基于忆阻的递归神经网络的动力学分析
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摘要
在传统的计算机架构中,信息存储与处理是分离的,其信息存储与处理的传递通道经由总线来连接,这难以突破“冯·诺依曼瓶颈”,严重制约了高性能计算的发展.而人脑由于独有的突触可塑性,对于信息存储与处理是合一的,没有明显的界限.因此,研制兼具信息存储与处理功能的新型电子存储器件,用以支持信息存储与处理融合的计算体系架构,是下一代超高性能计算的极具潜力的可行发展方向.忆阻作为一种新型的存储器件,其特性极其类似于人脑突触,有望实现类似于人脑突触的信息存储与处理的一体化功能,高效地融合存储与处理,为构建突破“冯·诺依曼瓶颈”的新型计算机体系提供一种全新的设计架构.
具有混杂互补金属氧化物半导体阵列结构的忆阻神经系统兼具阻变、高速、低功耗、高集成度等特性,这种新型电子信息系统是一种能够模仿神经功能、可自适应调节的微电子电路,在进行数据存储的同时实现逻辑运算功能,达到信息存储与处理的融合,为构建新型计算机架构奠定器件基础.然而,基于忆阻的新型神经系统在系统理论方面还有很多关键瓶颈问题亟待解决.探究其动态行为演化机制,有助于有效调控类神经元的阈值激发功能,为基于忆阻的信息存储与处理提供基础理论支撑,在动态信息的类脑存储与运算等方面孕育出许多重大的创新机遇.
本文主要研究基于忆阻的神经动力学系统.针对几类基于忆阻的递归神经网络,利用不连续动力系统理论、线性矩阵不等式、数学分析技巧,结合忆阻电路特性,讨论其动态演化行为学,得到了一些初步的动力学理论判据.本文一个有趣的的理论结果是:忆阻系统能够通过微分包含和集值映像理论得到巧妙地分析.本文的主要工作如下:
探究了基于忆阻的递归神经网络的动力学基础理论.建立了一类基于忆阻的Lotka-Volterra神经网络和多种反馈函数刺激下基于忆阻的神经网络,在Filippov解的数学框架下,得到了基于忆阻的Lotka-Volterra神经网络的吸引性、完全稳定性和多种反馈函数刺激下基于忆阻的神经网络的Lagrange稳定性,获得的结果也许可应用于忆阻的神经联想记忆.这些理论分析可刻画忆阻装置的基本电气性能,为应用提供便利.
讨论了基于忆阻的递归神经网络的控制设计策略.通过构建基于忆阻的多模型神经网络,分析了其指数镇定和最优控制.获得的判据可应用于忆阻系统的闭环控制,改进和拓展了现有的一些相关结果.
探讨了基于忆阻的递归神经网络的动力学应用.结合一类基于忆阻的线性阈值神经网络,通过网络的局部抑制和局部不变集理论,分析了其模式记忆行为.提出的结果拓展了传统的递归神经网络的模式记忆理论.
本文针对忆阻神经动力学系统的初步研究有助于探寻这种新型电子信息系统的纳米尺度电荷输运机理,进一步明确基于忆阻的信息存储与计算机理,为研制信息存储与处理的一体化的高性能电子存储系统奠定基石.
Within the architecture of traditional computer, information memory and processingare separate. The delivery channels of information memory and processing are connectedvia bus, which will be hard to break “Von Neumann challenge”, severely restricting the ad-vancement of high performance computing. However, the combination is that of informationmemory and processing for human brain, due to the synaptic plasticity. Therefore, devel-oping new memory devices with storage and processing, in order to support the computingarchitecture of information storage and fusion processor, may be potential future directionsfor the next generation ultra-high-performance computing. As a new memory device, thefeatures of memristor most closely resemble cerebral synapses. It is believed that memristormay achieve integrated function of information memory and processing, similar to cerebralsynapses, giving a new design scheme for new-type computer architecture that can breakthrough the “Von Neumann challenge”.
Memristive neural systems made of hybrid complementary metal oxide semiconduc-tor array structure have demonstrated the superior capabilities in the resistance changingmemory, super-speed, low-power dissipation, high integration density, etc, which can forma basis for the realization of powerful brain-like “neural” computer. This neuromorphicelectronic system can enable data storage and to achieve logic operation, which may makegreat breakthrough in the respect of blending of information memory and processing, andlay a good foundation for structuring new-type computer architecture. Nevertheless, somesignificant problems in nonlinear system theory based on memristive neural systems remainto be resolved. Exploring the evolving dynamic mechanism of memristive neural systemswill contribute to regulate the threshold stimulating function of neurons, which can providebasic theory support to information memory and processing based on memristor, and breedlots of major opportunities for storage and computation on dynamic information.
The dissertation focuses on memristive neurodynamic systems. Several classes ofmemristor-based recurrent neural networks are formulated and studied. Some preliminarytheoretic principles on dynamic behaviors of these networks are derived. The analysis inthe dissertation employs results from the theory of discontinuous dynamical systems, linearmatrix inequalities and mathematical analysis techniques. An interesting theoretical resultof this research work is that the memristive systems can be cleverly analyzed according tothe theories of differential inclusions and set-valued maps. The main contents are sketchedout as follows:
The basic theories of dynamics on memristor-based recurrent neural networks are dis-cussed. By means of structuring a class of memristor-based Lotka-Volterra neural networksand a class of memristor-based neural networks with various feedback functions, withinmathematical framework of the Filippov solution, the attractivity, complete stability ofmemristor-based Lotka-Volterra neural networks, and the Lagrange stability of memristor-based neural networks with various feedback functions are analyzed, respectively. Theseresults can be applied to the memristive dynamic memories. The theoretical analysis cancharacterize the fundamental electrical properties of memristor devices and provide conve-nience for applications.
The control design of memristor-based recurrent neural networks is studied. By intro-ducing a class of memristor-based multi-model neural networks, the exponential stabiliza-tion and optimal control are presented. The obtained results can be applied to the closed-loopcontrol of memristive systems. These analytical results were the improvement and extensionof the existing results in the literature.
The application of dynamics on memristor-based recurrent neural networks is inves-tigated. Combining with a class of memristor-based linear threshold neural networks, thepattern memory analysis is established by using local inhibition and local invariant sets. Thederived results extend some previous works on pattern memory analysis of conventional re-current neural networks.
The study on dynamic analysis of memristive neurodynamic systems will be helpfulin approaching nanoscale charge transport mechanisms of this new electronic informationsystem, and making more explicit mechanisms on information storage and computing basedon memristor. Such a study also sets the base and tone for the future development of highperformance electronic storage systems that can realize integration of information memoryand processing.
具有混杂互补金属氧化物半导体阵列结构的忆阻神经系统兼具阻变、高速、低功耗、高集成度等特性,这种新型电子信息系统是一种能够模仿神经功能、可自适应调节的微电子电路,在进行数据存储的同时实现逻辑运算功能,达到信息存储与处理的融合,为构建新型计算机架构奠定器件基础.然而,基于忆阻的新型神经系统在系统理论方面还有很多关键瓶颈问题亟待解决.探究其动态行为演化机制,有助于有效调控类神经元的阈值激发功能,为基于忆阻的信息存储与处理提供基础理论支撑,在动态信息的类脑存储与运算等方面孕育出许多重大的创新机遇.
本文主要研究基于忆阻的神经动力学系统.针对几类基于忆阻的递归神经网络,利用不连续动力系统理论、线性矩阵不等式、数学分析技巧,结合忆阻电路特性,讨论其动态演化行为学,得到了一些初步的动力学理论判据.本文一个有趣的的理论结果是:忆阻系统能够通过微分包含和集值映像理论得到巧妙地分析.本文的主要工作如下:
探究了基于忆阻的递归神经网络的动力学基础理论.建立了一类基于忆阻的Lotka-Volterra神经网络和多种反馈函数刺激下基于忆阻的神经网络,在Filippov解的数学框架下,得到了基于忆阻的Lotka-Volterra神经网络的吸引性、完全稳定性和多种反馈函数刺激下基于忆阻的神经网络的Lagrange稳定性,获得的结果也许可应用于忆阻的神经联想记忆.这些理论分析可刻画忆阻装置的基本电气性能,为应用提供便利.
讨论了基于忆阻的递归神经网络的控制设计策略.通过构建基于忆阻的多模型神经网络,分析了其指数镇定和最优控制.获得的判据可应用于忆阻系统的闭环控制,改进和拓展了现有的一些相关结果.
探讨了基于忆阻的递归神经网络的动力学应用.结合一类基于忆阻的线性阈值神经网络,通过网络的局部抑制和局部不变集理论,分析了其模式记忆行为.提出的结果拓展了传统的递归神经网络的模式记忆理论.
本文针对忆阻神经动力学系统的初步研究有助于探寻这种新型电子信息系统的纳米尺度电荷输运机理,进一步明确基于忆阻的信息存储与计算机理,为研制信息存储与处理的一体化的高性能电子存储系统奠定基石.
Within the architecture of traditional computer, information memory and processingare separate. The delivery channels of information memory and processing are connectedvia bus, which will be hard to break “Von Neumann challenge”, severely restricting the ad-vancement of high performance computing. However, the combination is that of informationmemory and processing for human brain, due to the synaptic plasticity. Therefore, devel-oping new memory devices with storage and processing, in order to support the computingarchitecture of information storage and fusion processor, may be potential future directionsfor the next generation ultra-high-performance computing. As a new memory device, thefeatures of memristor most closely resemble cerebral synapses. It is believed that memristormay achieve integrated function of information memory and processing, similar to cerebralsynapses, giving a new design scheme for new-type computer architecture that can breakthrough the “Von Neumann challenge”.
Memristive neural systems made of hybrid complementary metal oxide semiconduc-tor array structure have demonstrated the superior capabilities in the resistance changingmemory, super-speed, low-power dissipation, high integration density, etc, which can forma basis for the realization of powerful brain-like “neural” computer. This neuromorphicelectronic system can enable data storage and to achieve logic operation, which may makegreat breakthrough in the respect of blending of information memory and processing, andlay a good foundation for structuring new-type computer architecture. Nevertheless, somesignificant problems in nonlinear system theory based on memristive neural systems remainto be resolved. Exploring the evolving dynamic mechanism of memristive neural systemswill contribute to regulate the threshold stimulating function of neurons, which can providebasic theory support to information memory and processing based on memristor, and breedlots of major opportunities for storage and computation on dynamic information.
The dissertation focuses on memristive neurodynamic systems. Several classes ofmemristor-based recurrent neural networks are formulated and studied. Some preliminarytheoretic principles on dynamic behaviors of these networks are derived. The analysis inthe dissertation employs results from the theory of discontinuous dynamical systems, linearmatrix inequalities and mathematical analysis techniques. An interesting theoretical resultof this research work is that the memristive systems can be cleverly analyzed according tothe theories of differential inclusions and set-valued maps. The main contents are sketchedout as follows:
The basic theories of dynamics on memristor-based recurrent neural networks are dis-cussed. By means of structuring a class of memristor-based Lotka-Volterra neural networksand a class of memristor-based neural networks with various feedback functions, withinmathematical framework of the Filippov solution, the attractivity, complete stability ofmemristor-based Lotka-Volterra neural networks, and the Lagrange stability of memristor-based neural networks with various feedback functions are analyzed, respectively. Theseresults can be applied to the memristive dynamic memories. The theoretical analysis cancharacterize the fundamental electrical properties of memristor devices and provide conve-nience for applications.
The control design of memristor-based recurrent neural networks is studied. By intro-ducing a class of memristor-based multi-model neural networks, the exponential stabiliza-tion and optimal control are presented. The obtained results can be applied to the closed-loopcontrol of memristive systems. These analytical results were the improvement and extensionof the existing results in the literature.
The application of dynamics on memristor-based recurrent neural networks is inves-tigated. Combining with a class of memristor-based linear threshold neural networks, thepattern memory analysis is established by using local inhibition and local invariant sets. Thederived results extend some previous works on pattern memory analysis of conventional re-current neural networks.
The study on dynamic analysis of memristive neurodynamic systems will be helpfulin approaching nanoscale charge transport mechanisms of this new electronic informationsystem, and making more explicit mechanisms on information storage and computing basedon memristor. Such a study also sets the base and tone for the future development of highperformance electronic storage systems that can realize integration of information memoryand processing.
引文
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