( A, B )---3*30*2---( 1, 0 )( 0, 1 )
让网络的输入只有3个节点,AB训练集各由5张二值化的图片组成,让A中有7个1,B中全是0,让A的5行1的数量为1,1,1,2,2;让A的3列1的数量为2,2,3.排列组合A,比较迭代次数的顺序。
|   差值结构  |   A-B  |   迭代次数  |   行  |   列  | |||||||||||
|   d  |   1  |   1  |   0  |   6*3*2*1*4-0*0*0*0*0  |   3124.859  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||
|   0  |   1  |   1  |   6*3*2*1*4-0*0*0*0*0  |   3124.859  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   1  |   0  |   6*3*2*1*4-0*0*0*0*0  |   3124.859  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   0  |   1  |   6*3*2*1*4-0*0*0*0*0  |   3124.859  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   0  |   0  |   6*3*2*1*4-0*0*0*0*0  |   3124.859  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||||||||
|   c  |   1  |   1  |   0  |   6*4*3*1*4-0*0*0*0*0  |   7107.332  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||
|   1  |   0  |   0  |   6*4*3*1*4-0*0*0*0*0  |   7107.332  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   1  |   1  |   6*4*3*1*4-0*0*0*0*0  |   7107.332  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   0  |   1  |   6*4*3*1*4-0*0*0*0*0  |   7107.332  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   0  |   0  |   6*4*3*1*4-0*0*0*0*0  |   7107.332  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||||||||
|   b  |   1  |   1  |   0  |   6*6*1*1*2-0*0*0*0*0  |   9197.935  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||
|   1  |   1  |   0  |   6*6*1*1*2-0*0*0*0*0  |   9197.935  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   0  |   1  |   6*6*1*1*2-0*0*0*0*0  |   9197.935  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   0  |   1  |   6*6*1*1*2-0*0*0*0*0  |   9197.935  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   1  |   0  |   6*6*1*1*2-0*0*0*0*0  |   9197.935  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||||||||
|   a  |   1  |   0  |   0  |   4*4*4*3*3-0*0*0*0*0  |   26733.89  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||
|   1  |   0  |   0  |   4*4*4*3*3-0*0*0*0*0  |   26733.89  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   0  |   0  |   4*4*4*3*3-0*0*0*0*0  |   26733.89  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   1  |   1  |   4*4*4*3*3-0*0*0*0*0  |   26733.89  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   0  |   1  |   1  |   4*4*4*3*3-0*0*0*0*0  |   26733.89  |   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | |||
|   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||||||||
|   1  |   1  |   1  |   2  |   2  |   2  |   2  |   3  | ||||||||
收敛误差7e-4,每组收敛199次。统计平均值。
因为符合上述条件的差值结构的行和列可以自由变换,按照对称性只有4个不同的结构。
迭代次数的大小顺序是a>b>c>d.
这4个结构的平均列都相同,所以这4个结构的势能相同,
![]()
但他们的迭代次数并不相同。这意味着还有一个变量导致了总能量的差异。
现在让a保持行分布1,1,1,2,2;列分布2,2,3不变,让a变化1步
|   a  |   a  |   a  |   a  |   a  |   b  | |||||||||||||||||
|   1  |   0  |   0  |   0  |   1  |   1  |   0  |   1  |   1  |   1  |   0  |   1  |   1  |   1  |   0  |   1  |   1  |   0  | |||||
|   1  |   0  |   0  |   1  |   0  |   0  |   0  |   1  |   1  |   1  |   0  |   1  |   1  |   1  |   0  |   1  |   1  |   0  | |||||
|   1  |   0  |   0  |   →  |   1  |   0  |   0  |   →  |   1  |   0  |   0  |   →  |   0  |   1  |   0  |   →  |   0  |   0  |   1  |   →  |   0  |   0  |   1  | 
|   0  |   1  |   1  |   1  |   0  |   0  |   1  |   0  |   0  |   0  |   1  |   0  |   0  |   0  |   1  |   0  |   0  |   1  | |||||
|   0  |   1  |   1  |   0  |   1  |   1  |   1  |   0  |   0  |   0  |   1  |   0  |   0  |   0  |   1  |   0  |   1  |   0  | |||||
|   a  |   c  |   c  |   c  |   c  |   c  | |||||||||||||||||
|   1  |   0  |   0  |   1  |   0  |   0  |   1  |   0  |   0  |   0  |   1  |   1  |   1  |   1  |   0  |   1  |   1  |   0  | |||||
|   1  |   0  |   0  |   1  |   0  |   0  |   1  |   0  |   0  |   1  |   0  |   1  |   0  |   1  |   1  |   1  |   0  |   0  | |||||
|   1  |   0  |   0  |   →  |   1  |   0  |   1  |   →  |   0  |   1  |   0  |   →  |   1  |   0  |   0  |   →  |   1  |   0  |   0  |   →  |   0  |   1  |   1  | 
|   0  |   1  |   1  |   0  |   1  |   0  |   1  |   0  |   1  |   1  |   0  |   0  |   1  |   0  |   0  |   0  |   0  |   1  | |||||
|   0  |   1  |   1  |   0  |   1  |   1  |   0  |   1  |   1  |   0  |   1  |   0  |   0  |   0  |   1  |   1  |   0  |   0  | 
由于对称性a只有两种可能的变化,一种横着走一步,变成b,或者竖着走一步变成c。但a在一步内不可能变成d。
但是b或c都可以1步变成d
|   c  |   d  | |||||||||
|   1  |   1  |   0  |   1  |   1  |   0  |   1  |   1  |   0  | ||
|   1  |   0  |   0  |   0  |   1  |   1  |   0  |   1  |   1  | ||
|   0  |   1  |   1  |   →  |   1  |   0  |   0  |   →  |   0  |   1  |   0  | 
|   0  |   0  |   1  |   0  |   0  |   1  |   0  |   0  |   1  | ||
|   1  |   0  |   0  |   1  |   0  |   0  |   1  |   0  |   0  | ||
|   b  | d |   d  | ||||||||
|   1  |   1  |   0  |   1  |   1  |   0  |   1  |   1  |   0  | ||
|   1  |   1  |   0  |   1  |   0  |   0  |   0  |   1  |   1  | ||
|   0  |   0  |   1  |   →  |   0  |   1  |   1  |   →  |   0  |   0  |   1  | 
|   0  |   0  |   1  |   0  |   0  |   1  |   0  |   1  |   0  | ||
|   0  |   1  |   0  |   0  |   1  |   0  |   1  |   0  |   0  | 
也就是a距离d至少有两步。比如假设横向移动1步的能量小于纵向移动一步的能量,则由a变化到b,c,d的能量排序b<c<d.

所以得到总能量

迭代次数与结构的总能量成反比,总能量越低成键越稳定,使键断裂的难度越大,迭代次数越大。


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