用共振耦合的神经网络模型制作一个网络分类minst的0和5。求出这网络的迭代次数曲线表达式n（δ）和准确率表达式p-max（δ），并用预期准确率p-max去估算n，然后根据迭代耗时推算收敛需要的时间。
实验用minst数据集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5，让左右两个网络的权重部分共享，实现耦合达到分类的目的。
| 具体进样顺序 |
|||
| δ=0.1 |
迭代次数 |
||
| minst 0-1 |
1 |
判断是否达到收敛 |
|
| minst 5-1 |
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 5-2 |
4 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| minst 0-3 |
5 |
判断是否达到收敛 |
|
| minst 5-3 |
6 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| minst 0-4 |
7 |
判断是否达到收敛 |
|
| minst 5-4 |
8 |
判断是否达到收敛 |
|
| 梯度下降 |
|||
| minst 0-5 |
9 |
判断是否达到收敛 |
|
| minst 5-5 |
10 |
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 5-4999 |
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 5-1 |
10000 |
判断是否达到收敛 |
|
| …… |
|||
| 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=0.01 |
|||
| … |
|||
收敛条件是
if (Math.abs(f2[0]-y[0])< δ && Math.abs(f2[1]-y[1])< δ )
本文尝试了δ从0.1到7*1e-8在内的34个值，测试集是misnt0和5的前4999张图片。
这个网络简写成
S（minst0）81-（con3*3）49-30-2-（1,0）
S（minst5）81-（con3*3）49-30-2-（0,1）
w=w，w1=w1,w2=w2
进一步简写成
d2（minst0,5）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)
测试集中有980个0和892个5.取199次的平均值得到的数据
| δ |
f2[0] |
f2[1] |
迭代次数n |
平均准确率p-ave |
耗时ms/次 |
耗时ms/199次 |
耗时min/199次 |
最大准确率p-max |
| 0.1 |
0.660538 |
0.339487 |
3508.41206 |
0.839472469 |
2072.085427 |
412362 |
6.8727 |
0.966880342 |
| 0.01 |
0.799421 |
0.200578 |
4482.32161 |
0.810634368 |
1780.070352 |
354234 |
5.9039 |
0.968482906 |
| 0.001 |
0.763423 |
0.236577 |
6103.9397 |
0.786378474 |
2940.020101 |
585080 |
9.751333333 |
0.969017094 |
| 1.00E-04 |
0.753734 |
0.246266 |
8919.69849 |
0.787398531 |
4092.266332 |
814361 |
13.57268333 |
0.973824786 |
| 9.00E-05 |
0.708516 |
0.291484 |
9349.0201 |
0.789873513 |
4198.964824 |
835609 |
13.92681667 |
0.977029915 |
| 8.00E-05 |
0.758765 |
0.241235 |
9539.44221 |
0.787393162 |
4214.80402 |
838746 |
13.9791 |
0.974893162 |
| 7.00E-05 |
0.778867 |
0.221133 |
10203.4322 |
0.782045913 |
3937.050251 |
783473 |
13.05788333 |
0.97542735 |
| 6.00E-05 |
0.829118 |
0.170882 |
9851.55276 |
0.782902225 |
3857.748744 |
767692 |
12.79486667 |
0.973824786 |
| 5.00E-05 |
0.733651 |
0.266349 |
10868.8342 |
0.787677705 |
4189.417085 |
833694 |
13.8949 |
0.976495726 |
| 4.00E-05 |
0.743704 |
0.256296 |
11182.1005 |
0.779836683 |
4362.693467 |
868200 |
14.47 |
0.973290598 |
| 3.00E-05 |
0.738682 |
0.261318 |
12931.1709 |
0.795706631 |
4800.527638 |
955306 |
15.92176667 |
0.975961538 |
| 2.00E-05 |
0.708536 |
0.291464 |
14625.3216 |
0.825572843 |
5780.939698 |
1150408 |
19.17346667 |
0.976495726 |
| 1.00E-05 |
0.658289 |
0.341711 |
20225.7739 |
0.834425869 |
7647.241206 |
1521803 |
25.36338333 |
0.979166667 |
| 9.00E-06 |
0.758791 |
0.241209 |
21326.7688 |
0.817288902 |
6774.356784 |
1348104 |
22.4684 |
0.97542735 |
| 8.00E-06 |
0.753766 |
0.246234 |
23468.9447 |
0.832222007 |
8397.552764 |
1671113 |
27.85188333 |
0.979166667 |
| 7.00E-06 |
0.773867 |
0.226133 |
24229.2161 |
0.829567173 |
8309.20603 |
1653545 |
27.55908333 |
0.977564103 |
| 6.00E-06 |
0.713566 |
0.286434 |
27358.9749 |
0.845300219 |
8964.457286 |
1783943 |
29.73238333 |
0.977029915 |
| 5.00E-06 |
0.738692 |
0.261308 |
31394.1859 |
0.842385002 |
9733.542714 |
1936975 |
32.28291667 |
0.977564103 |
| 4.00E-06 |
0.804018 |
0.195982 |
36071.5075 |
0.83582979 |
11502.59799 |
2289032 |
38.15053333 |
0.977029915 |
| 3.00E-06 |
0.788943 |
0.211057 |
43770.6281 |
0.852137289 |
13661.28643 |
2718596 |
45.30993333 |
0.977564103 |
| 2.00E-06 |
0.819094 |
0.180906 |
53362.9598 |
0.863309604 |
16638.07538 |
3310977 |
55.18295 |
0.981303419 |
| 1.00E-06 |
0.869346 |
0.130654 |
76472.8291 |
0.886483701 |
23692.66834 |
4714857 |
78.58095 |
0.977029915 |
| 9.00E-07 |
0.82412 |
0.17588 |
86231.8492 |
0.884258364 |
28147.44221 |
5601343 |
93.35571667 |
0.979700855 |
| 8.00E-07 |
0.864321 |
0.135679 |
91895.4472 |
0.894829382 |
30774.17085 |
6124068 |
102.0678 |
0.983440171 |
| 7.00E-07 |
0.839196 |
0.160804 |
94373.5528 |
0.898337843 |
31463.31156 |
6261215 |
104.3535833 |
0.982371795 |
| 6.00E-07 |
0.844221 |
0.155779 |
101428.583 |
0.903228751 |
33708.29648 |
6707953 |
111.7992167 |
0.978098291 |
| 5.00E-07 |
0.81407 |
0.18593 |
95963.7688 |
0.888207061 |
32263.78894 |
6420494 |
107.0082333 |
0.983440171 |
| 4.00E-07 |
0.79397 |
0.20603 |
112533.327 |
0.895860177 |
34013.57789 |
6768702 |
112.8117 |
0.980769231 |
| 3.00E-07 |
0.849246 |
0.150754 |
120549.251 |
0.912801185 |
36167.75879 |
7197384 |
119.9564 |
0.982371795 |
| 2.00E-07 |
0.904522 |
0.095478 |
135646.754 |
0.92351179 |
49923.53266 |
9934783 |
165.5797167 |
0.982905983 |
| 1.00E-07 |
0.854271 |
0.145729 |
159863.347 |
0.937051712 |
59632.27136 |
11866824 |
197.7804 |
0.986111111 |
| 9.00E-08 |
0.844221 |
0.155779 |
170566.653 |
0.933269446 |
56600.34673 |
11263473 |
187.72455 |
0.982905983 |
| 8.00E-08 |
0.829146 |
0.170854 |
175717.402 |
0.937279882 |
52882.64322 |
10523650 |
175.3941667 |
0.984508547 |
| 7.00E-08 |
0.819095 |
0.180905 |
178000.92 |
0.932474874 |
52960.86432 |
10539229 |
175.6538167 |
0.983440171 |
p-ave是199组数据的平均准确率
p-max是199组数据的最大准确率
得到p-ave曲线
这仍然是一条开口向上，有极小值的曲线，与p-max曲线对比
p-max曲线是随着迭代次数n的增加单调的增加的，所以这提示如果在实用中更看重网络的收敛效率，应该将δ设置为一个相对较大的值比如0.1，
| δ |
迭代次数n |
平均准确率p-ave |
耗时ms/次 |
耗时ms/199次 |
耗时min/199次 |
最大准确率p-max |
| 0.1 |
3508.412 |
0.839472469 |
2072.08543 |
412362 |
6.8727 |
0.966880342 |
| 7.00E-08 |
178000.9 |
0.932474874 |
52960.8643 |
10539229 |
175.6538167 |
0.983440171 |
| 0.039126392 |
0.983161325 |
比较当δ=0.1和δ=7e-8的数据，可以看到当δ=0.1只用4%的时间就达到了0.966880342而要多花24倍的时间才能将p-max提升2%达到δ=7e-8的0.98344017。
选择δ∈[7*1e-8,4*1e-6]的区间拟合n（δ）曲线，因为在这个区间p-ave上升速率最快
| x |
δ |
7.00E-08,8.00E-08,9.00E-08,1.00E-07,2.00E-07,3.00E-07,4.00E-07,5.00E-07,6.00E-07,7.00E-07,8.00E-07,9.00E-07,1.00E-06,2.00E-06,3.00E-06,4.00E-06 |
| y |
n |
178000.9196,175717.402,170566.6533,159863.3467,135646.7538,120549.2513,112533.3266,95963.76884,101428.5829,94373.55276,91895.44724,86231.84925,76472.82915,53362.9598,43770.62814,36071.50754 |
| 拟合方程式：y=ax^b |
||
| a = 440.686865460085 |
||
| b = -0.370577332113339 |
||
| 相关系数 R2：0.952006869270214 |
所以d2（minst0,5）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)的n（δ）曲线近似的为
实测值与计算值比较
| δ |
实测n |
计算n |
实测值/计算值 |
| 0.1 |
3508.41206 |
1034.44508 |
3.391588519 |
| 0.01 |
4482.32161 |
2428.20177 |
1.845942816 |
| 0.001 |
6103.9397 |
5699.83263 |
1.070898059 |
| 1.00E-04 |
8919.69849 |
13379.4862 |
0.666669734 |
| 9.00E-05 |
9349.0201 |
13912.21 |
0.672001078 |
| 8.00E-05 |
9539.44221 |
14532.8934 |
0.656403506 |
| 7.00E-05 |
10203.4322 |
15270.1249 |
0.668195722 |
| 6.00E-05 |
9851.55276 |
16167.8233 |
0.609330805 |
| 5.00E-05 |
10868.8342 |
17297.9377 |
0.628331214 |
| 4.00E-05 |
11182.1005 |
18789.1434 |
0.595136257 |
| 3.00E-05 |
12931.1709 |
20902.8953 |
0.618630609 |
| 2.00E-05 |
14625.3216 |
24291.9218 |
0.602065235 |
| 1.00E-05 |
20225.7739 |
31406.2995 |
0.644003726 |
| 9.00E-06 |
21326.7688 |
32656.7872 |
0.653057777 |
| 8.00E-06 |
23468.9447 |
34113.7468 |
0.68796151 |
| 7.00E-06 |
24229.2161 |
35844.285 |
0.675957577 |
| 6.00E-06 |
27358.9749 |
37951.4947 |
0.720893211 |
| 5.00E-06 |
31394.1859 |
40604.2656 |
0.773174578 |
| 4.00E-06 |
36071.5075 |
44104.6433 |
0.817861904 |
| 3.00E-06 |
43770.6281 |
49066.3529 |
0.892070138 |
| 2.00E-06 |
53362.9598 |
57021.5747 |
0.935838059 |
| 1.00E-06 |
76472.8291 |
73721.4892 |
1.037320732 |
| 9.00E-07 |
86231.8492 |
76656.818 |
1.124907757 |
| 8.00E-07 |
91895.4472 |
80076.8081 |
1.147591287 |
| 7.00E-07 |
94373.5528 |
84138.9822 |
1.121638868 |
| 6.00E-07 |
101428.583 |
89085.3349 |
1.13855533 |
| 5.00E-07 |
95963.7688 |
95312.3093 |
1.006834999 |
| 4.00E-07 |
112533.327 |
103528.911 |
1.086974889 |
| 3.00E-07 |
120549.251 |
115175.766 |
1.046654651 |
| 2.00E-07 |
135646.754 |
133849.434 |
1.013427923 |
| 1.00E-07 |
159863.347 |
173049.931 |
0.92379896 |
| 9.00E-08 |
170566.653 |
179940.167 |
0.947907606 |
| 8.00E-08 |
175717.402 |
187968.071 |
0.934825796 |
| 7.00E-08 |
178000.92 |
197503.405 |
0.901254943 |
这个表达式计算值偏大，但在除了δ=0.1的整个区间上都相对精确。
然后拟合p-max(δ)曲线
| x |
-ln(δ) |
16.11809565,11.51292546,9.210340372,6.907755279 |
| y |
p-max |
0.986111111,0.979166667,0.973824786,0.969017094 |
| 拟合方程式：y=ax^b |
||
| a = 0.930243883115587 |
||
| b = 0.020924631383507 |
||
| 相关系数 R2：0.996178566840283 |
计算值与实测值比较
| 实测值 |
计算值 |
实测值/计算值 |
| 7.00E-08 |
6.40E-07 |
0.109452272 |
| 1.00E-07 |
8.88E-08 |
1.125541632 |
| 1.00E-06 |
2.94E-05 |
0.034008949 |
| 1.00E-05 |
9.33E-06 |
1.072224911 |
| 1.00E-04 |
1.34E-04 |
0.746517811 |
| 0.001 |
8.76E-04 |
1.140918972 |
| 0.01 |
0.001053 |
9.500364968 |
| 0.1 |
0.001774 |
56.38338167 |
| 预期p-max |
计算δ |
计算迭代次数n |
耗时min |
耗时day |
| 9.99E-01 |
7.66E-14 |
31955366.83 |
31534.0064 |
21.89861559 |
尽管误差可能接近1个数量级，但是还是用这两个表达式估算了
d2（minst0,5）81-con（3*3）49-30-2-（2*k） ,k∈(0,1)的p-max=0.999的耗时，计算结果预计需要21.8天，表明在21.8天内让网络的δ=7.66E-14，可以收敛199次，其中会有至少1次的准确率等于0.999.
| 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 |
f2[0] f2[1] 迭代次数n 最大准确率p-max δ 耗时ms/次
0.901780783 0.099378155 2807 0.943910256 0.1 2798
0.908153712 0.093250136 3897 0.678418803 0.1 2525
0.917838958 0.081119376 2807 0.958333333 0.1 1845
0.093186235 0.903902557 3744 0.943376068 0.1 2119
0.921205379 0.082460685 3545 0.86965812 0.1 2096
0.919531337 0.077757196 2879 0.726495726 0.1 1762
0.931560352 0.07010653 3339 0.935897436 0.1 2054
0.903449988 0.098702967 1839 0.943376068 0.1 1390
0.069850929 0.930925323 2928 0.903846154 0.1 1822
0.071194381 0.931373399 3158 0.947115385 0.1 1890
0.099861396 0.900071632 2838 0.90491453 0.1 1768
0.086171039 0.913218708 3412 0.879273504 0.1 1979
0.901373282 0.096244284 3873 0.891025641 0.1 2162
0.910176023 0.091052593 5621 0.819444444 0.1 3022
0.917323795 0.082733495 2263 0.699786325 0.1 1539
0.091392447 0.905195413 2172 0.920405983 0.1 1486
0.070957561 0.930895641 3900 0.916132479 0.1 2320
0.901388359 0.096798037 3417 0.889423077 0.1 2105
0.903250357 0.097416978 2553 0.870726496 0.1 1616
0.912298729 0.086786 4843 0.580662393 0.1 2501
0.910252395 0.089923423 4207 0.842948718 0.1 2302
0.914367251 0.084084334 3339 0.955128205 0.1 2007
0.901617504 0.098625028 2623 0.888888889 0.1 1648
0.918370107 0.080194998 3615 0.887286325 0.1 2055
0.923511499 0.077265411 2531 0.927350427 0.1 1608
0.085124556 0.911321553 4160 0.931089744 0.1 2299
0.072439428 0.929513163 2696 0.926282051 0.1 1713
0.925919345 0.075310732 1885 0.956730769 0.1 1366
0.900257642 0.098993493 3181 0.927884615 0.1 1914
0.910361057 0.091046942 3467 0.747863248 0.1 2013
0.904220367 0.097763516 3615 0.882478632 0.1 2091
0.068342921 0.931897994 3560 0.68482906 0.1 2057
0.085361891 0.914521971 2658 0.917200855 0.1 1698
0.926242929 0.072486953 1885 0.941239316 0.1 1421
0.951166903 0.049418416 5363 0.686965812 0.1 2771
0.096963125 0.904329651 2440 0.932692308 0.1 1620
0.9182534 0.083991332 2227 0.84775641 0.1 1546
0.925720733 0.076221733 4331 0.803418803 0.1 2378
0.091256068 0.907150909 2254 0.950320513 0.1 1537
0.913139471 0.086623451 4843 0.650106838 0.1 2502
0.900542268 0.09405505 3545 0.857371795 0.1 2046
0.09793484 0.900297325 3436 0.903311966 0.1 1995
0.906216153 0.094979063 3181 0.951388889 0.1 1849
0.910424439 0.091390802 5231 0.944978632 0.1 2672
0.935485754 0.063708012 3827 0.549145299 0.1 2171
0.098993831 0.903811372 2910 0.886217949 0.1 1756
0.930693573 0.069295714 2401 0.930555556 0.1 1572
0.932033293 0.067486138 4207 0.853632479 0.1 2338
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412362
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6.26E-08 0.99999994 194194 0.968482906 7.00E-08 58033
0.999999942 5.81E-08 93837 0.876068376 7.00E-08 28478
0.999999931 6.66E-08 244207 0.822649573 7.00E-08 73224
0.999999936 6.38E-08 317023 0.966880342 7.00E-08 94305
0.999999945 5.54E-08 233781 0.965277778 7.00E-08 69864
0.99999994 5.78E-08 238669 0.965277778 7.00E-08 71101
0.999999939 6.16E-08 188689 0.971688034 7.00E-08 56752
0.999999936 6.35E-08 128713 0.971688034 7.00E-08 38959
0.999999943 5.59E-08 117103 0.963141026 7.00E-08 35438
0.999999937 6.37E-08 164239 0.787393162 7.00E-08 49262
0.999999936 6.41E-08 148705 0.967948718 7.00E-08 44479
6.62E-08 0.999999934 184578 0.974358974 7.00E-08 55017
0.999999934 6.65E-08 113839 0.970619658 7.00E-08 34233
0.999999948 5.18E-08 110651 0.883012821 7.00E-08 33348
0.999999937 6.37E-08 247003 0.97542735 7.00E-08 73595
0.999999953 4.64E-08 168777 0.897435897 7.00E-08 50431
0.999999935 6.71E-08 110317 0.961538462 7.00E-08 33095
0.999999938 6.20E-08 220717 0.919337607 7.00E-08 66087
0.999999945 5.64E-08 154243 0.728632479 7.00E-08 46062
6.20E-08 0.999999939 75978 0.957264957 7.00E-08 23257
0.999999933 6.69E-08 73845 0.897970085 7.00E-08 22501
0.999999933 6.51E-08 223809 0.951388889 7.00E-08 66768
0.999999938 6.30E-08 127099 0.962606838 7.00E-08 38100
10539229 k