更改

}}

}}

'''神经形态工程 Neuromorphic engineering'''（也称为'''神经形态计算 Neuromorphic computing'''或'''类脑计算 Brain-inspired computing'''）<ref name=":3">{{Cite journal | doi = 10.1145/2601069| title = Neuromorphic computing gets ready for the (really) big time| journal = [[Communications of the ACM]]| volume = 57| issue = 6| year = 2014| last1 = Monroe | first1 = D. | pages = 13–15| s2cid = 20051102}}</ref><ref name=":4">{{Cite journal | doi = 10.1088/0957-4484/21/17/175202| pmid = 20368686| title = Nanotube devices based crossbar architecture: Toward neuromorphic computing| journal = Nanotechnology| volume = 21| issue = 17| pages = 175202| year = 2010| last1 = Zhao | first1 = W. S. | last2 = Agnus | first2 = G. | last3 = Derycke | first3 = V. | last4 = Filoramo | first4 = A. | last5 = Bourgoin | first5 = J. -P. | last6 = Gamrat | first6 = C. | bibcode = 2010Nanot..21q5202Z| url = https://zenodo.org/record/3428659}}</ref><ref name="humanbrainproject">{{YouTube|id=6RoiZ90mGfw|title=The Human Brain Project SP 9: Neuromorphic Computing Platform}}</ref>是指使用包含电子模拟电路的超大规模集成电路系统来模拟神经系统中生理结构的研究方法。神经形态计算机或神经形态芯片包括任何使用由硅制成的人造神经元进行计算的设备。<ref name=":5">{{cite journal|last1=Mead|first1=Carver|title=Neuromorphic electronic systems|journal=Proceedings of the IEEE|date=1990|volume=78|issue=10|pages=1629–1636|doi=10.1109/5.58356|url=https://authors.library.caltech.edu/53090/1/00058356.pdf}}</ref><ref name=":2" />近年来，'''神经形态学 neuromorphic'''被用来描述能够实现神经系统模型功能（如感知、运动控制，多感官整合等）的模拟、数字、模拟/数字混合模式超大规模集成电路和软件系统。神经形态计算的硬件实现可以通过基于氧化物的记忆电阻器 Memristor（简称忆阻器）、<ref name="Maan 1–13">{{Cite journal|last1=Maan|first1=A. K.|last2=Jayadevi|first2=D. A.|last3=James|first3=A. P.|date=2016-01-01|title=A Survey of Memristive Threshold Logic Circuits|journal=IEEE Transactions on Neural Networks and Learning Systems|volume=PP|issue=99|pages=1734–1746|doi=10.1109/TNNLS.2016.2547842|pmid=27164608|issn=2162-237X|arxiv=1604.07121|bibcode=2016arXiv160407121M|s2cid=1798273}}</ref>自旋电子存储器、阈值开关和晶体管来实现。<ref name=":6">{{Cite journal|title = Mott Memory and Neuromorphic Devices|journal = Proceedings of the IEEE|date = 2015-08-01|issn = 0018-9219|pages = 1289–1310|volume = 103|issue = 8|doi = 10.1109/JPROC.2015.2431914|first1 = You|last1 = Zhou|first2 = S.|last2 = Ramanathan|s2cid = 11347598|url = https://zenodo.org/record/895565}}</ref><ref name=":2">{{Cite document|title=Neuromorphic Circuits With Neural Modulation Enhancing the Information Content of Neural Signaling {{!}} International Conference on Neuromorphic Systems 2020|language=EN|doi=10.1145/3407197.3407204|s2cid=220794387}}</ref>对基于软件的脉冲神经网络系统的训练可以通过误差反向传播机制来实现，例如，使用snnTorch等基于Python的框架，<ref name=":7">{{cite journal |last1=Eshraghian|first1=Jason K.|last2=Ward|first2=Max|last3=Neftci |first3=Emre|last4=Wang|first4=Xinxin|last5=Lenz|first5=Gregor|last6=Dwivedi|first6=Girish|last7=Bennamoun|first7=Mohammed|last8=Jeong|first8=Doo Seok|last9=Lu|first9=Wei D.|title=Training Spiking Neural Networks Using Lessons from Deep Learning |date=1 October 2021 |arxiv=2109.12894 }}</ref> 或使用BindsNet等典型的受生物启发的学习模式。<ref name=":8">{{Cite web | url=https://github.com/Hananel-Hazan/bindsnet | title=Hananel-Hazan/bindsnet: Simulation of spiking neural networks (SNNs) using PyTorch.| date=31 March 2020}}</ref>

'''神经形态工程 Neuromorphic engineering'''（也称为'''神经形态计算 Neuromorphic computing'''或'''类脑计算 Brain-inspired computing'''）<ref name=":3">{{Cite journal | doi = 10.1145/2601069| title = Neuromorphic computing gets ready for the (really) big time| journal = [[Communications of the ACM]]| volume = 57| issue = 6| year = 2014| last1 = Monroe | first1 = D. | pages = 13–15}}</ref><ref name=":4">{{Cite journal | doi = 10.1088/0957-4484/21/17/175202| pmid = 20368686| title = Nanotube devices based crossbar architecture: Toward neuromorphic computing| journal = Nanotechnology| volume = 21| issue = 17| pages = 175202| year = 2010| last1 = Zhao | first1 = W. S. | last2 = Agnus | first2 = G. | last3 = Derycke | first3 = V. | last4 = Filoramo | first4 = A. | last5 = Bourgoin | first5 = J. -P. | last6 = Gamrat | first6 = C. | bibcode = 2010Nanot..21q5202Z| url = https://zenodo.org/record/3428659}}</ref><ref name="humanbrainproject">{{YouTube|id=6RoiZ90mGfw|title=The Human Brain Project SP 9: Neuromorphic Computing Platform}}</ref>是指使用包含电子模拟电路的超大规模集成电路系统来模拟神经系统中生理结构的研究方法。神经形态计算机或神经形态芯片包括任何使用由硅制成的人造神经元进行计算的设备。<ref name=":5">{{cite journal|last1=Mead|first1=Carver|title=Neuromorphic electronic systems|journal=Proceedings of the IEEE|date=1990|volume=78|issue=10|pages=1629–1636|doi=10.1109/5.58356|url=https://authors.library.caltech.edu/53090/1/00058356.pdf}}</ref><ref name=":2" />近年来，'''神经形态学 neuromorphic'''被用来描述能够实现神经系统模型功能（如感知、运动控制，多感官整合等）的模拟、数字、模拟/数字混合模式超大规模集成电路和软件系统。神经形态计算的硬件实现可以通过基于氧化物的记忆电阻器 Memristor（简称忆阻器）、<ref name="Maan 1–13">{{Cite journal|last1=Maan|first1=A. K.|last2=Jayadevi|first2=D. A.|last3=James|first3=A. P.|date=2016-01-01|title=A Survey of Memristive Threshold Logic Circuits|journal=IEEE Transactions on Neural Networks and Learning Systems|volume=PP|issue=99|pages=1734–1746|doi=10.1109/TNNLS.2016.2547842|pmid=27164608|issn=2162-237X|arxiv=1604.07121|bibcode=2016arXiv160407121M}}</ref>自旋电子存储器、阈值开关和晶体管来实现。<ref name=":6">{{Cite journal|title = Mott Memory and Neuromorphic Devices|journal = Proceedings of the IEEE|date = 2015-08-01|issn = 0018-9219|pages = 1289–1310|volume = 103|issue = 8|doi = 10.1109/JPROC.2015.2431914|first1 = You|last1 = Zhou|first2 = S.|last2 = Ramanathan|url = https://zenodo.org/record/895565}}</ref><ref name=":2">{{Cite document|title=Neuromorphic Circuits With Neural Modulation Enhancing the Information Content of Neural Signaling {{!}} International Conference on Neuromorphic Systems 2020|language=EN|doi=10.1145/3407197.3407204}}</ref>对基于软件的脉冲神经网络系统的训练可以通过误差反向传播机制来实现，例如，使用snnTorch等基于Python的框架，<ref name=":7">{{cite journal |last1=Eshraghian|first1=Jason K.|last2=Ward|first2=Max|last3=Neftci |first3=Emre|last4=Wang|first4=Xinxin|last5=Lenz|first5=Gregor|last6=Dwivedi|first6=Girish|last7=Bennamoun|first7=Mohammed|last8=Jeong|first8=Doo Seok|last9=Lu|first9=Wei D.|title=Training Spiking Neural Networks Using Lessons from Deep Learning |date=1 October 2021 |arxiv=2109.12894 }}</ref> 或使用BindsNet等典型的受生物启发的学习模式。<ref name=":8">{{Cite web | url=https://github.com/Hananel-Hazan/bindsnet | title=Hananel-Hazan/bindsnet: Simulation of spiking neural networks (SNNs) using PyTorch.| date=31 March 2020}}</ref>

==代表性成果==

==代表性成果==

早在2006年，佐治亚理工学院的研究人员就研发出了一种现场可编程神经阵列。<ref name=":12">{{Cite book|title = A field programmable neural array|last1 = Farquhar|first1 = Ethan|date = May 2006|journal = IEEE International Symposium on Circuits and Systems|pages = 4114–4117|last2 = Hasler|first2 = Paul.|doi = 10.1109/ISCAS.2006.1693534|isbn = 978-0-7803-9389-9|s2cid = 206966013}}</ref>在此之后，一系列越来越复杂的浮栅晶体管阵列被成功研发出来，这些晶体管阵列可以通过在'''金属-氧化物半导体效应晶体管MOSFET'''的栅极上编程来模拟大脑中神经元的离子通道特性，这也是以硅为主要材料的可编程神经元阵列的最早成功案例之一。

早在2006年，佐治亚理工学院的研究人员就研发出了一种现场可编程神经阵列。<ref name=":12">{{Cite book|title = A field programmable neural array|last1 = Farquhar|first1 = Ethan|date = May 2006|journal = IEEE International Symposium on Circuits and Systems|pages = 4114–4117|last2 = Hasler|first2 = Paul.|doi = 10.1109/ISCAS.2006.1693534|isbn = 978-0-7803-9389-9}}</ref>在此之后，一系列越来越复杂的浮栅晶体管阵列被成功研发出来，这些晶体管阵列可以通过在'''金属-氧化物半导体效应晶体管MOSFET'''的栅极上编程来模拟大脑中神经元的离子通道特性，这也是以硅为主要材料的可编程神经元阵列的最早成功案例之一。

惠普实验室在莫特忆阻器上的研究表明，尽管它们可以是非易失性的，但是在[[相变]]温度以下时表现出的易失性行为可以被用来制造类神经元电阻器（一种生物学启发的模仿神经元行为的硬件）<ref name=":0">{{Cite journal | doi = 10.1038/nmat3510| pmid = 23241533| title = A scalable neuristor built with Mott memristors| journal = Nature Materials| volume = 12| issue = 2| pages = 114–7| year = 2012| last1 = Pickett | first1 = M. D. | last2 = Medeiros-Ribeiro | first2 = G. | last3 = Williams | first3 = R. S. | bibcode = 2013NatMa..12..114P| s2cid = 16271627| url = https://semanticscholar.org/paper/b6ba6f496ace2b947f111059663e76bb60e9efeb}}</ref>。2013年9月，他们通过模型和仿真展示了这些类神经元电阻器的脉冲行为如何产生[[图灵机]]的所需元素。<ref name=":14">{{cite journal|doi=10.1088/0957-4484/24/38/384002|title=Phase transitions enable computational universality in neuristor-based cellular automata|author1=Matthew D Pickett|author2=R Stanley Williams|name-list-style=amp|date=September 2013|publisher=IOP Publishing Ltd|journal=Nanotechnology|volume=24|issue=38|pmid=23999059|bibcode=2013Nanot..24L4002P|at=384002}}</ref>

惠普实验室在莫特忆阻器上的研究表明，尽管它们可以是非易失性的，但是在[[相变]]温度以下时表现出的易失性行为可以被用来制造类神经元电阻器（一种生物学启发的模仿神经元行为的硬件）<ref name=":0">{{Cite journal | doi = 10.1038/nmat3510| pmid = 23241533| title = A scalable neuristor built with Mott memristors| journal = Nature Materials| volume = 12| issue = 2| pages = 114–7| year = 2012| last1 = Pickett | first1 = M. D. | last2 = Medeiros-Ribeiro | first2 = G. | last3 = Williams | first3 = R. S. | bibcode = 2013NatMa..12..114P| url = https://semanticscholar.org/paper/b6ba6f496ace2b947f111059663e76bb60e9efeb}}</ref>。2013年9月，他们通过模型和仿真展示了这些类神经元电阻器的脉冲行为如何产生[[图灵机]]的所需元素。<ref name=":14">{{cite journal|doi=10.1088/0957-4484/24/38/384002|title=Phase transitions enable computational universality in neuristor-based cellular automata|author1=Matthew D Pickett|author2=R Stanley Williams|name-list-style=amp|date=September 2013|publisher=IOP Publishing Ltd|journal=Nanotechnology|volume=24|issue=38|pmid=23999059|bibcode=2013Nanot..24L4002P|at=384002}}</ref>

'''神经栅格 Neurogrid<ref name=":15">{{cite journal|last1=Boahen|first1=Kwabena|title=Neurogrid: A Mixed-Analog-Digital Multichip System for Large-Scale Neural Simulations|journal=Proceedings of the IEEE|date=24 April 2014|volume=102|issue=5|pages=699–716|doi=10.1109/JPROC.2014.2313565|s2cid=17176371}}</ref>'''是由斯坦福大学Brains in Silicon公司研发的、使用神经形态工程原理设计的硬件。该电路板由16个定制设计的芯片组成。在设计中，每个NeuroCore芯片的模拟电路对65536个神经元的神经元素进行模拟，以最大限度地提高能量效率。模拟出的神经元通过设计的数字电路连接，以最大化脉冲吞吐量。<ref name=":16">{{cite journal|doi=10.1038/503022a|pmid = 24201264|title = Neuroelectronics: Smart connections|journal = Nature|volume = 503|issue = 7474|pages = 22–4|year = 2013|last1 = Waldrop|first1 = M. Mitchell|bibcode = 2013Natur.503...22W|doi-access = free}}</ref><ref name=":17">{{cite journal|doi=10.1109/JPROC.2014.2313565|title = Neurogrid: A Mixed-Analog-Digital Multichip System for Large-Scale Neural Simulations|journal = Proceedings of the IEEE|volume = 102|issue = 5|pages = 699–716|year = 2014|last1 = Benjamin|first1 = Ben Varkey|last2 = Peiran Gao|last3 = McQuinn|first3 = Emmett|last4 = Choudhary|first4 = Swadesh|last5 = Chandrasekaran|first5 = Anand R.|last6 = Bussat|first6 = Jean-Marie|last7 = Alvarez-Icaza|first7 = Rodrigo|last8 = Arthur|first8 = John V.|last9 = Merolla|first9 = Paul A.|last10 = Boahen|first10 = Kwabena|s2cid = 17176371}}</ref>

'''神经栅格 Neurogrid<ref name=":15">{{cite journal|last1=Boahen|first1=Kwabena|title=Neurogrid: A Mixed-Analog-Digital Multichip System for Large-Scale Neural Simulations|journal=Proceedings of the IEEE|date=24 April 2014|volume=102|issue=5|pages=699–716|doi=10.1109/JPROC.2014.2313565}}</ref>'''是由斯坦福大学Brains in Silicon公司研发的、使用神经形态工程原理设计的硬件。该电路板由16个定制设计的芯片组成。在设计中，每个NeuroCore芯片的模拟电路对65536个神经元的神经元素进行模拟，以最大限度地提高能量效率。模拟出的神经元通过设计的数字电路连接，以最大化脉冲吞吐量。<ref name=":16">{{cite journal|doi=10.1038/503022a|pmid = 24201264|title = Neuroelectronics: Smart connections|journal = Nature|volume = 503|issue = 7474|pages = 22–4|year = 2013|last1 = Waldrop|first1 = M. Mitchell|bibcode = 2013Natur.503...22W|doi-access = free}}</ref><ref name=":17">{{cite journal|doi=10.1109/JPROC.2014.2313565|title = Neurogrid: A Mixed-Analog-Digital Multichip System for Large-Scale Neural Simulations|journal = Proceedings of the IEEE|volume = 102|issue = 5|pages = 699–716|year = 2014|last1 = Benjamin|first1 = Ben Varkey|last2 = Peiran Gao|last3 = McQuinn|first3 = Emmett|last4 = Choudhary|first4 = Swadesh|last5 = Chandrasekaran|first5 = Anand R.|last6 = Bussat|first6 = Jean-Marie|last7 = Alvarez-Icaza|first7 = Rodrigo|last8 = Arthur|first8 = John V.|last9 = Merolla|first9 = Paul A.|last10 = Boahen|first10 = Kwabena}}</ref>

其他与神经形态工程有关的研究还包括脑计划 BRAIN initiative，<ref name="economist">[https://www.economist.com/news/science-and-technology/21582495-computers-will-help-people-understand-brains-better-and-understanding-brains Neuromorphic computing: The machine of a new soul], The Economist, 2013-08-03</ref> 和IBM研发的TrueNorth芯片。<ref name=":21">{{cite journal|last1=Modha|first1=Dharmendra|title=A million spiking-neuron integrated circuit with a scalable communication network and interface|journal=Science|date=Aug 2014|volume=345|issue=6197|pages=668–673|doi=10.1126/science.1254642|pmid=25104385|bibcode=2014Sci...345..668M|s2cid=12706847}}</ref>使用纳米晶体、纳米线和导电聚合物也能够用于制造神经形态学硬件。<ref name=":22">{{Cite web|url=http://jessamynfairfield.com/wp-content/uploads/2017/03/PWMar17Fairfield.pdf|title=Smarter Machines|last=Fairfield|first=Jessamyn|date=March 1, 2017}}</ref>

其他与神经形态工程有关的研究还包括脑计划 BRAIN initiative，<ref name="economist">[https://www.economist.com/news/science-and-technology/21582495-computers-will-help-people-understand-brains-better-and-understanding-brains Neuromorphic computing: The machine of a new soul], The Economist, 2013-08-03</ref> 和IBM研发的TrueNorth芯片。<ref name=":21">{{cite journal|last1=Modha|first1=Dharmendra|title=A million spiking-neuron integrated circuit with a scalable communication network and interface|journal=Science|date=Aug 2014|volume=345|issue=6197|pages=668–673|doi=10.1126/science.1254642|pmid=25104385|bibcode=2014Sci...345..668M}}</ref>使用纳米晶体、纳米线和导电聚合物也能够用于制造神经形态学硬件。<ref name=":22">{{Cite web|url=http://jessamynfairfield.com/wp-content/uploads/2017/03/PWMar17Fairfield.pdf|title=Smarter Machines|last=Fairfield|first=Jessamyn|date=March 1, 2017}}</ref>

2017年10月，英特尔发布了神经形态芯片 Loihi。该芯片采用异步[[脉冲神经网络]]实现了自适应、自修改、事件驱动的细粒度并行计算，实现了高效的学习和推理。<ref name=":23">{{cite journal |last1=Davies |first1=Mike |title=Loihi: A Neuromorphic Manycore Processor with On-Chip Learning |journal=IEEE Micro |date=January 16, 2018 |volume=38 |issue=1 |pages=82–99 |display-authors=etal|doi=10.1109/MM.2018.112130359 |s2cid=3608458 }}</ref><ref name="Morris2017">{{cite web |last1=Morris |first1=John |title=Why Intel built a neuromorphic chip |url=https://www.zdnet.com/article/why-intel-built-a-neuromorphic-chip/ |website=ZDNet |access-date=17 August 2018 |language=en}}</ref>

2017年10月，英特尔发布了神经形态芯片 Loihi。该芯片采用异步[[脉冲神经网络]]实现了自适应、自修改、事件驱动的细粒度并行计算，实现了高效的学习和推理。<ref name=":23">{{cite journal |last1=Davies |first1=Mike |title=Loihi: A Neuromorphic Manycore Processor with On-Chip Learning |journal=IEEE Micro |date=January 16, 2018 |volume=38 |issue=1 |pages=82–99 |display-authors=etal|doi=10.1109/MM.2018.112130359 }}</ref><ref name="Morris2017">{{cite web |last1=Morris |first1=John |title=Why Intel built a neuromorphic chip |url=https://www.zdnet.com/article/why-intel-built-a-neuromorphic-chip/ |website=ZDNet |access-date=17 August 2018 |language=en}}</ref>

===人格权问题===

===人格权问题===

随着神经形态系统的日益发展，一些学者主张赋予这些系统人格权。如果是大脑赋予了人类人格，那么在多大程度上模仿人类大脑的神经形态系统才能被赋予人格权利？“人类大脑计划”旨在推进以大脑为灵感的计算机技术发展，该计划的批评者认为，神经形态计算机技术的进步可能导致机器意识或人格的形成。<ref name=":28">{{Cite journal|last=Aicardi|first=Christine|date=September 2018|title=Accompanying technology development in the Human Brain Project: From foresight to ethics management|journal=Futures|volume=102|pages=114–124|doi=10.1016/j.futures.2018.01.005|doi-access=free}}</ref>这些批评者认为，如果这些系统被当作人来对待，那么人类使用神经形态系统执行任务（包括终止神经形态系统）的行为，在道德上就可能是不被允许的，因为这些行为将违反神经形态系统的自主性。<ref name=":29">{{Cite journal|last=Lim|first=Daniel|date=2014-06-01|title=Brain simulation and personhood: a concern with the Human Brain Project|journal=Ethics and Information Technology|language=en|volume=16|issue=2|pages=77–89|doi=10.1007/s10676-013-9330-5|s2cid=17415814|issn=1572-8439}}</ref>

随着神经形态系统的日益发展，一些学者主张赋予这些系统人格权。如果是大脑赋予了人类人格，那么在多大程度上模仿人类大脑的神经形态系统才能被赋予人格权利？“人类大脑计划”旨在推进以大脑为灵感的计算机技术发展，该计划的批评者认为，神经形态计算机技术的进步可能导致机器意识或人格的形成。<ref name=":28">{{Cite journal|last=Aicardi|first=Christine|date=September 2018|title=Accompanying technology development in the Human Brain Project: From foresight to ethics management|journal=Futures|volume=102|pages=114–124|doi=10.1016/j.futures.2018.01.005|doi-access=free}}</ref>这些批评者认为，如果这些系统被当作人来对待，那么人类使用神经形态系统执行任务（包括终止神经形态系统）的行为，在道德上就可能是不被允许的，因为这些行为将违反神经形态系统的自主性。<ref name=":29">{{Cite journal|last=Lim|first=Daniel|date=2014-06-01|title=Brain simulation and personhood: a concern with the Human Brain Project|journal=Ethics and Information Technology|language=en|volume=16|issue=2|pages=77–89|doi=10.1007/s10676-013-9330-5|issn=1572-8439}}</ref>

受神经元启发、使用忆阻器实现的阈值逻辑函数<ref name="Maan 1–13" />在高级模式识别中有着广泛的应用，最近报道中其应用包括语音识别<ref name=":35">{{Cite journal|title = Memristor pattern recogniser: isolated speech word recognition|journal = Electronics Letters|pages = 1370–1372|volume = 51|issue = 17|doi = 10.1049/el.2015.1428|first1 = A.K.|last1 = Maan|first2 = A.P.|last2 = James|first3 = S.|last3 = Dimitrijev|year = 2015|bibcode = 2015ElL....51.1370M|hdl = 10072/140989|s2cid = 61454815|url = https://semanticscholar.org/paper/48d3ab11ec6e213b62f11eedcfb7b7febb058674|hdl-access = free}}</ref>、人脸识别<ref name=":36">{{Cite journal|title = Memristive Threshold Logic Face Recognition|journal = Procedia Computer Science|date = 2014-01-01|pages = 98–103|volume = 41|series = 5th Annual International Conference on Biologically Inspired Cognitive Architectures, 2014 BICA|doi = 10.1016/j.procs.2014.11.090|first1 = Akshay Kumar|last1 = Maan|first2 = Dinesh S.|last2 = Kumar|first3 = Alex Pappachen|last3 = James|doi-access = free}}</ref>和物体识别<ref name=":37">{{Cite journal|title = Memristive Threshold Logic Circuit Design of Fast Moving Object Detection|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems|date = 2015-10-01|issn = 1063-8210|pages = 2337–2341|volume = 23|issue = 10|doi = 10.1109/TVLSI.2014.2359801|first1 = A.K.|last1 = Maan|first2 = D.S.|last2 = Kumar|first3 = S.|last3 = Sugathan|first4 = A.P.|last4 = James|arxiv = 1410.1267|s2cid = 9647290}}</ref>。阈值逻辑函数还可以用来取代传统的数字逻辑门。<ref name=":38">{{Cite journal|title = Resistive Threshold Logic|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems|date = 2014-01-01|issn = 1063-8210|pages = 190–195|volume = 22|issue = 1|doi = 10.1109/TVLSI.2012.2232946|first1 = A.P.|last1 = James|first2 = L.R.V.J.|last2 = Francis|first3 = D.S.|last3 = Kumar|arxiv = 1308.0090|s2cid = 7357110}}</ref><ref name=":39">{{Cite journal|title = Threshold Logic Computing: Memristive-CMOS Circuits for Fast Fourier Transform and Vedic Multiplication|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems|date = 2015-11-01|issn = 1063-8210|pages = 2690–2694|volume = 23|issue = 11|doi = 10.1109/TVLSI.2014.2371857|first1 = A.P.|last1 = James|first2 = D.S.|last2 = Kumar|first3 = A.|last3 = Ajayan|arxiv = 1411.5255|s2cid = 6076956}}</ref>

受神经元启发、使用忆阻器实现的阈值逻辑函数<ref name="Maan 1–13" />在高级模式识别中有着广泛的应用，最近报道中其应用包括语音识别<ref name=":35">{{Cite journal|title = Memristor pattern recogniser: isolated speech word recognition|journal = Electronics Letters|pages = 1370–1372|volume = 51|issue = 17|doi = 10.1049/el.2015.1428|first1 = A.K.|last1 = Maan|first2 = A.P.|last2 = James|first3 = S.|last3 = Dimitrijev|year = 2015|bibcode = 2015ElL....51.1370M|hdl = 10072/140989|url = https://semanticscholar.org/paper/48d3ab11ec6e213b62f11eedcfb7b7febb058674|hdl-access = free}}</ref>、人脸识别<ref name=":36">{{Cite journal|title = Memristive Threshold Logic Face Recognition|journal = Procedia Computer Science|date = 2014-01-01|pages = 98–103|volume = 41|series = 5th Annual International Conference on Biologically Inspired Cognitive Architectures, 2014 BICA|doi = 10.1016/j.procs.2014.11.090|first1 = Akshay Kumar|last1 = Maan|first2 = Dinesh S.|last2 = Kumar|first3 = Alex Pappachen|last3 = James|doi-access = free}}</ref>和物体识别<ref name=":37">{{Cite journal|title = Memristive Threshold Logic Circuit Design of Fast Moving Object Detection|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems|date = 2015-10-01|issn = 1063-8210|pages = 2337–2341|volume = 23|issue = 10|doi = 10.1109/TVLSI.2014.2359801|first1 = A.K.|last1 = Maan|first2 = D.S.|last2 = Kumar|first3 = S.|last3 = Sugathan|first4 = A.P.|last4 = James|arxiv = 1410.1267}}</ref>。阈值逻辑函数还可以用来取代传统的数字逻辑门。<ref name=":38">{{Cite journal|title = Resistive Threshold Logic|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems|date = 2014-01-01|issn = 1063-8210|pages = 190–195|volume = 22|issue = 1|doi = 10.1109/TVLSI.2012.2232946|first1 = A.P.|last1 = James|first2 = L.R.V.J.|last2 = Francis|first3 = D.S.|last3 = Kumar|arxiv = 1308.0090}}</ref><ref name=":39">{{Cite journal|title = Threshold Logic Computing: Memristive-CMOS Circuits for Fast Fourier Transform and Vedic Multiplication|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems|date = 2015-11-01|issn = 1063-8210|pages = 2690–2694|volume = 23|issue = 11|doi = 10.1109/TVLSI.2014.2371857|first1 = A.P.|last1 = James|first2 = D.S.|last2 = Kumar|first3 = A.|last3 = Ajayan|arxiv = 1411.5255}}</ref>

对于理想的无源记忆电路，电路的内部记忆可以用精确的方程（Caravelli-Traversa-Di Ventra方程) 来描述:<ref name=":40">{{cite journal |last=Caravelli  |display-authors=etal|arxiv=1608.08651 |title=The complex dynamics of memristive circuits: analytical results and universal slow relaxation |year=2017 |doi=10.1103/PhysRevE.95.022140 |pmid= 28297937 |volume=95 |issue= 2 |pages= 022140 |journal=Physical Review E|bibcode=2017PhRvE..95b2140C |s2cid=6758362}}</ref>

对于理想的无源记忆电路，电路的内部记忆可以用精确的方程（Caravelli-Traversa-Di Ventra方程) 来描述:<ref name=":40">{{cite journal |last=Caravelli  |display-authors=etal|arxiv=1608.08651 |title=The complex dynamics of memristive circuits: analytical results and universal slow relaxation |year=2017 |doi=10.1103/PhysRevE.95.022140 |pmid= 28297937 |volume=95 |issue= 2 |pages= 022140 |journal=Physical Review E|bibcode=2017PhRvE..95b2140C}}</ref>