在前面的陆续实验中已经将二分类minst0，1到二分类minst0，9这9个实验都做完了，并得到了各自网络的迭代次数与准确率公式，可以近似的估算预期准确率的网络训练时间。实验的具体过程以minst0，9为例如下
实验用minst数据集，将28*28的图片缩小到9*9，网络用一个3*3的卷积核，网络结构是81*49*30*2，画成图
这个网络由两部分组成，左右两边分别向1,0和0,1收敛，左边输入minst的0，右边输入minst的9，让左右两个网络的权重共享，由前面的实验表明这种效果相当于将两个弹簧并联,组成一个振子力学系统。
| 具体进样顺序 |
|||
| δ=0.5 |
|||
| 初始化权重 |
|||
| 迭代次数 |
|||
| minst 0-1 |
1 |
判断是否达到收敛 |
|
| minst 9-1 |
2 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| minst 0-2 |
3 |
判断是否达到收敛 |
|
| minst 9-2 |
4 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| …… |
|||
| minst 0-4999 |
9997 |
判断是否达到收敛 |
|
| minst 9-4999 |
9998 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| …… |
|||
| 如果4999图片内没有达到收敛标准再次从头循环 |
|||
| minst 0-1 |
9999 |
判断是否达到收敛 |
|
| minst 9-1 |
10000 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| …… |
|||
| 每当网路达到收敛标准记录迭代次数和对应的准确率测试结果 |
|||
| 将这一过程重复199次 |
|||
| δ=0.4 |
|||
| … |
|||
| δ=2e-7 |
|||
收敛条件是
if (Math.abs(f2[0]-y[0])< δ && Math.abs(f2[1]-y[1])< δ )
这个网络简写成
S（minst0）81-（con3*3）49-30-2-（1,0）
S（minst9）81-（con3*3）49-30-2-（0,1）
w=w，w1=w1,w2=w2
进一步简写成
d2（minst0,9）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)
经实验表明网络的迭代次数n和准确率都可以用
这两个公式近似。
迭代次数的表格是
| 01 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
09 |
|
| δ |
迭代次数n |
迭代次数n |
迭代次数n |
迭代次数n |
迭代次数n |
迭代次数n |
迭代次数n |
迭代次数n |
迭代次数n |
| 0.1 |
2081.131 |
2785.725 |
2567.6482 |
2352.869 |
3508.41206 |
2763.37186 |
2232.146 |
2617.372 |
2362.905 |
| 1.00E-02 |
2850.236 |
3620.905 |
3501.4322 |
3239.744 |
4482.321608 |
3516.39698 |
3104.673 |
3487.045 |
3377.824 |
| 1.00E-03 |
4126.91 |
4846.435 |
4664.5226 |
4525.779 |
6103.939698 |
4851.05528 |
4367.447 |
4888.638 |
4638.894 |
| 1.00E-04 |
5887.709 |
7709.22 |
7099.9296 |
6481.905 |
8919.698492 |
7646.13065 |
6468.623 |
6770.578 |
7127.503 |
| 9*1e-5 |
5996.663 |
7951.16 |
7262.7085 |
6723.286 |
9349.020101 |
7773.49749 |
6437.633 |
7345.497 |
7156.286 |
| 8*1e-5 |
6169.337 |
8182.51 |
7505.9246 |
6901.276 |
9539.442211 |
7928.66834 |
6564.357 |
7308.02 |
7367.859 |
| 7*1e-5 |
6184.608 |
8193.28 |
7687.3618 |
6983.593 |
10203.43216 |
8338.36683 |
6779.578 |
7442.362 |
7518.492 |
| 6*1e-5 |
6469.729 |
8780.59 |
8094.2965 |
7224.774 |
9851.552764 |
8790.82412 |
6887.774 |
7950.407 |
7833.106 |
| 5*1e-5 |
6686.593 |
9227.095 |
8405.3869 |
7523.724 |
10868.83417 |
8774.35176 |
7299.528 |
7781.106 |
8203.98 |
| 4*1e-5 |
7160.337 |
9473.415 |
8815.392 |
7910.116 |
11182.1005 |
9638.64322 |
7553.477 |
8625.352 |
8463.402 |
| 3*1e-5 |
7711.472 |
10478 |
9679.4221 |
8599.352 |
12931.17085 |
10600.9447 |
8293.955 |
9775.462 |
9201.839 |
| 2*1e-5 |
8744.005 |
12060.84 |
10461.668 |
9137.015 |
14625.32161 |
11411.0804 |
8723.643 |
11628.49 |
10848.2 |
| 1.00E-05 |
9885.658 |
19757.36 |
12683.543 |
11235.33 |
20225.77387 |
14872.995 |
10555.44 |
14918.06 |
13375.71 |
| 9*1e-6 |
9949.095 |
22245.54 |
13059.99 |
11316.15 |
21326.76884 |
15159.2814 |
10476.27 |
14988.04 |
13466.41 |
| 8*1e-6 |
10597.78 |
22214.93 |
13171.085 |
11563.64 |
23468.94472 |
17935.0302 |
10925.47 |
16597.2 |
14629.72 |
| 7*1e-6 |
10781.61 |
28045.61 |
13862.523 |
12665.93 |
24229.21608 |
18620.4975 |
11219.57 |
17736.16 |
14828.54 |
| 6*1e-6 |
11409.87 |
28410.34 |
15417.608 |
13010.63 |
27358.97487 |
19321.8744 |
11748.35 |
20981.81 |
15859.35 |
| 5*1e-6 |
11777.72 |
33681.76 |
15919.558 |
13712.61 |
31394.18593 |
21230.9698 |
12474.75 |
21156.49 |
18927.24 |
| 4*1e-6 |
12539.73 |
37281.58 |
18205.724 |
14354.06 |
36071.50754 |
24558.2714 |
13049.01 |
24769.43 |
19663.64 |
| 3*1e-6 |
13767.38 |
45173.59 |
22269.518 |
16352.39 |
43770.62814 |
31304.9246 |
14324.43 |
32129.62 |
26072.95 |
| 2*1e-6 |
14645.3 |
60366.62 |
31163.588 |
18902.75 |
53362.9598 |
46862.8643 |
16918.78 |
53448.89 |
34811.55 |
| 1.00E-06 |
18080.93 |
90392.45 |
47298.698 |
29535.1 |
76472.82915 |
100355.884 |
21313.81 |
73646.55 |
70131.85 |
| 9*1e-7 |
18234.14 |
99247.65 |
50701.342 |
28357.42 |
86231.84925 |
103772.698 |
21287.42 |
81385.9 |
77841.01 |
| 8*1e-7 |
19182.81 |
95016.96 |
50896.834 |
32744.68 |
91895.44724 |
119839 |
24145.12 |
91615.03 |
108462 |
| 7*1e-7 |
20378.61 |
113411.5 |
62449.558 |
35204.73 |
94373.55276 |
129092.693 |
27625.46 |
109482.4 |
123232.6 |
| 6*1e-7 |
20348.53 |
116304.3 |
64837.91 |
39191.89 |
101428.5829 |
127953.05 |
29357.48 |
109426.8 |
140167.9 |
| 5*1e-7 |
22365.02 |
129507.3 |
77875.121 |
48544.11 |
95963.76884 |
156705.337 |
40684.06 |
124867.1 |
149534.4 |
| 4*1e-7 |
23351.5 |
135768.1 |
88745.734 |
60192.69 |
112533.3266 |
161217.764 |
40085.21 |
137533.3 |
164962.1 |
| 3*1e-7 |
27243.87 |
149701.4 |
114492.68 |
69731.63 |
120549.2513 |
205342.492 |
62320.85 |
159985.3 |
249506.1 |
| 2*1e-7 |
34178.87 |
155856.8 |
141850.72 |
99327.43 |
135646.7538 |
256312.372 |
74617.93 |
187551.5 |
289655.7 |
| 1.00E-07 |
38643.19 |
207402.7 |
1.82E+05 |
155931.3 |
159863.3467 |
318339.688 |
133071.7 |
||
将迭代次数画成图
对应同一个δ迭代次数n由少到多的顺序是1<7<4<3<5<2<8<6<9
或许可以理解成从造型上0和1的差别最大，0和9造型上差别最小。
2和8，6和9严重缠绕
3和5轻微缠绕
表明形态上2与8，6与9的外形的相似程度要大于3和5
对应这两个公式的系数表格
| a |
b |
c |
d |
|
| 0-1 |
619.83644 |
-0.242 |
0.99638 |
0.001 |
| 0-2 |
44.40443 |
-0.54071 |
0.95803 |
0.01119 |
| 0-3 |
4.35078 |
-0.67353 |
0.97375 |
0.00612 |
| 0-4 |
0.8431 |
-0.755 |
0.95801 |
0.0135 |
| 0-5 |
440.68687 |
-0.37058 |
0.93024 |
0.02092 |
| 0-6 |
77.8576 |
-0.52061 |
0.95824 |
0.01032 |
| 0-7 |
2.55183 |
-0.66474 |
0.97483 |
0.00749 |
| 0-8 |
14.32362 |
-0.61749 |
0.93612 |
0.02125 |
| 0-9 |
1.7063 |
-0.77752 |
0.9557 |
0.01331 |
用公式计算n
| 01 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
09 |
|
| δ |
计算n |
计算n |
计算n |
计算n |
计算n |
计算n |
计算n |
计算n |
计算n |
| 0.1 |
1082.124 |
154.2184378 |
20.51620942 |
4.795999 |
1034.451 |
258.1731 |
11.79212 |
59.36668 |
10.22293 |
| 1.00E-02 |
1889.196 |
535.6070682 |
96.74468691 |
27.28218 |
2428.232 |
856.0931 |
54.49187 |
246.0553 |
61.24849 |
| 1.00E-03 |
3298.201 |
1860.185692 |
456.2019355 |
155.1955 |
5699.938 |
2838.775 |
251.8093 |
1019.818 |
366.9572 |
| 1.00E-04 |
5758.072 |
6460.502511 |
2151.231376 |
882.8341 |
13379.82 |
9413.281 |
1163.622 |
4226.811 |
2198.545 |
| 0.00009 |
5906.775 |
6839.239814 |
2309.437248 |
955.9298 |
13912.56 |
9944.039 |
1248.04 |
4510.946 |
2386.232 |
| 0.00008 |
6077.561 |
7288.975874 |
2500.108891 |
1044.831 |
14533.26 |
10572.88 |
1349.683 |
4851.251 |
2615.079 |
| 0.00007 |
6277.163 |
7834.717443 |
2735.383611 |
1155.66 |
15270.51 |
11334.03 |
1474.963 |
5268.212 |
2901.181 |
| 0.00006 |
6515.751 |
8515.734976 |
3034.652115 |
1298.3 |
16168.24 |
12281.11 |
1634.118 |
5794.316 |
3270.598 |
| 0.00005 |
6809.675 |
9398.017049 |
3431.1512 |
1489.899 |
17298.39 |
13503.93 |
1844.669 |
6484.788 |
3768.706 |
| 0.00004 |
7187.512 |
10603.18751 |
3987.600644 |
1763.29 |
18789.65 |
15167.45 |
2139.629 |
7442.807 |
4482.721 |
| 0.00003 |
7705.73 |
12387.73955 |
4840.181471 |
2191.051 |
20903.48 |
17618.01 |
2590.539 |
8889.661 |
5606.4 |
| 0.00002 |
8500.175 |
15424.33221 |
6360.106537 |
2975.784 |
24292.62 |
21758.64 |
3391.916 |
11418.78 |
7684.198 |
| 1.00E-05 |
10052.57 |
22437.59474 |
10144.18413 |
5022.028 |
31407.26 |
31214.11 |
5377.145 |
17518.74 |
13172.11 |
| 0.000009 |
10312.18 |
23752.96519 |
10890.20778 |
5437.835 |
32657.8 |
32974.09 |
5767.247 |
18696.38 |
14296.6 |
| 0.000008 |
10610.34 |
25314.91729 |
11789.32457 |
5943.553 |
34114.82 |
35059.31 |
6236.942 |
20106.84 |
15667.69 |
| 0.000007 |
10958.81 |
27210.30052 |
12898.76827 |
6574.006 |
35845.42 |
37583.27 |
6815.87 |
21835 |
17381.8 |
| 0.000006 |
11375.34 |
29575.50283 |
14309.97621 |
7385.415 |
37952.71 |
40723.74 |
7551.33 |
24015.53 |
19595.09 |
| 0.000005 |
11888.48 |
32639.70527 |
16179.67734 |
8475.332 |
40605.59 |
44778.57 |
8524.294 |
26877.31 |
22579.39 |
| 0.000004 |
12548.12 |
36825.31256 |
18803.62829 |
10030.53 |
44106.11 |
50294.74 |
9887.315 |
30847.98 |
26857.26 |
| 0.000003 |
13452.83 |
43023.13626 |
22823.99402 |
12463.86 |
49068.02 |
58420.72 |
11970.99 |
36844.71 |
33589.54 |
| 0.000002 |
14839.79 |
53569.34924 |
29991.23781 |
16927.84 |
57023.57 |
72150.91 |
15674.19 |
47327.09 |
46038.22 |
| 1.00E-06 |
17550 |
77926.70255 |
47835.14816 |
28567.95 |
73724.21 |
103504.9 |
24848.02 |
72609.39 |
78917.88 |
| 0.0000009 |
18003.23 |
82495.03902 |
51353.04095 |
30933.28 |
76659.67 |
109340.9 |
26650.7 |
77490.34 |
85655.01 |
| 0.0000008 |
18523.77 |
87919.76381 |
55592.84815 |
33810.08 |
80079.81 |
116255.5 |
28821.18 |
83336.21 |
93869.58 |
| 0.0000007 |
19132.13 |
94502.50887 |
60824.45701 |
37396.42 |
84142.16 |
124624.8 |
31496.43 |
90498.88 |
104139.3 |
| 0.0000006 |
19859.33 |
102716.9551 |
67479.04255 |
42012.15 |
89088.74 |
135038.5 |
34895.02 |
99536.46 |
117399.8 |
| 0.0000005 |
20755.17 |
113359.0581 |
76295.6639 |
48212.18 |
95316 |
148484.2 |
39391.13 |
111397.6 |
135279.6 |
| 0.0000004 |
21906.78 |
127895.8468 |
88668.96875 |
57058.95 |
103533 |
166775.6 |
45689.71 |
127854.7 |
160909.5 |
| 0.0000003 |
23486.25 |
149421.147 |
107627.1016 |
70901.03 |
115180.4 |
193721.1 |
55318.47 |
152709.2 |
201244.5 |
| 0.0000002 |
25907.64 |
186048.5847 |
141424.4148 |
96294.49 |
133854.9 |
239249.9 |
72431.1 |
196155.2 |
275828.1 |
| 1.00E-07 |
30639.18 |
270642.6889 |
225567.8102 |
162509.6 |
173057.4 |
343218.8 |
114823.8 |
300942 |
472819.5 |
| 实测值/计算值 |
|||||||||
| δ |
01 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
09 |
| 0.1 |
1.92319 |
18.06350161 |
125.1521755 |
490.59 |
3.391568 |
10.70356 |
189.2914 |
44.08823 |
231.1377 |
| 1.00E-02 |
1.508703 |
6.760375684 |
36.19250083 |
118.7494 |
1.84592 |
4.107494 |
56.97498 |
14.17179 |
55.14951 |
| 1.00E-03 |
1.251261 |
2.605350111 |
10.22468835 |
29.16179 |
1.070878 |
1.708855 |
17.34427 |
4.793637 |
12.64151 |
| 1.00E-04 |
1.022514 |
1.193284886 |
3.30040261 |
7.342155 |
0.666653 |
0.812271 |
5.559044 |
1.601817 |
3.241918 |
| 9*1e-5 |
1.015218 |
1.162579499 |
3.144795794 |
7.033243 |
0.671984 |
0.781724 |
5.158194 |
1.628372 |
2.99899 |
| 8*1e-5 |
1.015101 |
1.122587061 |
3.002239083 |
6.605159 |
0.656387 |
0.749906 |
4.863629 |
1.50642 |
2.817452 |
| 7*1e-5 |
0.985255 |
1.045765857 |
2.8103414 |
6.042948 |
0.668179 |
0.735693 |
4.596438 |
1.412692 |
2.591529 |
| 6*1e-5 |
0.992937 |
1.03110184 |
2.667289751 |
5.564797 |
0.609315 |
0.7158 |
4.214979 |
1.372104 |
2.395007 |
| 5*1e-5 |
0.981925 |
0.981812967 |
2.449727932 |
5.049822 |
0.628315 |
0.649763 |
3.957094 |
1.199901 |
2.176869 |
| 4*1e-5 |
0.996219 |
0.893449728 |
2.210700806 |
4.485998 |
0.59512 |
0.635482 |
3.530275 |
1.158884 |
1.888006 |
| 3*1e-5 |
1.000745 |
0.845836317 |
1.999805621 |
3.924761 |
0.618613 |
0.601711 |
3.201633 |
1.099644 |
1.64131 |
| 2*1e-5 |
1.028685 |
0.781935635 |
1.644888852 |
3.070456 |
0.602048 |
0.524439 |
2.571893 |
1.018365 |
1.411754 |
| 1.00E-05 |
0.983396 |
0.880547146 |
1.250326547 |
2.23721 |
0.643984 |
0.476483 |
1.963019 |
0.851549 |
1.015457 |
| 9*1e-6 |
0.964791 |
0.936537389 |
1.199241576 |
2.081002 |
0.653038 |
0.459733 |
1.816512 |
0.801655 |
0.941931 |
| 8*1e-6 |
0.998817 |
0.877542863 |
1.117204412 |
1.945577 |
0.68794 |
0.511563 |
1.751735 |
0.82545 |
0.933751 |
| 7*1e-6 |
0.98383 |
1.030698098 |
1.074716773 |
1.926669 |
0.675936 |
0.495446 |
1.646095 |
0.812281 |
0.853107 |
| 6*1e-6 |
1.003035 |
0.960603617 |
1.077402772 |
1.761666 |
0.72087 |
0.474462 |
1.555798 |
0.873677 |
0.809353 |
| 5*1e-6 |
0.990684 |
1.031925985 |
0.98392307 |
1.617944 |
0.773149 |
0.474132 |
1.463435 |
0.787151 |
0.838253 |
| 4*1e-6 |
0.999332 |
1.012389914 |
0.968202697 |
1.431037 |
0.817835 |
0.488287 |
1.319772 |
0.802951 |
0.732154 |
| 3*1e-6 |
1.023381 |
1.049983542 |
0.975706424 |
1.311985 |
0.89204 |
0.535853 |
1.196595 |
0.872028 |
0.776222 |
| 2*1e-6 |
0.986894 |
1.126887219 |
1.039089755 |
1.116667 |
0.935805 |
0.649512 |
1.079404 |
1.129351 |
0.756144 |
| 1.00E-06 |
1.030253 |
1.159967534 |
0.98878545 |
1.033854 |
1.037282 |
0.969576 |
0.857767 |
1.014284 |
0.888669 |
| 9*1e-7 |
1.012826 |
1.203074102 |
0.987309432 |
0.916729 |
1.124866 |
0.949074 |
0.798757 |
1.050272 |
0.908774 |
| 8*1e-7 |
1.035578 |
1.080723502 |
0.915528451 |
0.968489 |
1.147548 |
1.030825 |
0.837756 |
1.099342 |
1.155455 |
| 7*1e-7 |
1.065151 |
1.200090255 |
1.026717884 |
0.941393 |
1.121596 |
1.035851 |
0.877098 |
1.209765 |
1.183343 |
| 6*1e-7 |
1.024633 |
1.132279377 |
0.960859951 |
0.93287 |
1.138512 |
0.94753 |
0.841308 |
1.099364 |
1.193937 |
| 5*1e-7 |
1.077564 |
1.142451933 |
1.020701789 |
1.006885 |
1.006796 |
1.055367 |
1.032823 |
1.120913 |
1.105373 |
| 4*1e-7 |
1.065948 |
1.061551672 |
1.000865747 |
1.054921 |
1.086932 |
0.966675 |
0.877336 |
1.0757 |
1.025186 |
| 3*1e-7 |
1.159992 |
1.00187529 |
1.063790456 |
0.983507 |
1.046613 |
1.05999 |
1.126583 |
1.047647 |
1.239815 |
| 2*1e-7 |
1.319258 |
0.837720831 |
1.003014393 |
1.031496 |
1.013386 |
1.071316 |
1.030192 |
0.956138 |
1.050131 |
| 1.00E-07 |
1.261235 |
0.766333873 |
0.808921687 |
0.95952 |
0.923759 |
0.927513 |
1.158921 |
0 |
0 |
可以看到这组表达式在δ∈[1e-7,1e-4]的区间上是相对精确的
δ越小越准确，当δ<1e-5时实测值/计算值<2。
将计算的n画成图
在这图里2与8，6与9缠绕，3与5交叉都有反应。
计算p-max
| 计算p-max |
||||||||||
| δ |
-lnδ |
01 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
09 |
| 0.1 |
2.302585 |
0.9972114 |
0.967013 |
0.978732998 |
0.968857609 |
0.946613 |
0.966523 |
0.980939 |
0.952859 |
0.966368 |
| 1.00E-02 |
4.60517 |
0.9979028 |
0.974543 |
0.982893661 |
0.977966231 |
0.96044 |
0.973462 |
0.986045 |
0.966998 |
0.975325 |
| 1.00E-03 |
6.907755 |
0.9983075 |
0.978974 |
0.985335688 |
0.98333408 |
0.968621 |
0.977544 |
0.989044 |
0.975366 |
0.980603 |
| 1.00E-04 |
9.21034 |
0.9985947 |
0.982131 |
0.987072012 |
0.987160488 |
0.974468 |
0.98045 |
0.991177 |
0.981347 |
0.984365 |
| 0.00009 |
9.315701 |
0.9986061 |
0.982256 |
0.987140726 |
0.987312083 |
0.9747 |
0.980565 |
0.991262 |
0.981584 |
0.984514 |
| 0.00008 |
9.433484 |
0.9986187 |
0.982394 |
0.987216633 |
0.987479562 |
0.974956 |
0.980693 |
0.991355 |
0.981846 |
0.984679 |
| 0.00007 |
9.567015 |
0.9986327 |
0.982549 |
0.987301559 |
0.987666958 |
0.975243 |
0.980835 |
0.991459 |
0.982139 |
0.984863 |
| 0.00006 |
9.721166 |
0.9986487 |
0.982724 |
0.987398145 |
0.987880107 |
0.975569 |
0.980997 |
0.991578 |
0.982473 |
0.985072 |
| 0.00005 |
9.903488 |
0.9986672 |
0.982929 |
0.987510437 |
0.988127947 |
0.975948 |
0.981185 |
0.991716 |
0.982861 |
0.985316 |
| 0.00004 |
10.12663 |
0.9986895 |
0.983174 |
0.987645107 |
0.988425224 |
0.976404 |
0.98141 |
0.991882 |
0.983326 |
0.985608 |
| 0.00003 |
10.41431 |
0.9987174 |
0.983482 |
0.987814439 |
0.988799085 |
0.976976 |
0.981694 |
0.99209 |
0.983912 |
0.985976 |
| 0.00002 |
10.81978 |
0.9987556 |
0.983902 |
0.988045369 |
0.989309069 |
0.977757 |
0.982081 |
0.992374 |
0.984711 |
0.986477 |
| 1.00E-05 |
11.51293 |
0.9988176 |
0.984586 |
0.988420916 |
0.990138732 |
0.979028 |
0.982711 |
0.992835 |
0.986011 |
0.987293 |
| 0.000009 |
11.61829 |
0.9988267 |
0.984687 |
0.988476025 |
0.99026051 |
0.979214 |
0.982803 |
0.992903 |
0.986202 |
0.987413 |
| 0.000008 |
11.73607 |
0.9988368 |
0.984798 |
0.988537046 |
0.990395363 |
0.979421 |
0.982906 |
0.992978 |
0.986413 |
0.987545 |
| 0.000007 |
11.8696 |
0.9988481 |
0.984922 |
0.988605494 |
0.990546641 |
0.979653 |
0.98302 |
0.993062 |
0.98665 |
0.987694 |
| 0.000006 |
12.02375 |
0.998861 |
0.985065 |
0.988683566 |
0.990719206 |
0.979917 |
0.983151 |
0.993158 |
0.986921 |
0.987863 |
| 0.000005 |
12.20607 |
0.998876 |
0.985231 |
0.988774632 |
0.990920511 |
0.980226 |
0.983304 |
0.99327 |
0.987237 |
0.988061 |
| 0.000004 |
12.42922 |
0.9988941 |
0.98543 |
0.988884265 |
0.991162889 |
0.980597 |
0.983488 |
0.993405 |
0.987617 |
0.9883 |
| 0.000003 |
12.7169 |
0.998917 |
0.985683 |
0.989022755 |
0.991469111 |
0.981067 |
0.98372 |
0.993575 |
0.988097 |
0.988601 |
| 0.000002 |
13.12236 |
0.9989483 |
0.986029 |
0.989212748 |
0.9918893 |
0.981711 |
0.984039 |
0.993809 |
0.988756 |
0.989014 |
| 1.00E-06 |
13.81551 |
0.9989997 |
0.986597 |
0.98952442 |
0.992578802 |
0.982769 |
0.984562 |
0.994192 |
0.989838 |
0.989692 |
| 9E-07 |
13.92087 |
0.9990073 |
0.986681 |
0.989570429 |
0.99268061 |
0.982925 |
0.984639 |
0.994249 |
0.989998 |
0.989792 |
| 8E-07 |
14.03865 |
0.9990157 |
0.986774 |
0.989621456 |
0.992793526 |
0.983099 |
0.984724 |
0.994311 |
0.990176 |
0.989903 |
| 7E-07 |
14.17219 |
0.9990252 |
0.986878 |
0.989678793 |
0.992920414 |
0.983293 |
0.984821 |
0.994382 |
0.990375 |
0.990027 |
| 6E-07 |
14.32634 |
0.999036 |
0.986998 |
0.989744319 |
0.993065437 |
0.983516 |
0.984931 |
0.994462 |
0.990602 |
0.99017 |
| 5E-07 |
14.50866 |
0.9990486 |
0.987138 |
0.989820922 |
0.993234989 |
0.983776 |
0.985059 |
0.994557 |
0.990869 |
0.990337 |
| 4E-07 |
14.7318 |
0.9990639 |
0.987306 |
0.989913385 |
0.993439666 |
0.98409 |
0.985214 |
0.99467 |
0.99119 |
0.990538 |
| 3E-07 |
15.01948 |
0.9990832 |
0.98752 |
0.990030557 |
0.993699073 |
0.984488 |
0.985411 |
0.994814 |
0.991598 |
0.990793 |
| 2E-07 |
15.42495 |
0.9991098 |
0.987814 |
0.990191969 |
0.994056484 |
0.985037 |
0.985682 |
0.995013 |
0.992159 |
0.991144 |
| 1.00E-07 |
16.1181 |
0.9991537 |
0.9883 |
0.99045838 |
0.994646543 |
0.985943 |
0.986129 |
0.99534 |
0.993086 |
0.991724 |
画成图
按δ=1e-7时的p-max大小排列
1>7>4>8>9>3>2>6>5
和迭代次数n顺序比较
1<7<4<3<5<2<8<6<9
1，7，4，3，5的顺序基本是规律的，2，8，6，9的相对顺序不规则。
迭代次数和识别难度的排序不一致的可能原因是与各个数据集本身的难度不同有关。
最后比较让网络的准确率p-max=0.999的计算耗时
| 计算δ |
计算n |
耗时min/199 |
耗时 天/199 |
耗时 年/199 |
|
| 0-1 |
1.02E-06 |
1.75E+04 |
2.64E+01 |
0.018316985 |
|
| 0-2 |
4.74E-19 |
3.59E+11 |
4.16E+08 |
288722.7808 |
791.0213174 |
| 0-3 |
3.74E-29 |
6.10E+19 |
6.15E+16 |
4.27E+13 |
1.17E+11 |
| 0-4 |
2.09E-10 |
17146949 |
16793.50574 |
11.66215676 |
|
| 0-5 |
7.66E-14 |
31955366.8 |
31534.0064 |
21.89861559 |
|
| 0-6 |
2.89E-25 |
4.64E+14 |
5.12E+11 |
355881000.7 |
975016.4404 |
| 0-7 |
3.90E-12 |
97869735 |
94623.68699 |
65.71089375 |
|
| 0-8 |
5.50E-10 |
7479334.5 |
8967.287082 |
6.227282696 |
|
| 0-9 |
7.67E-13 |
4484458556 |
5164961.655 |
3586.778927 |
9.826791581 |
意思是比如二分类0，1对应的网络
d2（minst0,1）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)让这个网络的准确率等于0.999可以让收敛标准δ=1.75E+04可以在26.4min里收敛199次其中至少有一次的准确率可以达到0.999.或者让d2（minst0,1）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)
的收敛标准δ=1.75E+04，准确率等于0.999的概率是5.025‰，估计耗时0.13min。
预期时间最长的二分类0，3的网络
d2（minst0,3）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)
让这个网络的收敛标准δ= 3.74E-29收敛199次预期需要1170亿年其中至少有1次可以达到0.999，或者让δ= 3.74E-29收敛准确率等于0.999的概率为5.025‰，需要5.88亿年。
按照预期时间排序
1<8<4<5<7<9<2<6<3
按δ=1e-7时的p-max大小排列
1>7>4>8>9>3>2>6>5
迭代次数n顺序比较
1<7<4<3<5<2<8<6<9
对比表明迭代次数n大并不必然的导致更难分类。
关于调参
r学习率，
x权重分母，（0-1的随机数）/x
n迭代次数
p-ave 网络收敛199次的准确率的平均值
p-max网络收敛199次的准确率的最大值
| δ |
r |
x |
n |
p-ave |
p-max |
| 减小 |
不变 |
不变 |
增加 |
增加 |
增加 |
| 减小 |
不变 |
减小 |
增加 |
增加 |
增加 |
| 减小 |
减小 |
不变 |
增加 |
增加 |
增加 |
| 不变 |
减小 |
减小 |
增加 |
增加 |
小幅增加，几乎是定值 |
| 不变 |
不变 |
减小 |
增加 |
增加 |
几乎是定值 |
| 不变 |
减小 |
不变 |
增加 |
增加 |
几乎是定值 |
| 减小 |
减小 |
减小 |
增加 |
增加 |
增加 |
- δ，r或者x的减小都会使网络的平均性能p-ave和最大性能p-max增加
- 当δ保持不变并且非常小时，虽然r或者x减小同样会使最大性能p-max增加但是幅度相当小，几乎可以认为当δ保持不变并且非常小时最大性能p-max是定值
- 在网络的平均性能p-ave和收敛时间之间存在一种平衡，若想网络平均性能p-ave稳定就要增加收敛时间，或者希望网络收敛加快就会导致网络平均性能p-ave不稳定。
比如这个网络
d2（minst0,3）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)
先让学习率r=1e-3,再次让学习率r=0.1，会导致网络看起来收敛速度快好多，但性能时好时坏。
因为r增大会导致迭代次数n减小，使得网络在更短的时间里可能达到更小的δ，而δ减小导致准确率增加；
r增大同时会导致平均性能下降，使网络性能不稳定。
| 实验数据 |
| 学习率 0.1 |
| 权重初始化方式 |
| Random rand1 =new Random(); |
| int ti1=rand1.nextInt(98)+1; |
| int xx=1; |
| if(ti1%2==0) |
| { xx=-1;} |
| tw[a][b]=xx*((double)ti1/x); |
| 第一层第二层和卷积核的权重的初始化的x分别为1000,1000,200 |
http://www.qinms.com/webapp/curvefit/cf.aspx
具体数据位置
| 0-1 |
1个卷积核二分类0,1的特征频率曲线 |
2019/1/20 |
| 0-2 |
神经网络收敛标准与准确率之间的数学关系 |
2018/12/29 |
| 0-3 |
估算带卷积核二分类0,3的网络的收敛时间和迭代次数 |
2019/1/21 |
| 0-4 |
二分类0,4神经网络的收敛时间和准确率的估算表达式 |
2019/1/24 |
| 0-5 |
共振耦合二分类0，5神经网络迭代次数和准确率估算表达式 |
2019/1/24 |
| 0-6 |
二分类minst0，6收敛时间估算表达式 |
2019/1/26 |
| 0-7 |
神经网络训练时间计算实例：二分类minst0，7 |
2019/1/31 |
| 0-8 |
神经网络收敛精度计算实例：二分类minst0，8 |
2019/2/1 |
| 0-9 |
计算神经网络准确率实例二分类minst0，9 |
2019/2/8 |