細胞類神經網路:缺陷花樣與穩定性

Abstract

在這篇論文中，探討的是一維細胞類神經網路在其輸出函數是片段線性輸出函數，且此函數在線性區域以外的斜率 ，我們在最鄰近的細胞之間採用一組對稱的耦合，用兩個參數來描述細胞本身與最鄰近細胞間各自的權數。在這些條件下我們研究存在穩定缺陷平衡的花樣(參閱定義1.1和定義1.2)。特別地，我們給予一個無窮維觀點的Gerschgorin 定理並且導出一個 -extendability的概念來決定兩個局部花樣是否可以接合在一起。使用這些工具方法，我們給定一個在 空間的區域，其相對應的缺陷花樣擁有非零的空間熵而其相關聯的馬賽克花樣的空間熵卻為零。更有甚者，在那些區域所產生的花樣並不是有限型式的子替換。

Of concern is one-dimensional Cellular Neural Networks (CNNs) with a piecewise-linear output function for which the slope of the output outside linear zone is . We impose a symmetric coupling between the nearest neighbors. Two parameters and are used to describe the weights between the cell with itself and its nearest neighbors, respectively. We study patterns that exist as stable defect equilibrium (see Definition 1.1 and 1.2). In particular, we given an infinite-dimensional version of Gerschgorin’s Theorem and derive a concept of -extendability to determine whether two local-defect patterns can be glued together. Using such tools, we give a region in -space for which the corresponding defect patterns have non-zero spatial entropy. Moreover, the patterns generated in those regions are not subshift of finite type.