Correlation Between Eigenvalue Spectra and Dynamics of Neural Networks
Correlation Between Eigenvalue Spectra and Dynamics of Neural Networks
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DOI：
10.1162/neco.2009.12-07-671
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发表时间：
2009-10-01
影响因子：
2.9
通讯作者：
Zhao, Hong
中科院分区：
文献类型：
--
作者：
Zhou, Qingguo;Jin, Tao;Zhao, Hong
这封信提出了突触矩阵的特征值谱与具有联想记忆的不对称神经网络的动态特性之间的相关性的研究。对于这种类型的神经网络，人们发现本质上有两个不同的动态阶段：混沌阶段，几乎所有轨迹都会收敛到单个混沌吸引子；记忆阶段，几乎所有轨迹都被吸引到充当记忆的定点吸引子。我们发现，如果一个神经网络是在混沌阶段设计的，那么它的突触矩阵的特征值谱就像一个随机矩阵（即所有特征值均匀分布在复杂计划中的一个圆内），而如果它是在记忆阶段设计的，那么特征值谱将分为两部分：一部分对应于随机背景，另一部分对应于记忆吸引子的数量。这封信讨论了这些现象的机制。
This letter presents a study of the correlation between the eigenvalue spectra of synaptic matrices and the dynamical properties of asymmetric neural networks with associative memories. For this type of neural network, it was found that there are essentially two different dynamical phases: the chaos phase, with almost all trajectories converging to a single chaotic attractor, and the memory phase, with almost all trajectories being attracted toward fixed-point attractors acting as memories. We found that if a neural network is designed in the chaos phase, the eigenvalue spectrum of its synaptic matrix behaves like that of a random matrix (i.e., all eigenvalues lie uniformly distributed within a circle in the complex plan), and if it is designed in the memory phase, the eigenvalue spectrum will split into two parts: one part corresponds to a random background, the other part equal in number to the memory attractors. The mechanism for these phenomena is discussed in this letter.