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Neuromorphic Computing is Turing-Complete

Authors:

Catherine Schuman,

Bill KayAuthors Info & Claims

ICONS '22: Proceedings of the International Conference on Neuromorphic Systems 2022

Article No.: 16, Pages 1 - 10

https://doi.org/10.1145/3546790.3546806

Published: 07 September 2022 Publication History

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Abstract

Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and GPUs. They have the potential to drive critical use cases such as autonomous vehicles, edge computing and internet of things in the future. For this reason, they are sought to be an indispensable part of the future computing landscape. Neuromorphic systems are mainly used for spike-based machine learning applications, although there are some non-machine learning applications in graph theory, differential equations, and spike-based simulations. These applications suggest that neuromorphic computing might be capable of general-purpose computing. However, general-purpose computability of neuromorphic computing has not been established yet. In this work, we prove that neuromorphic computing is Turing-complete and therefore capable of general-purpose computing. Specifically, we present a model of neuromorphic computing, with just two neuron parameters (threshold and leak), and two synaptic parameters (weight and delay). We devise neuromorphic circuits for computing all the μ-recursive functions (i.e., constant, successor and projection functions) and all the μ-recursive operators (i.e., composition, primitive recursion and minimization operators). Given that the μ-recursive functions and operators are precisely the ones that can be computed using a Turing machine, this work establishes the Turing-completeness of neuromorphic computing.

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Neuromorphic Computing is Turing-Complete

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cover image ACM Other conferences

ICONS '22: Proceedings of the International Conference on Neuromorphic Systems 2022

July 2022

213 pages

ISBN:9781450397896

DOI:10.1145/3546790

Editors:
Thomas E. Potok
Oak Ridge National Laboratory
,
Catherine Schuman
University of Tennessee Knoxville
,
Melika Payvand
University of Zurich
,
Prasanna Date
Oak Ridge National Laboratory
,
Shruti Kulkarni
Oak Ridge National Laboratory
,
Yiran Chen
Duke University
,
Robinson Pino
U.S. Department of Energy
,
Brad Aimone
Sandia National Laboratories
,
Mutsumi Kimura
Ryukoku University
,
Gregory Cohen
Western Sydney University
,
David Whittaker
Elm Street Ventures
,
Gordon Hirsch Wilson
Rain Neuromorphics

Copyright © 2022 ACM.

© 2022 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of the United States government. As such, the United States Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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Published: 07 September 2022

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ICONS

ICONS: International Conference on Neuromorphic Systems

July 27 - 29, 2022

TN, Knoxville, USA

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Cited By

Preda APantis-Simut CMarciu MAnghel DAllosh AIon LManolescu ANemnes G(2024)Design of Nanoscale Quantum Interconnects Aided by Conditional Generative Adversarial NetworksApplied Sciences10.3390/app1403111114:3(1111)Online publication date: 29-Jan-2024
https://doi.org/10.3390/app14031111
Date PSmith W(2024)Quantum discriminator for binary classificationScientific Reports10.1038/s41598-023-46469-214:1Online publication date: 15-Jan-2024
https://doi.org/10.1038/s41598-023-46469-2
Vetter JDate PFahim FKulkarni SMaksymovych PTalin ATallada MVanna-iampikul PYoung ABrooks DCao YGu-Yeon WLim SLiu FMarinella MSumpter BMiniskar N(2023)Abisko: Deep codesign of an architecture for spiking neural networks using novel neuromorphic materialsThe International Journal of High Performance Computing Applications10.1177/1094342023117853737:3-4(351-379)Online publication date: 22-Jun-2023
https://doi.org/10.1177/10943420231178537
Maheshwari DYoung ADate PKulkarni SWitherspoon BMiniskar N(2023)An FPGA-Based Neuromorphic Processor with All-to-All Connectivity2023 IEEE International Conference on Rebooting Computing (ICRC)10.1109/ICRC60800.2023.10386808(1-5)Online publication date: 5-Dec-2023
https://doi.org/10.1109/ICRC60800.2023.10386808
Wurm ASeay RDate PKulkarni SYoung AVetter J(2023)Arithmetic Primitives for Efficient Neuromorphic Computing2023 IEEE International Conference on Rebooting Computing (ICRC)10.1109/ICRC60800.2023.10386397(1-5)Online publication date: 5-Dec-2023
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Date PKulkarni SYoung ASchuman CPotok TVetter J(2023)Encoding integers and rationals on neuromorphic computers using virtual neuronScientific Reports10.1038/s41598-023-35005-x13:1Online publication date: 6-Jul-2023
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Date PKulkarni SYoung ASchuman CPotok TVetter J(2022)Virtual Neuron: A Neuromorphic Approach for Encoding Numbers2022 IEEE International Conference on Rebooting Computing (ICRC)10.1109/ICRC57508.2022.00017(100-105)Online publication date: Dec-2022
https://doi.org/10.1109/ICRC57508.2022.00017

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