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==Neuromemristive systems==

==Neuromemristive systems==

==神经记忆电阻系统==

==神经记忆电阻系统==

Neuromemristive systems are a subclass of neuromorphic computing systems that focus on the use of [[memristors]] to implement [[neuroplasticity]]. While neuromorphic engineering focuses on mimicking biological behavior, neuromemristive systems focus on abstraction.<ref>{{Cite web|url=https://digitalops.sandia.gov/Mediasite/Play/a10cf6ceb55d47608bb8326dd00e46611d|title=002.08 N.I.C.E. Workshop 2014: Towards Intelligent Computing with Neuromemristive Circuits and Systems - Feb. 2014|website=digitalops.sandia.gov|access-date=2019-08-26}}</ref> For example, a neuromemristive system may replace the details of a [[Cerebral cortex|cortical]] microcircuit's behavior with an abstract neural network model.<ref>C. Merkel and D. Kudithipudi, "Neuromemristive extreme learning machines for pattern classification," ISVLSI, 2014.</ref>

Neuromemristive systems are a subclass of neuromorphic computing systems that focus on the use of [[memristors]] to implement [[neuroplasticity]]. While neuromorphic engineering focuses on mimicking biological behavior, neuromemristive systems focus on abstraction.<ref name=":33">{{Cite web|url=https://digitalops.sandia.gov/Mediasite/Play/a10cf6ceb55d47608bb8326dd00e46611d|title=002.08 N.I.C.E. Workshop 2014: Towards Intelligent Computing with Neuromemristive Circuits and Systems - Feb. 2014|website=digitalops.sandia.gov|access-date=2019-08-26}}</ref> For example, a neuromemristive system may replace the details of a [[Cerebral cortex|cortical]] microcircuit's behavior with an abstract neural network model.<ref name=":34">C. Merkel and D. Kudithipudi, "Neuromemristive extreme learning machines for pattern classification," ISVLSI, 2014.</ref>

Neuromemristive systems are a subclass of neuromorphic computing systems that focus on the use of memristors to implement neuroplasticity. While neuromorphic engineering focuses on mimicking biological behavior, neuromemristive systems focus on abstraction. For example, a neuromemristive system may replace the details of a cortical microcircuit's behavior with an abstract neural network model.C. Merkel and D. Kudithipudi, "Neuromemristive extreme learning machines for pattern classification," ISVLSI, 2014.

神经记忆电阻系统是神经形态计算系统的一个亚类，主要研究利用'''<font color="ff8000">记忆电阻器Memristors</font>'''实现'''<font color="ff8000">神经可塑性Neuroplasticity</font>'''。神经形态工程的重点是模拟生物行为，而神经记忆电阻系统的重点是提取。<ref name=":33" />举个例子，一个神经记忆系统可能用抽象的神经网络模型替代'''<font color="ff8000">皮层Cortical</font>'''微电路的行为细节。<ref name=":34" />

神经记忆电阻系统是神经形态计算系统的一个亚类，主要研究利用记忆电阻器实现神经可塑性。神经形态工程的重点是模拟生物行为，而神经记忆电阻系统的重点是提取。例如，一个神经记忆系统可以用一个抽象的神经网络模型取代皮层微电路的行为细节。默克尔和 d. Kudithipudi，“用于模式分类的神经记忆极端学习机器”，ISVLSI，2014。

There exist several neuron inspired threshold logic functions<ref name="Maan 1–13" /> implemented with memristors that have applications in high level [[pattern recognition]] applications. Some of the applications reported recently include [[speech recognition]],<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> [[face recognition]]<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> and [[object recognition]].<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> They also find applications in replacing conventional digital logic gates.<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>

There exist several neuron inspired threshold logic functions<ref name="Maan 1–13" /> implemented with memristors that have applications in high level [[pattern recognition]] applications. Some of the applications reported recently include [[speech recognition]],<ref>{{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> [[face recognition]]<ref>{{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> and [[object recognition]].<ref>{{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> They also find applications in replacing conventional digital logic gates.<ref>{{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>{{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、使用记忆电阻器实现的阈值逻辑函数<ref name="Maan 1–13" />在高级'''<font color="#ff8000">模式识别Pattern recognition</font>'''中有着广泛的应用，最近报道中其应用包括'''<font color="#ff8000">语音识别Speech recognition<ref name=":35" /></font>'''、'''<font color="#ff8000">人脸识别Face recognition<ref name=":36" /></font>'''和'''<font color="#ff8000">物体识别Object recognition<ref name=":37" /></font>'''。阈值逻辑函数还可以用来取代传统的数字逻辑门。<ref name=":38" /><ref name=":39" />

There exist several neuron inspired threshold logic functions implemented with memristors that have applications in high level pattern recognition applications. Some of the applications reported recently include speech recognition, face recognition and object recognition. They also find applications in replacing conventional digital logic gates.

For ideal passive memristive circuits there is an exact equation (Caravelli-Traversa-[[Di Ventra]] equation) for the internal memory of the circuit:<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" />

 

For ideal passive memristive circuits there is an exact equation (Caravelli-Traversa-[[Di Ventra]] equation) for the internal memory of the circuit:<ref>{{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>

 

 

:<math> \frac{d}{dt} \vec{W} = \alpha \vec{W}-\frac{1}{\beta} (I+\xi \Omega W)^{-1} \Omega \vec S </math>

:<math> \frac{d}{dt} \vec{W} = \alpha \vec{W}-\frac{1}{\beta} (I+\xi \Omega W)^{-1} \Omega \vec S </math>

:\frac{d}{dt} \vec{W} = \alpha \vec{W}-\frac{1}{\beta} (I+\xi \Omega W)^{-1} \Omega \vec S

:\frac{d}{dt} \vec{W} = \alpha \vec{W}-\frac{1}{\beta} (I+\xi \Omega W)^{-1} \Omega \vec S

as a function of the properties of the physical memristive network and the external sources. In the equation above, <math>\alpha</math> is the "forgetting" time scale constant, <math> \xi=r-1</math> and <math>r=\frac{R_\text{off}}{R_\text{on}}</math> is the ratio of ''off'' and ''on'' values of the limit resistances of the memristors, <math> \vec S </math> is the vector of the sources of the circuit and <math>\Omega</math> is a projector on the fundamental loops of the circuit. The constant <math>\beta</math> has the dimension of a voltage and is associated to the properties of the [[memristor]]; its physical origin is the charge mobility in the conductor. The diagonal matrix and vector <math>W=\operatorname{diag}(\vec W)</math> and <math>\vec W</math> respectively, are instead the internal value of the memristors, with values between 0 and 1. This equation thus requires adding extra constraints on the memory values in order to be reliable.

as a function of the properties of the physical memristive network and the external sources. In the equation above, <math>\alpha</math> is the "forgetting" time scale constant, <math> \xi=r-1</math> and <math>r=\frac{R_\text{off}}{R_\text{on}}</math> is the ratio of ''off'' and ''on'' values of the limit resistances of the memristors, <math> \vec S </math> is the vector of the sources of the circuit and <math>\Omega</math> is a projector on the fundamental loops of the circuit. The constant <math>\beta</math> has the dimension of a voltage and is associated to the properties of the [[memristor]]; its physical origin is the charge mobility in the conductor. The diagonal matrix and vector <math>W=\operatorname{diag}(\vec W)</math> and <math>\vec W</math> respectively, are instead the internal value of the memristors, with values between 0 and 1. This equation thus requires adding extra constraints on the memory values in order to be reliable.

<nowiki>as a function of the properties of the physical memristive network and the external sources. In the equation above, \alpha is the "forgetting" time scale constant,  \xi=r-1 and r=\frac{R_\text{off}}{R_\text{on}} is the ratio of off and on values of the limit resistances of the memristors,  \vec S is the vector of the sources of the circuit and \Omega is a projector on the fundamental loops of the circuit. The constant \beta has the dimension of a voltage and is associated to the properties of the memristor; its physical origin is the charge mobility in the conductor. The diagonal matrix and vector W=\operatorname{diag}(\vec W) and \vec W respectively, are instead the internal value of the memristors, with values between 0 and 1. This equation thus requires adding extra constraints on the memory values in order to be reliable.</nowiki>

Caravelli-Traversa-Di Ventra方程是描述物理记忆网络和外部源性质的函数。在上述方程中，<math>\alpha</math>是“遗忘”时间尺度常数，<math>\xi=r-1</math>，<math>r =\frac{R\text_{off}}{R_\text{on}}</math>是记忆电阻器off状态和on状态极限电阻值之比，<math>\vec S</math>是电路源的矢量，<math>\Omega</math>是电路基本环路的投影。常数<math>\beta</math>具有电压的量纲，与记忆电阻器的特性有关；其物理原型是导体中的电荷迁移率。对角矩阵和向量 <math>W=\operatorname{diag}(\vec W)</math>和<nowiki><math>\vec W<math></nowiki>'''<font color="#32CD32">是记忆电阻器的内阻</font>'''，值在0到1之间。因此，这个等式需要在'''<font color="32CD32">内存值</font>'''上添加额外约束以保证可靠性。

== See also==

==See also==

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== References ==

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*Telluride Neuromorphic Engineering Workshop

*Telluride Neuromorphic Engineering Workshop

*CapoCaccia Cognitive Neuromorphic Engineering Workshop

*CapoCaccia Cognitive Neuromorphic Engineering Workshop

*Institute of Neuromorphic Engineering

* Institute of Neuromorphic Engineering

*INE news site.

* INE news site.

*Frontiers in Neuromorphic Engineering Journal

* Frontiers in Neuromorphic Engineering Journal

*Computation and Neural Systems department at the California Institute of Technology.

*Computation and Neural Systems department at the California Institute of Technology.

*Human Brain Project official site

*Human Brain Project official site

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* 碲化物神经形态工程工作室

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*INE 新闻站点。

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*《神经形态工程学前沿》

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*人脑项目官方网站

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*打造硅脑: 基于生物神经元的计算机芯片可能有助于模拟更大、更复杂的大脑模型。2019年5月1日。SANDEEP RAVINDRAN

*打造硅脑: 基于生物神经元的计算机芯片可能有助于模拟更大、更复杂的大脑模型。2019年5月1日。SANDEEP RAVINDRAN.

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