( A, B )---6*m*2---( 1, 0 )( 0, 1 )
做一个3层网络分类A和B，让训练集A是3a2，B全为0. 收敛误差为7e-4，收敛199次，让隐藏层节点数为m=20，25，30，...，870统计迭代次数n的平均值。
A为3a2
|---|---|---|
| 1 | 0 | 0 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
得到数据为
|-----|-------|---|----------|---------|---|-----|---------|---|-------------|----------|
| m | n | | mn | Δmn | | m | n | | mn | Δmn |
| 20 | 33373 | | 667461.2 | | | 405 | 15089.5 | | 6111256.658 | 63222.49 |
| 25 | 29769 | | 744228 | 76766.8 | | 410 | 15080 | | 6182818.543 | 71561.88 |
| 30 | 27312 | | 819358.3 | 75130.3 | | 415 | 15062.1 | | 6250769.623 | 67951.08 |
| 35 | 25543 | | 893999.4 | 74641 | | 420 | 15041.4 | | 6317393.065 | 66623.44 |
| 40 | 24192 | | 967666.1 | 73666.8 | | 425 | 15016.9 | | 6382178.015 | 64784.95 |
| 45 | 23293 | | 1048176 | 80509.4 | | 430 | 15001.2 | | 6450520.754 | 68342.74 |
| 50 | 22476 | | 1123775 | 75599.6 | | 435 | 14989.7 | | 6520521.03 | 70000.28 |
| 55 | 21823 | | 1200267 | 76491.5 | | 440 | 14965.2 | | 6584692.864 | 64171.83 |
| 60 | 21173 | | 1270354 | 70087.4 | | 445 | 14948 | | 6651880.126 | 67187.26 |
| 65 | 20631 | | 1341037 | 70682.5 | | 450 | 14936.2 | | 6721279.146 | 69399.02 |
| 70 | 20258 | | 1418073 | 77036.5 | | 455 | 14917.7 | | 6787545.955 | 66266.81 |
| 75 | 19886 | | 1491434 | 73360.8 | | 460 | 14905.9 | | 6856734.573 | 69188.62 |
| 80 | 19606 | | 1568517 | 77083.6 | | 465 | 14887.6 | | 6922749.422 | 66014.85 |
| 85 | 19243 | | 1635672 | 67154.7 | | 470 | 14869 | | 6988415.829 | 65666.41 |
| 90 | 19065 | | 1715853 | 80180.6 | | 475 | 14862.6 | | 7059753.141 | 71337.31 |
| 95 | 18762 | | 1782428 | 66575 | | 480 | 14838.8 | | 7122623.518 | 62870.38 |
| 100 | 18571 | | 1857099 | 74671.3 | | 485 | 14822.6 | | 7188940.528 | 66317.01 |
| 105 | 18362 | | 1927990 | 70891.5 | | 490 | 14812.8 | | 7258286.281 | 69345.75 |
| 110 | 18188 | | 2000667 | 72676.8 | | 495 | 14791.8 | | 7321938.015 | 63651.73 |
| 115 | 18010 | | 2071122 | 70454.4 | | 500 | 14781.7 | | 7390846.734 | 68908.72 |
| 120 | 17878 | | 2145300 | 74178.6 | | 505 | 14766.2 | | 7456944.196 | 66097.46 |
| 125 | 17739 | | 2217337 | 72037 | | 510 | 14751.6 | | 7523302.161 | 66357.96 |
| 130 | 17596 | | 2287494 | 70156.4 | | 515 | 14734.2 | | 7588110.93 | 64808.77 |
| 135 | 17473 | | 2358863 | 71369.4 | | 520 | 14729.3 | | 7659257.688 | 71146.76 |
| 140 | 17362 | | 2430638 | 71775.4 | | 525 | 14708.4 | | 7721934.799 | 62677.11 |
| 145 | 17264 | | 2503209 | 72570.8 | | 530 | 14693.7 | | 7787662.864 | 65728.07 |
| 150 | 17140 | | 2570946 | 67737.2 | | 535 | 14683.5 | | 7855684.598 | 68021.73 |
| 155 | 17051 | | 2642889 | 71942.9 | | 540 | 14676.2 | | 7925162.111 | 69477.51 |
| 160 | 16969 | | 2715014 | 72124.8 | | 545 | 14658.2 | | 7988744.196 | 63582.09 |
| 165 | 16880 | | 2785126 | 70111.9 | | 550 | 14639 | | 8051461.055 | 62716.86 |
| 170 | 16800 | | 2855938 | 70811.4 | | 555 | 14633.8 | | 8121750.075 | 70289.02 |
| 175 | 16718 | | 2925693 | 69755.5 | | 560 | 14613.3 | | 8183465.729 | 61715.65 |
| 180 | 16652 | | 2997431 | 71738.4 | | 565 | 14601.3 | | 8249758.065 | 66292.34 |
| 185 | 16579 | | 3067154 | 69722.6 | | 570 | 14598 | | 8320834.221 | 71076.16 |
| 190 | 16504 | | 3135834 | 68679.5 | | 575 | 14580.9 | | 8384046.106 | 63211.88 |
| 195 | 16468 | | 3211251 | 75417.7 | | 580 | 14566.1 | | 8448335.377 | 64289.27 |
| 200 | 16387 | | 3277498 | 66247.3 | | 585 | 14551.4 | | 8512587.814 | 64252.44 |
| 205 | 16333 | | 3348172 | 70673.8 | | 590 | 14535 | | 8575667.789 | 63079.97 |
| 210 | 16268 | | 3416224 | 68051.8 | | 595 | 14532.5 | | 8646830.025 | 71162.24 |
| 215 | 16226 | | 3488505 | 72280.6 | | 600 | 14515.3 | | 8709156.784 | 62326.76 |
| 220 | 16162 | | 3555546 | 67041.4 | | 605 | 14503.5 | | 8774588.618 | 65431.83 |
| 225 | 16116 | | 3626051 | 70505.4 | | 610 | 14492.8 | | 8840625.779 | 66037.16 |
| 230 | 16087 | | 3699998 | 73947.1 | | 615 | 14482.7 | | 8906859.573 | 66233.79 |
| 235 | 16036 | | 3768553 | 68554.8 | | 620 | 14470.6 | | 8971745.829 | 64886.26 |
| 240 | 15996 | | 3839019 | 70466.2 | | 625 | 14456.1 | | 9035072.236 | 63326.41 |
| 245 | 15956 | | 3909192 | 70172.2 | | 630 | 14447.2 | | 9101717.638 | 66645.4 |
| 250 | 15916 | | 3979097 | 69905.1 | | 635 | 14429.5 | | 9162702.186 | 60984.55 |
| 255 | 15879 | | 4049071 | 69973.9 | | 640 | 14417.4 | | 9227111.558 | 64409.37 |
| 260 | 15838 | | 4117887 | 68815.9 | | 645 | 14411 | | 9295082.035 | 67970.48 |
| 265 | 15800 | | 4187089 | 69202.7 | | 650 | 14394.9 | | 9356717.337 | 61635.3 |
| 270 | 15763 | | 4256129 | 69040.2 | | 655 | 14389.2 | | 9424946.407 | 68229.07 |
| 275 | 15745 | | 4329822 | 73693.1 | | 660 | 14375.3 | | 9487725.528 | 62779.12 |
| 280 | 15708 | | 4398149 | 68326.1 | | 665 | 14364.2 | | 9552176.96 | 64451.43 |
| 285 | 15681 | | 4469148 | 70999.5 | | 670 | 14353.4 | | 9616792.814 | 64615.85 |
| 290 | 15635 | | 4534092 | 64943.7 | | 675 | 14336.5 | | 9677149.372 | 60356.56 |
| 295 | 15614 | | 4606223 | 72131.7 | | 680 | 14329.5 | | 9744034.372 | 66885 |
| 300 | 15586 | | 4675904 | 69680.6 | | 685 | 14322.2 | | 9810731.784 | 66697.41 |
| 305 | 15548 | | 4742292 | 66387.7 | | 690 | 14301.7 | | 9868189.296 | 57457.51 |
| 310 | 15523 | | 4812114 | 69822.7 | | 695 | 14294.4 | | 9934584.95 | 66395.65 |
| 315 | 15514 | | 4886801 | 74686.4 | | 700 | 14283.1 | | 9998156.281 | 63571.33 |
| 320 | 15483 | | 4954486 | 67685.3 | | 705 | 14269.9 | | 10060282.69 | 62126.41 |
| 325 | 15455 | | 5022983 | 68496.8 | | 710 | 14258.1 | | 10123233.52 | 62950.83 |
| 330 | 15429 | | 5091517 | 68534.1 | | 715 | 14245.4 | | 10185476.81 | 62243.29 |
| 335 | 15400 | | 5159059 | 67542 | | 720 | 14233.9 | | 10248432.96 | 62956.16 |
| 340 | 15380 | | 5229294 | 70235.1 | | 725 | 14222.8 | | 10311565.7 | 63132.74 |
| 345 | 15355 | | 5297555 | 68260.8 | | 730 | 14211.2 | | 10374184.07 | 62618.37 |
| 350 | 15331 | | 5366012 | 68457.1 | | 735 | 14197.1 | | 10434831.93 | 60647.86 |
| 355 | 15307 | | 5434021 | 68008.9 | | 740 | 14185.3 | | 10497115.68 | 62283.74 |
| 360 | 15291 | | 5504695 | 70674.2 | | 745 | 14173.9 | | 10559528.92 | 62413.24 |
| 365 | 15266 | | 5571971 | 67275.9 | | 750 | 14166.4 | | 10624797.74 | 65268.82 |
| 370 | 15239 | | 5638449 | 66477.8 | | 755 | 14150.4 | | 10683580.08 | 58782.34 |
| 375 | 15221 | | 5707717 | 69268.1 | | 760 | 14139.7 | | 10746136.48 | 62556.41 |
| 380 | 15192 | | 5773084 | 65367.4 | | 765 | 14125 | | 10805609.62 | 59473.14 |
| 385 | 15172 | | 5841299 | 68215.2 | | 770 | 14116.5 | | 10869710.8 | 64101.18 |
| 390 | 15152 | | 5909392 | 68092.4 | | 775 | 14105.9 | | 10932068.22 | 62357.41 |
| 395 | 15134 | | 5978059 | 68667.3 | | 780 | 14089.5 | | 10989804.12 | 57735.9 |
| 400 | 15120 | | 6048034 | 69975.2 | | 785 | 14075.1 | | 11048946.01 | 59141.88 |
| | | | | | | 790 | 14064.9 | | 11111294.42 | 62348.42 |
| | | | | | | 795 | 14054.2 | | 11173085.8 | 61791.38 |
| | | | | | | 800 | 14040 | | 11231971.86 | 58886.06 |
| | | | | | | 805 | 14025.9 | | 11290828.87 | 58857.01 |
| | | | | | | 810 | 14014.6 | | 11351848.79 | 61019.92 |
| | | | | | | 815 | 14000 | | 11409987.71 | 58138.92 |
| | | | | | | 820 | 13988.9 | | 11470914.07 | 60926.36 |
| | | | | | | 825 | 13976.1 | | 11530311.93 | 59397.86 |
| | | | | | | 830 | 13959.5 | | 11586395.43 | 56083.49 |
| | | | | | | 835 | 13949.3 | | 11647624.8 | 61229.37 |
| | | | | | | 840 | 13937.6 | | 11707561.21 | 59936.41 |
| | | | | | | 845 | 7303.58 | | 6171527.563 | -5536034 |
| | | | | | | 850 | 6069.6 | | 5159158.291 | -1012369 |
| | | | | | | 855 | 6739.67 | | 5762416.432 | 603258.1 |
| | | | | | | 860 | 6526.54 | | 5612822.412 | -149594 |
| | | | | | | 865 | 6857.13 | | 5931413.668 | 318591.3 |
| | | | | | | 870 | 7120.29 | | 6194653.568 | 263239.9 |
比较比热曲线
从25到840这条曲线就是单调减小的，没有明显的峰。负值出现在845处和第一台阶的位置相同。
做第二组，然让隐藏层节点数为m=2，4，6，...，48统计迭代次数平均值
得到数据
|----|------------|---|----------|-----------|
| m | n | | mn | Δmn |
| 2 | 229556.362 | | 459112.7 | |
| 4 | 117615.905 | | 470463.6 | 11350.894 |
| 6 | 79342.5276 | | 476055.2 | 5591.5477 |
| 8 | 61990.407 | | 495923.3 | 19868.09 |
| 10 | 51976.794 | | 519767.9 | 23844.683 |
| 12 | 44879.6332 | | 538555.6 | 18787.658 |
| 14 | 41321.4623 | | 578500.5 | 39944.874 |
| 16 | 37602.1759 | | 601634.8 | 23134.342 |
| 18 | 35282.9196 | | 635092.6 | 33457.739 |
| 20 | 32955.3417 | | 659106.8 | 24014.281 |
| 22 | 31585.3618 | | 694878 | 35771.126 |
| 24 | 30205.5226 | | 724932.5 | 30054.583 |
| 26 | 29030.7085 | | 754798.4 | 29865.879 |
| 28 | 28083.4422 | | 786336.4 | 31537.96 |
| 30 | 27225.3417 | | 816760.3 | 30423.869 |
| 32 | 26417.2412 | | 845351.7 | 28591.467 |
| 34 | 25838.4975 | | 878508.9 | 33157.196 |
| 36 | 25324.6985 | | 911689.1 | 33180.231 |
| 38 | 24711.3719 | | 939032.1 | 27342.985 |
| 40 | 24252.7688 | | 970110.8 | 31078.623 |
| 42 | 23861.1608 | | 1002169 | 32058 |
| 44 | 23309.3819 | | 1025613 | 23444.05 |
| 46 | 23098.7085 | | 1062541 | 36927.789 |
| 48 | 22728.0452 | | 1090946 | 28405.578 |
比热曲线为
明显在m<14的区间，比热随着温度的上升是增加的，m>14比热随着温度的上升是减小的。也就是结构3a2的相变点就在m=14左右。相比较3a1相变点出现在m=340，3a2的相变温度要远小的多，所以这意味着结构3a2点与点之间的作用力很弱。
有相变现象也表明同一个结构可能有多种不同的性质，所以调整隐藏层节点数可以理解成调整结构的存在形态。
|-----|------|-----|------|------|-----|-----|------|------|-----|
| | 迭代次数 | | | | 比热 | | | | |
| | 极小值 | 峰 | 第一台阶 | 第二台阶 | 极小值 | 极大值 | 相变点1 | 相变点2 | 负值 |
| 3a1 | 260 | 380 | 760 | 860 | 40 | 340 | 340 | | 580 |
| 3a2 | | | 845 | | | | 14 | | 845 |
| 3a3 | | | 700 | 840 | | | | | 680 |
| 3a4 | 360 | 620 | 680 | 900 | 240 | 620 | | 620 | 680 |
| 3a5 | | | 860 | | | | | | 840 |
| 3a6 | | | 860 | | | | | | 860 |