神经形态计算

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Neuromorphic engineering, also known as neuromorphic computing,[1][2][3] is the use of very-large-scale integration (VLSI) systems containing electronic analog circuits to mimic neuro-biological architectures present in the nervous system. A neuromorphic computer/chip is any device that uses physical artificial neurons (made from silicon) to do computations.[4][5] In recent times, the term neuromorphic has been used to describe analog, digital, mixed-mode analog/digital VLSI, and software systems that implement models of neural systems (for perception, motor control, or multisensory integration). The implementation of neuromorphic computing on the hardware level can be realized by oxide-based memristors,[6] spintronic memories, threshold switches, and transistors.[7][5] Training software-based neuromorphic systems of spiking neural networks can be achieved using error backpropagation, e.g., using Python based frameworks such as snnTorch,[8] or using canonical learning rules from the biological learning literature, e.g., using BindsNet.[9]


神经形态工程Neuromorphic engineering(也称为神经形态计算Neuromorphic computing)[1][2][3]是指使用包含电子模拟电路Analog circuit的超大规模集成电路Very-large-scale integration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。[4][5]近年来，神经形态学（neuromorphic）这个术语被用来描述能够实现神经系统Neural system模型功能(如感知Perception、运动控制Motor control，多感官整合Multisensory integration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、[6]自旋电子存储器、阈值开关和晶体管Transistor来实现。[7][5]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，[8]或使用BindsNet等典型的受生物启发的学习模式。[9]

A key aspect of neuromorphic engineering is understanding how the morphology of individual neurons, circuits, applications, and overall architectures creates desirable computations, affects how information is represented, influences robustness to damage, incorporates learning and development, adapts to local change (plasticity), and facilitates evolutionary change.


神经形态工程领域的一个关键问题，就是理解单个神经元形态、神经回路、应用和整体结构如何产生理想的计算，如何影响信息的表示和对破坏的鲁棒性，如何整合学习和发展，如何适应局部变化(可塑性) 并促进逐渐发展的变化。

Neuromorphic engineering is an interdisciplinary subject that takes inspiration from biology, physics, mathematics, computer science, and electronic engineering[5] to design artificial neural systems, such as vision systems, head-eye systems, auditory processors, and autonomous robots, whose physical architecture and design principles are based on those of biological nervous systems.[10] It was developed by Carver Mead[11] in the late 1980s.


神经形态工程是以生物学Biology、物理学Physics、数学Mathematics、计算机科学Computer science和电子工程Electronic engineering[5]等学科为基础，设计人工神经系统（如视觉系统Vision systems、头眼系统、听觉处理器以及物理结构和设计原则都受启发于生物神经系统的自主机器人）的一门交叉学科。[10]20世纪80年代后期，卡弗·米德极大地推动了神经形态工程领域的发展。[11]

Neurological inspiration

神经生物学启发

Neuromorphic engineering is set apart by the inspiration it takes from what we know about the structure and operations of the brain. Neuromorphic engineering translates what we know about the brain's function into computer systems. Work has mostly focused on replicating the analog nature of biological computation and the role of neurons in cognition.


神经形态工程形成的灵感来源于现已知的大脑Brain结构及运作机制知识，它将我们对大脑功能的了解用于研究和优化计算机系统。该领域工作主要集中于对生物计算Biological computation模拟特性和神经元Neuron在认知Cognition中所发挥作用的复刻。

The biological processes of neurons and their synapses are dauntingly complex, and thus very difficult to artificially simulate. A key feature of biological brains is that all of the processing in neurons use analog chemical signals. This makes it hard to replicate brains in computers because the current generation of computers is completely digital. However, the characteristics of these parts can be abstracted into mathematical functions that closely capture the essence of the neuron's operations.

神经元及其突触Synapse的生理学过程极其复杂，难以进行人工模拟。神经元在所有处理过程中都使用化学模拟信号，这是大脑的一个关键生理学特征。这个特征大大增加了在计算机中复制大脑的难度，因为目前的计算机是完全数字化的。然而，部分特征可以抽象为数学函数，这些函数能够紧密捕捉神经元运行的本质。

The goal of neuromorphic computing is not to perfectly mimic the brain and all of its functions, but instead to extract what is known of its structure and operations to be used in a practical computing system. No neuromorphic system will claim nor attempt to reproduce every element of neurons and synapses, but all adhere to the idea that computation is highly distributed throughout a series of small computing elements analogous to a neuron. While this sentiment is standard, researchers chase this goal with different methods.[12]

神经形态计算的目标不是完美地模拟大脑及其所有功能，而是利用已知的大脑结构和运转机制来研发或优化实际的计算系统。任何神经形态学系统都不会声称或试图复制神经元和突触中的每一个元素，但所有人都一致认可将计算高度分散Distribute于一系列类似于神经元的小型计算元素的理念。研究人员用不同的方法来追求这一普遍目标。[12]


Examples

代表性成果

As early as 2006, researchers at Georgia Tech published a field programmable neural array.[13] This chip was the first in a line of increasingly complex arrays of floating gate transistors that allowed programmability of charge on the gates of MOSFETs to model the channel-ion characteristics of neurons in the brain and was one of the first cases of a silicon programmable array of neurons.

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。[13]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。

In November 2011, a group of MIT researchers created a computer chip that mimics the analog, ion-based communication in a synapse between two neurons using 400 transistors and standard CMOS manufacturing techniques.[14][15]

2011年11月，麻省理工学院的一组研究人员研发出一种计算机芯片，该芯片上使用标准的互补金属氧化物半导体CMOS制造技术集成了400个晶体管，能够模拟神经元间突触中基于离子的通讯。[14][15]

In June 2012, spintronic researchers at Purdue University presented a paper on the design of a neuromorphic chip using lateral spin valves and memristors. They argue that the architecture works similarly to neurons and can therefore be used to test methods of reproducing the brain's processing. In addition, these chips are significantly more energy-efficient than conventional ones.[16]

2012年6月，普渡大学的自旋电子学Spintronic研究人员发表了一篇关于利用侧向自旋阀Lateral spin valves和记忆电阻器Memristors设计神经形态芯片的论文。他们认为，这种芯片结构的工作原理与神经元相似，因此可以用于大脑运行机制的复刻方法的测试。此外，这些芯片在能耗方面明显优于传统芯片。[16]

Research at HP Labs on Mott memristors has shown that while they can be non-volatile, the volatile behavior exhibited at temperatures significantly below the phase transition temperature can be exploited to fabricate a neuristor,[17] a biologically-inspired device that mimics behavior found in neurons.[17] In September 2013, they presented models and simulations that show how the spiking behavior of these neuristors can be used to form the components required for a Turing machine.[18]

惠普实验室HP labs在莫特记忆电阻器上的研究表明，尽管它们可以是非易失性Volatile的，但是在相变Phase transition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Neuristor(一种生物学启发的模仿神经元行为的硬件)[17]。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Turing machine的所需元素。[18]

Neurogrid, built by Brains in Silicon at Stanford University,[19] is an example of hardware designed using neuromorphic engineering principles. The circuit board is composed of 16 custom-designed chips, referred to as NeuroCores. Each NeuroCore's analog circuitry is designed to emulate neural elements for 65536 neurons, maximizing energy efficiency. The emulated neurons are connected using digital circuitry designed to maximize spiking throughput.[20][21]

神经栅格Neurogrid[19]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(NeuroCores)。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。[20][21]

A research project with implications for neuromorphic engineering is the Human Brain Project that is attempting to simulate a complete human brain in a supercomputer using biological data. It is made up of a group of researchers in neuroscience, medicine, and computing.[22] Henry Markram, the project's co-director, has stated that the project proposes to establish a foundation to explore and understand the brain and its diseases, and to use that knowledge to build new computing technologies. The three primary goals of the project are to better understand how the pieces of the brain fit and work together, to understand how to objectively diagnose and treat brain diseases, and to use the understanding of the human brain to develop neuromorphic computers. That the simulation of a complete human brain will require a supercomputer a thousand times more powerful than today's encourages the current focus on neuromorphic computers.[23] $1.3 billion has been allocated to the project by The European Commission.[24]

人类大脑计划Human Brain Project对神经形态工程具有较大影响，其主要任务是尝试用生物数据在超级计算机中模拟完整的人脑。人类大脑计划由神经科学、医学和计算机科学背景的研究人员组成。[22]该项目的联合主管亨利•马克拉姆(Henry Markram)表示，人类大脑计划的目的是建立一个探索和了解脑科学和脑疾病知识的基础，并利用这些知识来构建更先进的计算机技术。这个项目的三个主要目标分别是: 更好地理解大脑的各个部分是如何相互配合协同工作的; 理解如何客观地诊断和治疗脑部疾病; 以及利用对人类大脑的理解来开发神经形态计算机。模拟一个完整的人类大脑需要一台比现在强大一千倍的超级计算机，这不断激发着对神经形态计算机领域的研究兴趣。[23]欧盟委员会已经向人类大脑计划拨款13亿美元。[24]

Other research with implications for neuromorphic engineering involves the BRAIN Initiative[25] and the TrueNorth chip from IBM.[26] Neuromorphic devices have also been demonstrated using nanocrystals, nanowires, and conducting polymers.[27]

其他与神经形态工程有关的研究还包括脑计划BRAIN initiative，[25]和IBM研发的TrueNorth芯片。[26]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。[27]

Intel unveiled its neuromorphic research chip, called “Loihi”, in October 2017. The chip uses an asynchronous spiking neural network (SNN) to implement adaptive self-modifying event-driven fine-grained parallel computations used to implement learning and inference with high efficiency.[28][29]

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Spiking neural network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。[28][29]

IMEC, a Belgium-based nanoelectronics research center, demonstrated the world's first self-learning neuromorphic chip. The brain-inspired chip, based on OxRAM technology, has the capability of self-learning and has been demonstrated to have the ability to compose music.[30] IMEC released the 30-second tune composed by the prototype. The chip was sequentially loaded with songs in the same time signature and style. The songs were old Belgian and French flute minuets, from which the chip learned the rules at play and then applied them.[31]

比利时的微电子研究中心IMEC研发了世界上首个自学习神经形态芯片。这种基于 OxRAM(filamentary-oxide-based resistive memory technology) 技术的大脑启发芯片具有自学习能力，并且已被证明具有创作音乐的能力。[30]IMEC发布了由芯片原型机谱写的30秒旋律。向芯片加载一系列特征、风格统一的歌曲（古代比利时和法国长笛小步舞曲），芯片从中学习相关规则并将其应用于创作。[31]

The Blue Brain Project, led by Henry Markram, aims to build biologically detailed digital reconstructions and simulations of the mouse brain. The Blue Brain Project has created in silico models of rodent brains, while attempting to replicate as many details about its biology as possible. The supercomputer-based simulations offer new perspectives on understanding the structure and functions of the brain.

由亨利·马克拉姆领导的蓝脑计划The Blue Brain Project旨在建立小鼠大脑生理学细节的数字重建和模拟。蓝脑计划已经建立了啮齿动物大脑的电子模型，同时进行着尽可能多地复制其生理学细节的尝试。基于超级计算机的模拟为理解大脑的结构和功能提供了新的视角。

The European Union funded a series of projects at the University of Heidelberg, which led to the development of BrainScaleS (brain-inspired multiscale computation in neuromorphic hybrid systems), a hybrid analog neuromorphic supercomputer located at Heidelberg University, Germany. It was developed as part of the Human Brain Project neuromorphic computing platform and is the complement to the SpiNNaker supercomputer (which is based on digital technology). The architecture used in BrainScaleS mimics biological neurons and their connections on a physical level; additionally, since the components are made of silicon, these model neurons operate on average 864 times (24 hours of real time is 100 seconds in the machine simulation) that of their biological counterparts.[32]

欧盟资助了海德堡大学一系列促进BrainScaleS(神经形态混合系统中受大脑启发的多尺度计算)发展的项目，这是一台位于德国海德堡大学的混合模拟神经形态Neuromorphic超级计算机。它是作为人类大脑计划中神经形态计算平台的一部分而开发的，是SpiNNaker超级计算机(基于数字技术)的补充。BrainScaleS中使用的体系架构模拟了生物神经元及其在物理层面上的连接；此外，由于这些组件是由硅制成的，这些模型神经元平均运行速度是生物神经元的864倍，这意味着在机器模拟中，24小时的实时时间仅为100秒。[32]

Neuromorphic sensors

神经形态传感器

The concept of neuromorphic systems can be extended to sensors (not just to computation). An example of this applied to detecting light is the retinomorphic sensor or, when employed in an array, the event camera.

神经形态系统的概念可以扩展到传感器(而不仅仅是计算单元)。一个用于检测光线的例子是类视网膜传感器Retinomorphic sensor，或者事件摄像机Event camera阵列。


Ethical considerations

伦理问题

While the interdisciplinary concept of neuromorphic engineering is relatively new, many of the same ethical considerations apply to neuromorphic systems as apply to human-like machines and artificial intelligence in general. However, the fact that neuromorphic systems are designed to mimic a human brain gives rise to unique ethical questions surrounding their usage.

虽然神经形态工程这个跨学科概念相对较新，但许多适用于类人机器Human-like machines和人工智能的伦理考虑大体上也适用于神经形态系统。另一方面，神经形态系统是为了模仿人类大脑而设计，这一事实引起了一些针对性的独特伦理问题。

However, the practical debate is that neuromorphic hardware as well as artificial "neural networks" are immensely simplified models of how the brain operates or processes information at a much lower complexity in terms of size and functional technology and a much more regular structure in terms of connectivity. Comparing neuromorphic chips to the brain is a very crude comparison similar to comparing a plane to a bird just because they both have wings and a tail. The fact is that neural cognitive systems are many orders of magnitude more energy- and compute-efficient than current state-of-the-art AI and neuromorphic engineering is an attempt to narrow this gap by inspiring from the brain's mechanism just like many engineering designs have bio-inspired features.

然而，这种争论的实际情况是，神经形态硬件和人工“神经网络”是对大脑运作或处理信息过程的极其简化的模型，在大小和功能技术方面的复杂性Complexity相比而言比较低，在连接性Connectivity方面也具有更加规则的结构。将神经形态芯片Neuromorphic chips与大脑进行比较是一种非常粗糙的比较，类似于仅仅因为飞机有翅膀和尾巴就将它与鸟进行比较。事实上，当前最先进的人工智能在能耗效率Energy-efficiency和计算效率方面距离人脑神经认知系统仍有较大差距，而神经形态工程只是一种通过从大脑机制中获得灵感来缩小这种差距的尝试，就像许多工程设计中都具有生物启发的特征Bio-inspired features一样。

Democratic concerns

公众担忧

Significant ethical limitations may be placed on neuromorphic engineering due to public perception.[33] Special Eurobarometer 382: Public Attitudes Towards Robots, a survey conducted by the European Commission, found that 60% of European Union citizens wanted a ban of robots in the care of children, the elderly, or the disabled. Furthermore, 34% were in favor of a ban on robots in education, 27% in healthcare, and 20% in leisure. The European Commission classifies these areas as notably “human.” The report cites increased public concern with robots that are able to mimic or replicate human functions. Neuromorphic engineering, by definition, is designed to replicate the function of the human brain.[34]

由于公众认知的相关忧虑，神经形态工程学可能会受到严重的伦理限制。[33]欧盟委员会进行的一项调查发现，60% 的欧盟公民希望禁止机器人参与照顾儿童、老人或残疾人的工作。此外，34% 的人支持禁止机器人用于教育，27% 的人支持禁止机器人用于医疗保健，20% 的人支持禁止机器人用于休闲。欧盟委员会将以上领域划入“人类”范畴。报告指出，公众越来越关注能够模仿或复制人类功能的机器人。神经形态工程，顾名思义，是为了复制人脑的功能而设计的。[34]

The democratic concerns surrounding neuromorphic engineering are likely to become even more profound in the future. The European Commission found that EU citizens between the ages of 15 and 24 are more likely to think of robots as human-like (as opposed to instrument-like) than EU citizens over the age of 55. When presented an image of a robot that had been defined as human-like, 75% of EU citizens aged 15–24 said it corresponded with the idea they had of robots while only 57% of EU citizens over the age of 55 responded the same way. The human-like nature of neuromorphic systems, therefore, could place them in the categories of robots many EU citizens would like to see banned in the future.[34]

围绕神经形态工程的公众担忧可能在未来变得更加深刻。欧盟委员会发现，相比于55岁以上的欧盟公民，15至24岁的欧盟公民更有可能认为机器人像人(而不是像仪器)。当看到一张“类人”机器人的图片时，年龄在15岁至24岁之间的欧盟公民中有75% 的人表示这符合他们对机器人的想法，而55岁以上的欧盟公民中只有57% 的人有同样的反应。因此，神经形态系统可能因为其类似人类的特性而被归入许多欧盟公民希望在未来禁止使用的机器人类别。[34]

Personhood

人格问题

As neuromorphic systems have become increasingly advanced, some scholars模板:Who have advocated for granting personhood rights to these systems. If the brain is what grants humans their personhood, to what extent does a neuromorphic system have to mimic the human brain to be granted personhood rights? Critics of technology development in the Human Brain Project, which aims to advance brain-inspired computing, have argued that advancement in neuromorphic computing could lead to machine consciousness or personhood.[35] If these systems are to be treated as people, critics argue, then many tasks humans perform using neuromorphic systems, including the act of termination of neuromorphic systems, may be morally impermissible as these acts would violate the autonomy of the neuromorphic systems.[36]

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Personhood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。[35]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。[36]


Dual use (military applications)

军民两用技术（军事应用）

The Joint Artificial Intelligence Center, a branch of the U.S. military, is a center dedicated to the procurement and implementation of AI software and neuromorphic hardware for combat use. Specific applications include smart headsets/goggles and robots. JAIC intends to rely heavily on neuromorphic technology to connect "every fighter every shooter" within a network of neuromorphic-enabled units.

联合人工智能中心The Joint Artificial Intelligence Center(JAIC),是美国军队的一个分支，专门从事采购和实施用于战斗的人工智能软件和神经形态硬件。具体应用包括智能耳机/护目镜和机器人。JAIC打算高度依赖神经形态技术，使用神经形态技术来连接神经形态单位网络中的“每个战士每个射手”。


Legal considerations

法律问题

Skeptics have argued that there is no way to apply the electronic personhood, the concept of personhood that would apply to neuromorphic technology, legally. In a letter signed by 285 experts in law, robotics, medicine, and ethics opposing a European Commission proposal to recognize “smart robots” as legal persons, the authors write, “A legal status for a robot can’t derive from the Natural Person model, since the robot would then hold human rights, such as the right to dignity, the right to its integrity, the right to remuneration or the right to citizenship, thus directly confronting the Human rights. This would be in contradiction with the Charter of Fundamental Rights of the European Union and the Convention for the Protection of Human Rights and Fundamental Freedoms.”[37]

质疑者者认为，在法律上没有办法应用能够适用于神经形态技术的电子人格。在一封由285名法律、机器人技术、医学和伦理学专家的联名信中，作者们反对欧盟委员会提出的承认“智能机器人”为法人的提议。他们写道，“机器人的法律地位无法从自然人Natural Person模型中推导出来，因为机器人将被赋予人权Human rights，如尊严权、完整权、报酬权或公民权，从而直接面临人权问题。这将有悖于《欧联基本权利宪章》和《欧洲保障人权和根本自由公约》”。[37]

Ownership and property rights

所有权及财产权问题

There is significant legal debate around property rights and artificial intelligence. In Acohs Pty Ltd v. Ucorp Pty Ltd, Justice Christopher Jessup of the Federal Court of Australia found that the source code for Material Safety Data Sheets could not be copyrighted as it was generated by a software interface rather than a human author.[38] The same question may apply to neuromorphic systems: if a neuromorphic system successfully mimics a human brain and produces a piece of original work, who, if anyone, should be able to claim ownership of the work?[39]

法律界围绕财产权和人工智能有着重大争论。在Acohs Pty有限公司诉Ucorp Pty有限公司一案中，澳大利亚联邦法院的克里斯托弗·杰瑟普法官发现，版权保护不适用于材料安全数据表的源代码Source code，因为它是由软件界面Software interface生成而非人类工作者生成的。[38]同样的问题可能也适用于神经形态系统: 如果一个神经形态系统成功地模仿了人类的大脑，并产生了一部原创作品，那么该如何确认这部作品的所有权归属？[39]


Neuromemristive systems

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.[40] For example, a neuromemristive system may replace the details of a cortical microcircuit's behavior with an abstract neural network model.[41]

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Memristors实现神经可塑性Neuroplasticity。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。[40]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皮层Cortical微电路的行为细节。[41]

There exist several neuron inspired threshold logic functions[6] implemented with memristors that have applications in high level pattern recognition applications. Some of the applications reported recently include speech recognition,[42] face recognition[43] and object recognition.[44] They also find applications in replacing conventional digital logic gates.[45][46]

受神经元启发、使用记忆电阻器实现的阈值逻辑函数[6]在高级模式识别Pattern recognition中有着广泛的应用，最近报道中其应用包括语音识别Speech recognition[42]、人脸识别Face recognition[43]和物体识别Object recognition[44]。阈值逻辑函数还可以用来取代传统的数字逻辑门。[45][46]

For ideal passive memristive circuits there is an exact equation (Caravelli-Traversa-Di Ventra equation) for the internal memory of the circuit:[47]

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:[47]

[math]\displaystyle{ \frac{d}{dt} \vec{W} = \alpha \vec{W}-\frac{1}{\beta} (I+\xi \Omega W)^{-1} \Omega \vec S }[/math]

as a function of the properties of the physical memristive network and the external sources. In the equation above, [math]\displaystyle{ \alpha }[/math] is the "forgetting" time scale constant, [math]\displaystyle{ \xi=r-1 }[/math] and [math]\displaystyle{ 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]\displaystyle{ \vec S }[/math] is the vector of the sources of the circuit and [math]\displaystyle{ \Omega }[/math] is a projector on the fundamental loops of the circuit. The constant [math]\displaystyle{ \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]\displaystyle{ W=\operatorname{diag}(\vec W) }[/math] and [math]\displaystyle{ \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.

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]\displaystyle{ \alpha }[/math]是“遗忘”时间尺度常数，[math]\displaystyle{ \xi=r-1 }[/math]，[math]\displaystyle{ 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]\displaystyle{ \vec S }[/math]是电路源的矢量，[math]\displaystyle{ \Omega }[/math]是电路基本环路的投影。常数[math]\displaystyle{ \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]\displaystyle{ W=\operatorname{diag}(\vec W) }[/math]和[math]\displaystyle{ \vec W }[/math] 分别是记忆电阻器的内阻，值在0到1之间。因此，这个等式需要在内存值上添加额外约束以保证可靠性。


See also

相关词条

模板:Portal bar

References

模板:Reflist

External links

模板:Commons category


  • Telluride Neuromorphic Engineering Workshop
  • CapoCaccia Cognitive Neuromorphic Engineering Workshop
  • Institute of Neuromorphic Engineering
  • INE news site.
  • Frontiers in Neuromorphic Engineering Journal
  • Computation and Neural Systems department at the California Institute of Technology.
  • Human Brain Project official site
  • Building a Silicon Brain: Computer chips based on biological neurons may help simulate larger and more-complex brain models. May 1, 2019. SANDEEP RAVINDRAN

外部链接

  • 碲化物神经形态工程工作室
  • CapoCaccia认知神经形态工程工作室
  • 神经形态工程研究所
  • INE新闻站点。
  • 《神经形态工程学前沿》
  • 加州理工学院计算与神经系统系。
  • 人脑项目官方网站
  • 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.

模板:Differentiable computing 模板:Authority control

Category:Electrical engineering Category:Neuroscience

Category:Artificial intelligence Category:Robotics

类别: 电气工程类别: 神经科学 * 类别: 人工智能类别: 机器人


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