definition of an OBC derives from the above-described attributes of a computing system. The first requirement is that in an OBC the signals are carried by the phase and frequency of oscillatory signals. The second requirement is that signals must be processed by the (nonlinear) interactions between oscillators.
This definition narrows down OBC to a fairly specific class of circuit architectures. For example, it excludes spiking analog circuits from our definition of OBC. Spiking neural networks employ oscillatory signal representation[4], and so they fulfill the first requirement for OBC. But they use different processing techniques: their computing units integrate, count, and multiply spike sequences and do not rely on oscillator interactions.
Computing Models and Biological Motivation
There are a large number of various computing schemes (Boolean or non-Boolean, special, or general purpose) that may be implemented using oscillator dynamics. Most of these computing models are not specific to OBC; rather, they are oscillatory versions of some known analog computing model.
The motivation to study OBC comes largely from biology. The central nervous system is believed to use time-dependent signals (pulse or spike sequences) to communicate and process information—this dynamic nature of information processing in the brain is what probably distinguishes it most from today's digital computers. There is a large body of work on large-scale brain simulations[5], and the usefulness of oscillatory models in biology[6] is discussed extensively in the literature.
Historical Perspective and Physical Realization of Oscillators
Historically, the idea of OBC dates back to von Neumann's 1954 patent[1], and his concept is an early and still very relevant example of OBC. This scheme uses phases of oscillator signals to realize Boolean, digital computation and also serves as a perfect example of how one can translate a level-based computing scheme to a phase/frequency based representation.
The attractiveness of OBC largely hinges on finding a suitable oscillator as a building block of the computer. One may use electrical oscillators and even standard, fabrication-friendly CMOS circuitry. Transistor action, however, is not at all required to every oscillator type, and so the field is widely open for using emerging devices or possibly nonelectrical variables. OBCs realized with nanoscale, highly efficient oscillators have the potential to yield truly revolutionary devices.
Computing in OBCs and Applications in AI
Computing in OBCs occurs by oscillator interactions, more specifically, by oscillator synchronization. Various means of physical oscillator interconnections have been explored, and these interconnection topologies perform computing. Synchronization phenomena have a large literature in physics and nonlinear science[7]
One of the most promising applications for OBC is that they may be used as hardware accelerators in artificial intelligence (AI) hardware. In AI algorithms, the vast majority of computing power is spent on performing simple, repetitive calculations, such as calculating dot products, convolutions, applying nonlinearities, and recognizing or matching simple patterns. It is quite possible that Boolean, CMOS-based circuitry is suboptimal in doing these tasks. For this reason, deep learning algorithms and convolutional neural networks became major drivers for seeking out new, possibly non-Boolean hardware.
Conclusion
OBC has grown into a vast field with a diverse range of ideas and concepts that hold the potential for a breakthrough for new-generation computing hardware. The success of OBC will ultimately depend on the physical realization of the oscillators and their interactions. The field is still in its early stages, with no consensus on the "best way" to use oscillators in computing, and very few attempts to benchmark oscillator-based solutions against digital or level-based analog circuits. However, the potential for breakthroughs in next-generation computing hardware is significant, making OBC a promising area of research in the quest for "beyond Moore" electronic devices.
References
- ↑ 1.0 1.1 pubs.aip.org https://pubs.aip.org/aip/apr/article/7/1/011302/997386. Retrieved 2023-07-23. Missing or empty
|title=(help) - ↑ De Mol, Liesbeth (2021), "Turing Machines", in Zalta, Edward N., The Stanford Encyclopedia of Philosophy (Winter 2021 ed.), Metaphysics Research Lab, Stanford University, retrieved 2023-07-23
- ↑ asmedigitalcollection.asme.org https://asmedigitalcollection.asme.org/mechanismsrobotics/article-abstract/9/2/024502/473099/Nonlinear-Phase-Based-Oscillator-to-Generate-and?redirectedFrom=fulltext. Retrieved 2023-07-23. Missing or empty
|title=(help) - ↑ Pfeiffer, Michael; Pfeil, Thomas (2018). "Deep Learning With Spiking Neurons: Opportunities and Challenges". Frontiers in Neuroscience. 12. doi:10.3389/fnins.2018.00774. ISSN 1662-453X. PMID 30410432.
- ↑ "Algorithm for large-scale brain simulations: The new algorithm is a decisive step towards creating the technology to achieve simulations of brain-scale networks on future supercomputers of the exascale class -- and also significantly speeds up brain simulations on existing supercomputers". ScienceDaily. Retrieved 2023-07-23.
- ↑ Tyler, J.; Forger, D.; Kim, J. K. (2021). "Inferring causality in biological oscillators". Bioinformatics (Oxford, England). 38 (1): 196–203. doi:10.1093/bioinformatics/btab623. PMC 8696107 Check
|pmc=value (help). PMID 34463706 Check|pmid=value (help). - ↑ Pikovsky, Arkady; Rosenblum, Michael; Kurths, Jürgen (2001). Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge Nonlinear Science Series. Cambridge: Cambridge University Press. ISBN 978-0-521-53352-2. Search this book on
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