( 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3a2,3,5,6，B全为0. 收敛误差为7e-4，收敛199次，让隐藏层节点数为m=20，40，...，1100统计迭代次数n的平均值。
A为3a3
|---|---|
| 1 | 0 |
| 1 | 0 |
| 0 | 1 |
得到数据
|------|-------|---|----------|---------|
| m | n | | mn | Δmn |
| 30 | 27080 | | 812398.3 | |
| 20 | 32015 | | 640300 | |
| 40 | 24439 | | 977568 | 337268 |
| 60 | 21737 | | 1304241 | 326672 |
| 80 | 20318 | | 1625425 | 321185 |
| 100 | 19409 | | 1940919 | 315494 |
| 120 | 18760 | | 2251245 | 310326 |
| 140 | 18353 | | 2569434 | 318189 |
| 160 | 17999 | | 2879866 | 310432 |
| 180 | 17733 | | 3191895 | 312029 |
| 200 | 17520 | | 3504055 | 312161 |
| 220 | 17337 | | 3814204 | 310149 |
| 240 | 17186 | | 4124566 | 310362 |
| 260 | 17037 | | 4429735 | 305169 |
| 280 | 16914 | | 4735862 | 306127 |
| 300 | 16818 | | 5045510 | 309648 |
| 320 | 16718 | | 5349855 | 304345 |
| 340 | 16624 | | 5652319 | 302464 |
| 360 | 16544 | | 5955773 | 303454 |
| 380 | 16452 | | 6251808 | 296035 |
| 400 | 16370 | | 6548131 | 296323 |
| 420 | 16305 | | 6848007 | 299876 |
| 440 | 16231 | | 7141773 | 293766 |
| 460 | 16158 | | 7432863 | 291090 |
| 480 | 16096 | | 7726174 | 293311 |
| 500 | 16029 | | 8014435 | 288261 |
| 520 | 15965 | | 8301743 | 287308 |
| 540 | 15907 | | 8590008 | 288265 |
| 560 | 15845 | | 8873121 | 283113 |
| 580 | 15779 | | 9152001 | 278879 |
| 600 | 15707 | | 9424025 | 272024 |
| 620 | 15653 | | 9705034 | 281009 |
| 640 | 15581 | | 9971538 | 266503 |
| 660 | 15513 | | 10238454 | 266916 |
| 680 | 13121 | | 8922369 | -1E+06 |
| 700 | 8351 | | 5845813 | -3E+06 |
| 720 | 8086 | | 5822126 | -23686 |
| 740 | 7739 | | 5727157 | -94969 |
| 760 | 8498 | | 6458155 | 730998 |
| 780 | 7486 | | 5839045 | -619111 |
| 800 | 7804 | | 6242826 | 403781 |
| 820 | 4982 | | 4085285 | -2E+06 |
| 840 | 889.2 | | 746937.3 | -3E+06 |
| 860 | 542.3 | | 466375 | -280562 |
| 880 | 524.1 | | 461217.3 | -5157.7 |
| 900 | 521.3 | | 469198.5 | 7981.21 |
| 920 | 476 | | 437957 | -31242 |
| 940 | 458.7 | | 431167.1 | -6789.8 |
| 960 | 455.7 | | 437465.7 | 6298.59 |
| 980 | 434.6 | | 425935.6 | -11530 |
| 1000 | 395.7 | | 395733.7 | -30202 |
| 1020 | 369.2 | | 376554.3 | -19179 |
| 1040 | 332 | | 345300.9 | -31253 |
| 1060 | 348.8 | | 369679 | 24378.1 |
| 1080 | 312.7 | | 337714.4 | -31965 |
| 1100 | 352 | | 387194.5 | 49480.1 |
3a3的迭代次数曲线没有发现峰值，在m=700处出现第一台阶，m=840处出现第二台阶
其比热曲线几乎就是单调减小的，在680处出现负值，和第一台阶位置接近，m>680后比热曲线波动剧烈
所谓物质不过是振动的微观结构，虽然这个结构没有发现相变点，但可能的原因很多，比如网络本身可能承载的温度不够等，这个现象不足以否定这个假设。
让A为3a2
|---|---|
| 1 | 0 |
| 1 | 0 |
| 1 | 0 |
得到数据为
|------|------------|---|----------|---------|
| m | n | | mn | Δmn |
| 20 | 33238.5879 | | 664771.8 | |
| 40 | 24326.4171 | | 973056.7 | 308285 |
| 60 | 21214.4171 | | 1272865 | 299808 |
| 80 | 19584.9698 | | 1566798 | 293933 |
| 100 | 18583.995 | | 1858399 | 291602 |
| 120 | 17865.8643 | | 2143904 | 285504 |
| 140 | 17326.7085 | | 2425739 | 281835 |
| 160 | 16962.4975 | | 2714000 | 288260 |
| 180 | 16640.5879 | | 2995306 | 281306 |
| 200 | 16396.9899 | | 3279398 | 284092 |
| 220 | 16182.005 | | 3560041 | 280643 |
| 240 | 16003.3518 | | 3840804 | 280763 |
| 260 | 15840.206 | | 4118454 | 277649 |
| 280 | 15704.0553 | | 4397135 | 278682 |
| 300 | 15580.5477 | | 4674164 | 277029 |
| 320 | 15484.7387 | | 4955116 | 280952 |
| 340 | 15373.4322 | | 5226967 | 271851 |
| 360 | 15281.1608 | | 5501218 | 274251 |
| 380 | 15190.0854 | | 5772232 | 271015 |
| 400 | 15117.3819 | | 6046953 | 274720 |
| 420 | 15048.206 | | 6320247 | 273294 |
| 440 | 14972.5075 | | 6587903 | 267657 |
| 460 | 14901.402 | | 6854645 | 266742 |
| 480 | 14842.3166 | | 7124312 | 269667 |
| 500 | 14776.7387 | | 7388369 | 264057 |
| 520 | 14718.8392 | | 7653796 | 265427 |
| 540 | 14667.0101 | | 7920185 | 266389 |
| 560 | 14617.6231 | | 8185869 | 265684 |
| 580 | 14563.1608 | | 8446633 | 260764 |
| 600 | 14512.1457 | | 8707287 | 260654 |
| 620 | 14466.9095 | | 8969484 | 262196 |
| 640 | 14421.9045 | | 9230019 | 260535 |
| 660 | 14375.3518 | | 9487732 | 257713 |
| 680 | 14327.6432 | | 9742797 | 255065 |
| 700 | 14284.9899 | | 9999493 | 256696 |
| 720 | 14233.1005 | | 10247832 | 248339 |
| 740 | 14190.2362 | | 10500775 | 252942 |
| 760 | 14139.6432 | | 10746129 | 245354 |
| 780 | 14092.5779 | | 10992211 | 246082 |
| 800 | 14041.5628 | | 11233250 | 241039 |
| 820 | 13988.598 | | 11470650 | 237400 |
| 840 | 13935.8844 | | 11706143 | 235493 |
| 860 | 7140.65327 | | 6140962 | -6E+06 |
| 880 | 7375.29146 | | 6490256 | 349295 |
| 900 | 7535.56784 | | 6782011 | 291755 |
| 920 | 7011.05025 | | 6450166 | -331845 |
| 940 | 6888.9397 | | 6475603 | 25437.1 |
| 960 | 6642.11558 | | 6376431 | -99172 |
| 980 | 7658.29146 | | 7505126 | 1128695 |
| 1000 | 8069.37186 | | 8069372 | 564246 |
| 1020 | 5746.82412 | | 5861761 | -2E+06 |
| 1040 | 7214.81407 | | 7503407 | 1641646 |
| 1060 | 7154.07538 | | 7583320 | 79913.3 |
| 1080 | 7026.27136 | | 7588373 | 5053.17 |
| 1100 | 6179.37186 | | 6797309 | -791064 |
迭代次数曲线为
这条曲线数值几乎单调减小，在m=860处出现第一台阶
比热曲线也是单调减小的，在m=860处出现负值
让A为3a5
|---|---|---|---|---|---|----------|----------|
| 0 | 0 || 1 | ||||
| 0 | 1 || 0 | ||||
| 1 | 0 || 0 | ||||
| m || n ||| | mn | Δmn |
| 30 || 38607 ||| | 1158196 | |
| 20 || 44354 ||| | 887080.1 | |
| 40 || 35519 ||| | 1420741 | 533661 |
| 60 || 32169 ||| | 1930148 | 509407.3 |
| 80 || 30494 ||| | 2439526 | 509377.6 |
| 100 || 29391 ||| | 2939081 | 499554.9 |
| 120 || 28604 ||| | 3432497 | 493416.6 |
| 140 || 28036 ||| | 3925046 | 492548.8 |
| 160 || 27610 ||| | 4417588 | 492541.6 |
| 180 || 27247 ||| | 4904502 | 486913.7 |
| 200 || 26963 ||| | 5392528 | 488026 |
| 220 || 26701 ||| | 5874169 | 481641.5 |
| 240 || 26526 ||| | 6366285 | 492115.5 |
| 260 || 26336 ||| | 6847254 | 480969.5 |
| 280 || 26194 ||| | 7334445 | 487191.1 |
| 300 || 26046 ||| | 7813814 | 479368.3 |
| 320 || 25933 ||| | 8298415 | 484601.7 |
| 340 || 25816 ||| | 8777572 | 479156.3 |
| 360 || 25703 ||| | 9252921 | 475349.2 |
| 380 || 25605 ||| | 9730068 | 477147.2 |
| 400 || 25504 ||| | 10201650 | 471582.2 |
| 420 || 25403 ||| | 10669281 | 467630.9 |
| 440 || 25330 ||| | 11145375 | 476093.6 |
| 460 || 25239 ||| | 11610120 | 464745.6 |
| 480 || 25159 ||| | 12076542 | 466421.6 |
| 500 || 25088 ||| | 12544133 | 467591.3 |
| 520 || 25007 ||| | 13003535 | 459402.3 |
| 540 || 24947 ||| | 13471228 | 467692.6 |
| 560 || 24877 ||| | 13931179 | 459951.1 |
| 580 || 24811 ||| | 14390150 | 458970.7 |
| 600 || 24743 ||| | 14845791 | 455641.2 |
| 620 || 24672 ||| | 15296528 | 450736.9 |
| 640 || 24617 ||| | 15755141 | 458612.7 |
| 660 || 24544 ||| | 16199319 | 444178.1 |
| 680 || 24485 ||| | 16649797 | 450478 |
| 700 || 24409 ||| | 17086272 | 436475.3 |
| 720 || 24343 ||| | 17527195 | 440923.3 |
| 740 || 24275 ||| | 17963411 | 436215.6 |
| 760 || 24205 ||| | 18395941 | 432530.6 |
| 780 || 24124 ||| | 18816896 | 420955.1 |
| 800 || 24049 ||| | 19239043 | 422146.8 |
| 820 || 23968 ||| | 19653669 | 414626.1 |
| 840 || 20046 ||| | 16838973 | -2814696 |
| 860 || 12994 ||| | 11174749 | -5664224 |
| 880 || 11538 ||| | 10153294 | -1021455 |
| 900 || 11708 ||| | 10536770 | 383476.3 |
| 920 || 12679 ||| | 11664245 | 1127475 |
| 940 || 13394 ||| | 12589892 | 925646.9 |
| 960 || 11332 ||| | 10878947 | -1710946 |
| 980 || 15018 ||| | 14717492 | 3838546 |
| 1000 || 12860 ||| | 12859638 | -1857854 |
| 1020 || 11874 ||| | 12111987 | -747651 |
| 1040 || 11414 ||| | 11870764 | -241224 |
| 1060 || 13114 ||| | 13900494 | 2029730 |
| 1080 || 10756 ||| | 11616491 | -2284003 |
| 1100 || 12201 ||| | 13421083 | 1804593 |
迭代次数曲线在860处出现第一台阶
比热曲线在840处出现负值
让A为3a6
|---|---|---|
| 1 | 1 | 1 |
得到数据
|------|---------|---|---------|---------|
| m | n | | mn | Δmn |
| 30 | 20689 | | 620669 | |
| 20 | 26897.8 | | 537956 | |
| 40 | 17725.9 | | 709034 | 171078 |
| 60 | 14857.7 | | 891462 | 182427 |
| 80 | 13315.7 | | 1065254 | 173792 |
| 100 | 12354 | | 1235405 | 170151 |
| 120 | 11755.6 | | 1410669 | 175264 |
| 140 | 11289.4 | | 1580512 | 169843 |
| 160 | 10900.1 | | 1744014 | 163502 |
| 180 | 10618.7 | | 1911371 | 167357 |
| 200 | 10401.6 | | 2080315 | 168943 |
| 220 | 10204.7 | | 2245038 | 164724 |
| 240 | 10034.6 | | 2408306 | 163268 |
| 260 | 9896.56 | | 2573105 | 164799 |
| 280 | 9776.91 | | 2737535 | 164430 |
| 300 | 9661.93 | | 2898580 | 161046 |
| 320 | 9556.29 | | 3058012 | 159431 |
| 340 | 9464.4 | | 3217895 | 159883 |
| 360 | 9388.75 | | 3379950 | 162055 |
| 380 | 9302.08 | | 3534789 | 154839 |
| 400 | 9243.57 | | 3697429 | 162641 |
| 420 | 9172.18 | | 3852314 | 154885 |
| 440 | 9111.93 | | 4009251 | 156937 |
| 460 | 9054.57 | | 4165101 | 155850 |
| 480 | 8992.27 | | 4316288 | 151187 |
| 500 | 8946.68 | | 4473339 | 157051 |
| 520 | 8901.75 | | 4628912 | 155573 |
| 540 | 8850.82 | | 4779442 | 150530 |
| 560 | 8805.22 | | 4930924 | 151482 |
| 580 | 8768.75 | | 5085874 | 154950 |
| 600 | 8719.08 | | 5231448 | 145574 |
| 620 | 8679.8 | | 5381478 | 150030 |
| 640 | 8645.63 | | 5533205 | 151727 |
| 660 | 8606.75 | | 5680454 | 147249 |
| 680 | 8568.45 | | 5826544 | 146090 |
| 700 | 8532.86 | | 5973002 | 146457 |
| 720 | 8498.69 | | 6119056 | 146054 |
| 740 | 8458.86 | | 6259556 | 140500 |
| 760 | 8422.91 | | 6401411 | 141855 |
| 780 | 8387.12 | | 6541954 | 140543 |
| 800 | 8344.63 | | 6675703 | 133748 |
| 820 | 8307.66 | | 6812284 | 136581 |
| 840 | 8269.22 | | 6946146 | 133862 |
| 860 | 4415.72 | | 3797522 | -3E+06 |
| 880 | 3742.87 | | 3293725 | -503797 |
| 900 | 3756.39 | | 3380753 | 87027.7 |
| 920 | 4807.84 | | 4423212 | 1042459 |
| 940 | 4053.53 | | 3810321 | -612891 |
| 960 | 4066.19 | | 3903543 | 93222.6 |
| 980 | 3989.43 | | 3909644 | 6100.2 |
| 1000 | 4273.41 | | 4273412 | 363769 |
| 1020 | 4044.12 | | 4125003 | -148409 |
| 1040 | 3811.91 | | 3964391 | -160612 |
| 1060 | 4240.14 | | 4494544 | 530153 |
| 1080 | 4308.75 | | 4653454 | 158910 |
| 1100 | 3807.58 | | 4188336 | -465118 |
迭代次数曲线在860处出现第一台阶
比热曲线在860处出现第一个负值
综合前面的数据
|-----|------|-----|------|------|-----|-----|-----|
| | 迭代次数 | | | | 比热 | | |
| | 极小值 | 峰 | 第一台阶 | 第二台阶 | 极小值 | 极大值 | 负值 |
| 3a1 | 260 | 380 | 760 | 860 | 40 | 340 | 580 |
| 3a2 | | | 860 | | | | 860 |
| 3a3 | | | 700 | 840 | | | 680 |
| 3a4 | 360 | 620 | 680 | 900 | 240 | 620 | 680 |
| 3a5 | | | 860 | | | | 840 |
| 3a6 | | | 860 | | | | 860 |
3点结构只有6个，其中只有1，4有峰值，2，5，6没有峰值似乎是可以理解的，因为2，5，6就是3条直线。但是3a3也没有峰值
这两个结构有峰值
这个结构没有峰值
所以由此推测迭代次数曲线产生峰值的可能条件是同时有2a2和2a3.如果把迭代次数曲线的峰值理解为相变，则2a2，2a3的存在就是结构与结构之间成键的条件。