制作一个2*2*1无偏置的神经网络,输入分别是(0,0),(0,1),(1,0),(1,1)输出是0,1,1,0.实现XOR,并观察权重和损失函数的变化规律,

得到的权重

4886 H(输入) I(权重w1) J K(权重w2) L(输出)
4887 0 68.22722811 0.5 173.0133239 0.000448325
4888 * 0.911665381
4889 0 68.69855536 0.5 -188.4324098
4890 * 2.095660806
4891
4892 0 68.22722811 1 173.0133239 0.99461049
4893 * 0.911665381
4894 1 68.69855536 0.8904807 -188.4324098
4895 * 2.095660806
4896
4897 1 68.22722811 1 173.0133239 1
4898 * 0.911665381
4899 0 68.69855536 0.7133408 -188.4324098
4900 * 2.095660806
4901
4902 1 68.22722811 1 173.0133239 0.001435689
4903 * 0.911665381
4904 1 68.69855536 0.952904 -188.4324098
4905 * 2.095660806

得到的权重

w1[0][0]=68.22722811

w1[0][1]=0.911665381

w1[1][0]=68.69855536

w1[1][1]= 2.095660806

w2[0][0]= 173.013323903306

w2[1][0]= -188.43240978341

J4902的公式1/(1+EXP(1)^((-1)*(H4902*I4902+H4904*I4904)))

J4904的公式1/(1+EXP(1)^((-1)*(H4902*I4903+H4904*I4905)))

L4902的公式1/(1+EXP(1)^((-1)*(J4902*K4902+J4904*K4904)))

将收敛标准设为while(loss-0>0.0001),经过399迭代收敛,

W1[0][0]和w1[1][0]的曲线几乎重合

W2[0][0]和w2[1][0]的曲线几乎对称

最为奇怪的是w1[0][1]和w1[1][1]的曲线

损失函数的曲线

从这几幅图可以发现当迭代到81次左右的时候w1[0][1]和w1[1][1]的振动周期明显减小,振动加剧,同时损失函数大幅下降

具体数据

* w1[0][0] w1[1][0] w1[0][1] w1[1][1] w2[0][0] w2[1][0] 损失函数
初始权重 0.949609027 0.818490121 0.3832673 0.736533972 0.351438625 0.2005728
1 0.94987092 0.818938285 0.3828907 0.735922277 0.322665373 0.1721161 0.5685667
2 0.950503671 0.819935343 0.382281 0.734873478 0.268379448 0.1181614 0.5615342
3 0.951652226 0.82160748 0.3816298 0.733640083 0.194808679 0.044354 0.5481678
4 0.953382707 0.823988403 0.3810247 0.732397351 0.110537408 -0.041536 0.5298598
5 0.955580564 0.826916143 0.3803092 0.731097725 0.025578049 -0.130462 0.5086243
6 0.957919047 0.830004663 0.3790303 0.729407813 -0.049793437 -0.213163 0.4868925
7 0.959926768 0.832720058 0.3765114 0.726767826 -0.106264035 -0.281269 0.4671778
8 0.961134323 0.834539591 0.3720306 0.72255477 -0.136567583 -0.328286 0.4517094
9 0.961240323 0.835130146 0.3650353 0.716282275 -0.136277408 -0.350306 0.4421535
10 0.960228852 0.834474276 0.3553088 0.707758354 -0.104250423 -0.346396 0.4394754
11 0.958391601 0.832894629 0.3430318 0.697144857 -0.042724427 -0.31867 0.4439064
12 0.956244296 0.830965817 0.3287191 0.684901058 0.042922321 -0.272045 0.4549482
13 0.954366383 0.829343958 0.3130578 0.671635059 0.144749848 -0.213683 0.4713909
14 0.953224997 0.828577859 0.2967097 0.657921921 0.253152021 -0.152165 0.4913842
15 0.953054217 0.828976737 0.2801571 0.644162678 0.357977631 -0.096466 0.5126207
16 0.953836863 0.830584987 0.2636472 0.630539521 0.449708352 -0.054916 0.5326424
17 0.955387506 0.833263637 0.2472451 0.617073666 0.520504073 -0.034288 0.5491895
18 0.957491122 0.836831466 0.2309483 0.603742102 0.564983513 -0.03915 0.5604795
19 0.960036147 0.841201789 0.2147955 0.590585794 0.580698285 -0.071494 0.5653531
20 0.963093441 0.846463986 0.1989104 0.577751311 0.568319115 -0.130623 0.5633089
21 0.966918835 0.852886149 0.1834527 0.565438348 0.531559881 -0.213274 0.5544947
22 0.971884501 0.860844164 0.168488 0.553764694 0.476840318 -0.313954 0.539702
23 0.978369058 0.870708679 0.1538267 0.542598803 0.412673181 -0.425509 0.5203495
24 0.98665356 0.88273974 0.1389076 0.531435505 0.348788085 -0.539886 0.4983955
25 0.996870895 0.897039254 0.1227951 0.519385495 0.295070978 -0.649039 0.476131
26 1.009032922 0.913586404 0.1043214 0.505307441 0.260464857 -0.745846 0.4558691
27 1.023121056 0.932339958 0.0823396 0.488052085 0.251993881 -0.824897 0.4396234
28 1.039194037 0.953357526 0.0560161 0.466744705 0.274027882 -0.883061 0.4288728
29 1.057458915 0.976874185 0.0250741 0.441024905 0.32783629 -0.919779 0.4244537
30 1.078269344 1.00330223 -0.010072 0.411183517 0.411438612 -0.937068 0.4265427
31 1.102048502 1.033148602 -0.048325 0.378167977 0.519756825 -0.939261 0.4346719
32 1.129169074 1.066883235 -0.088042 0.34346102 0.645086366 -0.932471 0.4477534
33 1.159845973 1.104816632 -0.127269 0.308871113 0.777884775 -0.923863 0.4641386
34 1.194094957 1.147044048 -0.163977 0.276298942 0.907812929 -0.920816 0.4817608
35 1.231778825 1.193482378 -0.19626 0.247545549 1.024884653 -0.930114 0.4983746
36 1.272719541 1.243980233 -0.22244 0.224196806 1.120547202 -0.957293 0.5118442
37 1.316826753 1.298450423 -0.241102 0.207572189 1.18855749 -1.006208 0.5203954
38 1.364194084 1.356972594 -0.251115 0.198691861 1.2256036 -1.078788 0.5227779
39 1.415135087 1.41983425 -0.251684 0.198210526 1.231686556 -1.174941 0.5183437
40 1.470154376 1.487503441 -0.242475 0.206286354 1.210287176 -1.292559 0.5070927
41 1.529867289 1.560546299 -0.223804 0.222390575 1.168300945 -1.427604 0.4897175
42 1.594893717 1.639516843 -0.196848 0.245113323 1.115662855 -1.574328 0.4676325
43 1.665759812 1.724856057 -0.163765 0.272072999 1.064554257 -1.725695 0.4429168
44 1.742841125 1.816836896 -0.127588 0.30005733 1.028138553 -1.874071 0.4181018
45 1.82636498 1.915573395 -0.091804 0.325470647 1.018923492 -2.012182 0.3958072
46 1.91645935 2.021077892 -0.059648 0.345034938 1.047014562 -2.134212 0.3783331
47 2.013207613 2.133321603 -0.033289 0.356572263 1.118581577 -2.236822 0.3673509
48 2.116665873 2.25225405 -0.013124 0.359665811 1.234787261 -2.319893 0.363751
49 2.226827127 2.377767689 0.0026124 0.356040086 1.391343179 -2.386804 0.3675939
50 2.343557065 2.509634776 0.0178126 0.349546839 1.578857474 -2.444145 0.3780742
51 2.466552091 2.647467295 0.0379664 0.345690795 1.784124481 -2.500831 0.3934951
52 2.59535963 2.790738891 0.0692356 0.350740459 1.992289715 -2.566748 0.4113582
53 2.729457953 2.938864747 0.1173429 0.370619275 2.189438709 -2.651271 0.4286823
54 2.868354255 3.091297012 0.1865019 0.409806688 2.364963167 -2.761978 0.4425261
55 3.011658016 3.247592525 0.2784593 0.470351353 2.513276357 -2.903652 0.4505355
56 3.159111739 3.407436493 0.3916579 0.551022879 2.634803034 -3.077463 0.4513573
57 3.310582332 3.570628567 0.5207301 0.646810351 2.736248469 -3.280261 0.4448923
58 3.466022143 3.737044231 0.6568247 0.749247079 2.82991898 -3.504335 0.4324146
59 3.625409379 3.906583965 0.7891075 0.84787341 2.931727059 -3.738276 0.4164878
60 3.788683644 4.07912423 0.9070043 0.932401054 3.057944884 -3.969309 0.4005259
61 3.955697626 4.254484306 1.0022032 0.994643717 3.22155972 -4.186498 0.3880106
62 4.126197871 4.432414901 1.0697862 1.029656066 3.429345922 -4.383643 0.3816692
63 4.299831994 4.612604666 1.108561 1.036168867 3.680286384 -4.561025 0.3829257
64 4.476174326 4.794699403 1.120929 1.016606395 3.96550027 -4.725669 0.391653
65 4.654766111 4.978332242 1.1124516 0.976765796 4.269752884 -4.89005 0.4061066
66 4.835165251 5.163160667 1.0910451 0.925030505 4.574468845 -5.069409 0.4230784
67 5.016991697 5.348898514 1.065721 0.871052792 4.86156088 -5.27841 0.4384464
68 5.199952822 5.53533088 1.044959 0.824064378 5.116903345 -5.528258 0.4480816
69 5.383845159 5.722310888 1.0348956 0.791063906 5.332656072 -5.824909 0.4487612
70 5.56854096 5.909746506 1.0375469 0.775093761 5.508443416 -6.168308 0.4387772
71 5.753969022 6.097585361 1.0494166 0.773907861 5.651664366 -6.55227 0.4182571
72 5.940093686 6.285800552 1.0611383 0.77960579 5.776760231 -6.96507 0.3892887
73 6.1268922 6.474376977 1.0589026 0.779945346 5.902741229 -7.391365 0.3556821
74 6.314332704 6.663298012 1.027797 0.761578007 6.048663171 -7.815845 0.322062
75 6.502359133 6.852535231 0.9562885 0.71462116 6.228120161 -8.227752 0.2924342
76 6.690887641 7.04204495 0.8413117 0.637796129 6.44459138 -8.624573 0.2689776
77 6.879813965 7.231772896 0.6943163 0.543668201 6.689071338 -9.013415 0.25162
78 7.069030299 7.421665151 0.5462895 0.46181253 6.941697358 -9.408673 0.2382728
79 7.258447949 7.611680356 0.441565 0.431664114 7.180038399 -9.825067 0.2255716
80 7.448012062 7.801796489 0.4122986 0.478111913 7.392483835 -10.26921 0.2104003
81 7.637699594 7.992010378 0.4521815 0.585791578 7.588033299 -10.73486 0.1917986
82 7.827507765 8.182331311 0.5155915 0.698274719 7.795629128 -11.20261 0.1717303
83 8.017438035 8.372767254 0.5503337 0.753973822 8.048066703 -11.64912 0.1540097
84 8.20748141 8.563312146 0.5301572 0.721471802 8.362026217 -12.06186 0.1417868
85 8.397615111 8.753944705 0.4676911 0.612418628 8.728848142 -12.44698 0.1358829
86 8.587811396 8.944636079 0.4182337 0.489006346 9.116416937 -12.82711 0.1348122
87 8.778050367 9.135362795 0.4540081 0.438134135 9.488597483 -13.22614 0.1352463
88 8.968325521 9.326113815 0.5915127 0.491828165 9.835121966 -13.65062 0.1336842
89 9.158641351 9.516887126 0.7595328 0.595892367 10.18024044 -14.08477 0.129234
90 9.349005146 9.707683842 0.8668595 0.675340681 10.56039032 -14.50245 0.1243065
91 9.53941648 9.898502958 0.8705321 0.694321517 10.99450175 -14.88882 0.1222784
92 9.729865161 10.08933979 0.7841149 0.663410363 11.47371613 -15.25015 0.1248632
93 9.920336734 10.28018832 0.6741655 0.634974064 11.96600759 -15.61025 0.1314481
94 10.11082041 10.47104437 0.6294378 0.678854418 12.43604771 -15.99473 0.1391797
95 10.3013116 10.66190654 0.6851747 0.815134094 12.87167277 -16.41239 0.1443842
96 10.49180947 10.85277561 0.7965204 0.983553503 13.29075627 -16.85044 0.1454976
97 10.68231461 11.04365317 0.900369 1.105499924 13.72292182 -17.28609 0.1443225
98 10.87282734 11.23453961 0.9593665 1.137424773 14.18811445 -17.70308 0.1441074
99 11.06334678 11.4254334 0.9667774 1.078627849 14.68689038 -18.10057 0.1471061
100 11.25387117 11.6163319 0.9441944 0.966656895 15.20100911 -18.49312 0.1535742
101 11.4443988 11.80723282 0.9348288 0.863984002 15.70324482 -18.90241 0.1616427
102 11.63492866 11.99813495 0.9823221 0.828183868 16.17184838 -19.3455 0.1680401
103 11.82546047 12.18903786 1.0908287 0.873864988 16.60278294 -19.82554 0.169831
104 12.01599451 12.37994149 1.2147224 0.968152161 17.01099586 -20.33059 0.1663976
105 12.20653124 12.57084595 1.2961683 1.066357371 17.41931781 -20.84192 0.159789
106 12.39707077 12.76175139 1.29769 1.134432368 17.84592733 -21.34424 0.1529952
107 12.58761264 12.95265781 1.2140371 1.155056345 18.29619783 -21.83294 0.1481539
108 12.77815598 13.14356508 1.073635 1.132335467 18.76045407 -22.316 0.145745
109 12.96870002 13.33447295 0.9285891 1.093423702 19.21955727 -22.80904 0.1445786
110 13.15924436 13.52538123 0.8362033 1.081544365 19.65413123 -23.32768 0.1424923
111 13.34978886 13.71628983 0.8327137 1.125454564 20.05444015 -23.87952 0.1374335
112 13.54033348 13.90719876 0.9044747 1.200381709 20.42841108 -24.45792 0.1286959
113 13.73087826 14.09810806 1.0068382 1.246089654 20.79606099 -25.04631 0.1176625
114 13.92142327 14.28901778 1.0965795 1.215523626 21.17608449 -25.62917 0.1066785
115 14.11196857 14.47992781 1.1399131 1.101535086 21.57683053 -26.19959 0.0973921
116 14.30251417 14.67083802 1.1233025 0.939540405 21.99333222 -26.76154 0.0901849
117 14.49306001 14.86174831 1.0682735 0.786521622 22.4113075 -27.32638 0.0843931
118 14.68360601 15.05265862 1.031871 0.705909453 22.81298331 -27.90825 0.078889
119 14.87415213 15.24356894 1.0567008 0.739495446 23.18855407 -28.51471 0.0725858
120 15.06469836 15.43447927 1.0977892 0.852955653 23.54963838 -29.13631 0.0651875
121 15.25524473 15.62538963 1.0825257 0.983137686 23.91624946 -29.75687 0.0576853
122 15.4457912 15.81630004 0.9859633 1.072095382 24.30141549 -30.36594 0.0511587
123 15.63633773 16.00721051 0.8392662 1.073393845 24.70754981 -30.96153 0.0459894
124 15.82688429 16.19812104 0.6976157 0.995328003 25.12522375 -31.55093 0.0420075
125 16.01743085 16.3890316 0.6337854 0.924284049 25.53399806 -32.15016 0.038685
126 16.20797742 16.57994218 0.712757 0.944740015 25.91821424 -32.77133 0.035295
127 16.39852399 16.77085277 0.8663099 0.983409204 26.29316524 -33.40234 0.0314757
128 16.58907058 16.96176339 1.0038453 0.956903378 26.67991833 -34.02662 0.0277983
129 16.77961719 17.15267402 1.0397285 0.855936751 27.09172608 -34.63385 0.0247625
130 16.97016384 17.34358466 0.9466397 0.725206439 27.52629303 -35.22566 0.0225093
131 17.16071051 17.5344953 0.8233087 0.635569581 27.9620648 -35.81872 0.0208428
132 17.35125718 17.72540594 0.8290412 0.706448513 28.37226611 -36.4336 0.0192969
133 17.54180385 17.91631659 0.9004929 0.869787535 28.76865685 -37.06113 0.0174525
134 17.73235053 18.10722723 0.9240019 0.99965291 29.1760319 -37.68212 0.0155774
135 17.92289722 18.29813789 0.864626 0.990465874 29.61244752 -38.28274 0.0140215
136 18.11344391 18.48904855 0.7575055 0.851537825 30.07176345 -38.86758 0.0129306
137 18.30399061 18.67995922 0.6832131 0.716475272 30.52934941 -39.45541 0.0121535
138 18.4945373 18.87086988 0.787075 0.754960546 30.95930528 -40.06606 0.011396
139 18.685084 19.06178055 0.9402822 0.850522171 31.38123817 -40.68441 0.0104218
140 18.87563069 19.25269121 1.0021957 0.907613551 31.8189078 -41.29223 0.0094562
141 19.0661774 19.44360188 0.9048242 0.885614854 32.28525944 -41.8797 0.0086916
142 19.2567241 19.63451255 0.740666 0.808180504 32.76590843 -42.45764 0.0081851
143 19.44727081 19.82542322 0.6290485 0.767174328 33.24042262 -43.0416 0.0077995
144 19.63781751 20.01633389 0.6994403 0.890757017 33.69019754 -43.64589 0.0073872
145 19.82836422 20.20724456 0.8118225 1.001149123 34.13949767 -44.25178 0.0068418
146 20.01891092 20.39815523 0.9026929 0.967708619 34.60767004 -44.84444 0.0063298
147 20.20945763 20.5890659 0.9302706 0.822510254 35.09508837 -45.42361 0.0059501
148 20.40000434 20.77997657 0.8907625 0.661886542 35.59173182 -45.99679 0.0056848
149 20.59055104 20.97088725 0.8647202 0.56543348 36.08404787 -46.5744 0.0054725
150 20.78109775 21.16179792 0.9617299 0.632443521 36.55780127 -47.16755 0.0052452
151 20.97164446 21.35270859 1.0183029 0.749928774 37.03345693 -47.76033 0.0049428
152 21.16219116 21.54361926 0.9463302 0.871250327 37.52285369 -48.34349 0.0046629
153 21.35273787 21.73452993 0.8097573 0.965787499 38.0216383 -48.92033 0.0044503
154 21.54328458 21.92544061 0.6696492 0.991454752 38.52808864 -49.4921 0.0042807
155 21.73383129 22.11635128 0.5623405 0.955306984 39.03920119 -50.06119 0.0041437
156 21.924378 22.30726195 0.5619275 0.960832745 39.54213415 -50.63769 0.0040258
157 22.1149247 22.49817262 0.6686638 1.009458623 40.03679881 -51.22167 0.003881
158 22.30547141 22.68908329 0.8081175 0.998345048 40.5357538 -51.80316 0.0037121
159 22.49601812 22.87999397 0.9498439 0.920272728 41.04127989 -52.38026 0.0035626
160 22.68656483 23.07090464 1.0530908 0.815877538 41.55293957 -52.95324 0.0034378
161 22.87711154 23.26181531 1.0502067 0.710447056 42.07517876 -53.51869 0.0033343
162 23.06765825 23.45272598 0.9656251 0.624447043 42.60425351 -54.07952 0.0032633
163 23.25820495 23.64363666 0.9244299 0.622934482 43.12586879 -54.64701 0.003212
164 23.44875166 23.83454733 0.9832946 0.745616361 43.6337868 -55.22608 0.0031394
165 23.63929837 24.025458 1.0321749 0.897590454 44.14106417 -55.80624 0.00303
166 23.82984508 24.21636867 1.024316 1.041453287 44.65425308 -56.3823 0.0029219
167 24.02039179 24.40727935 0.9643003 1.12285767 45.17778666 -56.95086 0.0028318
168 24.21093849 24.59819002 0.8801928 1.076476396 45.71538922 -57.50899 0.0027689
169 24.4014852 24.78910069 0.7939593 0.960925834 46.25945464 -58.06252 0.0027407
170 24.59203191 24.98001136 0.7390852 0.859485783 46.80062316 -58.61881 0.0027278
171 24.78257862 25.17092204 0.8095335 0.879111295 47.32673624 -59.18773 0.0027073
172 24.97312533 25.36183271 0.9427325 0.957960199 47.84500448 -59.76339 0.0026501
173 25.16367204 25.55274338 1.0772126 1.035824953 48.36333116 -60.33935 0.0025753
174 25.35421874 25.74365405 1.1663956 1.085758176 48.88786005 -60.91082 0.0025024
175 25.54476545 25.93456473 1.1467106 1.088380511 49.42620492 -61.47189 0.0024445
176 25.73531216 26.1254754 1.0459757 1.047529078 49.97534097 -62.02488 0.0024169
177 25.92585887 26.31638607 0.9243413 0.985339615 50.5278774 -62.5755 0.0024123
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381 64.79738736 65.26216325 1.7415012 1.543943042 163.1392057 -178.088 5.74E-04
382 64.98793407 65.45307393 1.6927139 1.577671088 163.6881282 -178.6623 5.67E-04
383 65.17848078 65.6439846 1.6440895 1.611569576 164.2369888 -179.2366 5.60E-04
384 65.36902749 65.83489527 1.5956527 1.645657029 164.7857854 -179.8111 5.53E-04
385 65.5595742 66.02580594 1.5474263 1.679953216 165.3345156 -180.3856 5.46E-04
386 65.75012091 66.21671662 1.4994339 1.714478514 165.883177 -180.9601 5.39E-04
387 65.94066761 66.40762729 1.4517006 1.749252492 166.431767 -181.5348 5.32E-04
388 66.13121432 66.59853796 1.4042536 1.784290994 166.9802832 -182.1095 5.25E-04
389 66.32176103 66.78944863 1.3571217 1.819600302 167.5287235 -182.6843 5.18E-04
390 66.51230774 66.98035931 1.3103358 1.85516565 168.0770867 -183.2591 5.11E-04
391 66.70285445 67.17126998 1.263928 1.890929037 168.6253736 -183.8341 5.05E-04
392 66.89340116 67.36218065 1.2179325 1.926747197 169.1735893 -184.4091 4.98E-04
393 67.08394786 67.55309132 1.1723848 1.962314449 169.7217471 -184.9841 4.91E-04
394 67.27449457 67.744002 1.1273236 1.99702903 170.2698758 -185.5592 4.85E-04
395 67.46504128 67.93491267 1.0827928 2.029786509 170.8180311 -186.1343 4.78E-04
396 67.65558799 68.12582334 1.0388482 2.058735505 171.3663097 -186.7093 4.72E-04
397 67.8461347 68.31673401 0.9955709 2.081191955 171.9148549 -187.2841 4.66E-04
398 68.03668141 68.50764469 0.953095 2.094147855 172.4638275 -187.8585 4.60E-04
399 68.22722811 68.69855536 0.9116654 2.095660806 173.0133239 -188.4324 4.54E-04

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