二維細胞類神經網路之一般模版: 全域花樣

Abstract

此篇論文是研究如何將3×3的花樣擴展為4×4的花樣，進而利用置換矩陣去研究花樣生成的問題。從禁止集合的觀點來看，如果c_k是3×3中不允許的花樣，則可以找到4×4中不允許的花樣是收集c_k分別落在4×4花樣中第一、二、三及第四像限位置的所有4×4的花樣，我們也可找到其置換矩陣。因此，在二維細胞類神經網路之一般模版中，我們知道每一區可允許的局部花樣，且利用置換矩陣的遞迴公式，可找出全域的花樣。此外，可採用連結算子去估計空間熵的下界。

In this paper, we investigate how to extend 3×3 patterns to 4×4 patterns and then we can use transition matrices created to study pattern generation problems. From the viewpoint of forbidden sets, if c_k is a forbidden pattern in Sigma 3×3, then we can find the forbidden set in Sigma 4×4 is that collect all 4×4 patterns which c_k located in the first, second, third, and the fourth quadrant of 4×4 patterns respectively, then we also can find the transition matrix. Therefore, in two-dimensional CNN with general template, we have knew the admissible local patterns, then we can find global patterns by the recursive formula of transition matrix, Furthermore, we can use connecting operators to estimate a lower bound of spatial entropy.