ABSOLUTE STABILITY OF GLOBAL PATTERN-FORMATION AND PARALLEL MEMORY STORAGE BY COMPETITIVE NEURAL NETWORKS
ABSOLUTE STABILITY OF GLOBAL PATTERN-FORMATION AND PARALLEL MEMORY STORAGE BY COMPETITIVE NEURAL NETWORKS
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DOI：
10.1109/tsmc.1983.6313075
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发表时间：
1983-01-01
期刊：
影响因子：
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通讯作者：
GROSSBERG, S
中科院分区：
文献类型：
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作者：
COHEN, MA;GROSSBERG, S
考虑了通过竞争性蜂窝网络转换和存储输入模式的过程。这一过程发生在不同的学科中，如神经网络对视觉或语言模式的短期存储，发育生物学中由于激发形态发生梯度而形成的模式，在大分子进化过程中选择行为的控制，以及稳定的上下文敏感并行处理器的设计。除了能够响应任意输入模式和初始数据而接近可能无穷多个平衡点中的一个的系统之外，人们还在这些对象中发现了各种各样的其他行为，特别是行波、驻波、共振和混沌。因此，什么一般动力学约束导致全局接近平衡而不是大振幅波的问题是相当有兴趣的。用另一种术语来说，这是一个全球格局是否形成的问题。一个相关的问题是，当系统参数由于自组织(发展、学习)以不可预测的方式缓慢变化时，全局模式形成属性是否持续。这是全球格局形成的绝对稳定性问题。结果表明，许多具有绝对稳定性的模型系统可以写成形式(1)i=1，2，…，n，其中矩阵C=‖CIK‖是对称的，并且系统作为一个整体是竞争的。在这种情况下，本系统定义了一个全局李雅普诺夫函数。然后利用LaSalle不变性原理、多复变理论和Sard定理研究具有无限但完全不连通的平衡点集的系统的绝对稳定性。矩阵C的对称性很重要，因为存在形式(1)的竞争系统，其中C任意接近对称矩阵，但几乎所有轨迹都持续振荡，就像在投票悖论中一样。在不破坏对称性的情况下，减慢竞争反馈的速度，就像在系统中一样，也能使持续的振荡发生。因此，我们的结果表明，快速对称竞争反馈的使用是保证全局方向图形成的绝对稳定性的稳健设计约束。
The process whereby input patterns are transformed and stored by competitive cellular networks is considered. This process arises in such diverse subjects as the short-term storage of visual or language patterns by neural networks, pattern formation due to the firing of morphogenetic gradients in developmental biology, control of choice behavior during macromolecular evolution, and the design of stable context-sensitive parallel processors. In addition to systems capable of approaching one of perhaps infinitely many equilibrium points in response to arbitrary input patterns and initial data, one finds in these subjects a wide variety of other behaviors, notably traveling waves, standing waves, resonance, and chaos. The question of what general dynamical constraints cause global approach to equilibria rather than large amplitude waves is therefore of considerable interest. In another terminology, this is the question of whether global pattern formation occurs. A related question is whether the global pattern formation property persists when system parameters slowly change in an unpredictable fashion due to self-organization (development, learning). This is the question of absolute stability of global pattern formation. It is shown that many model systems which exhibit the absolute stability property can be written in the form(1) i = 1, 2, …, n, where the matrix C = ‖cik‖ is symmetric and the system as a whole is competitive. Under these circumstances, this system defines a global Liapunov function. The absolute stability of systems with infinite but totally disconnected sets of equilibrium points can then be studied using the LaSalle invariance principle, the theory of several complex variables, and Sard's theorem. The symmetry of matrix C is important since competitive systems of the form (1) exist wherein C is arbitrarily close to a symmetric matrix but almost all trajectories persistently oscillate, as in the voting paradox. Slowing down the competitive feedback without violating symmetry, as in the systemsalso enables sustained oscillations to occur. Our results thus show that the use of fast symmetric competitive feedback is a robust design constraint for guaranteeing absolute stability of global pattern formation.