是否所有二分类神经网络的准确率都能无限趋近100%？
制作一個二分類的神經網絡驗證是否只要經過足夠的迭代都能使準確率無限上升并接近1。
| r1 | r2 | ? | ? |
| <1 | <1 | 吸引子 | c |
| >1 | >1 | 排斥子 | p |
| >1 | <1 | 鞍點 | a |
| <1 | >1 | 反鞍點 | fa |
d2（c，p）-4-4-2-（2*k）,k∈{0,1}
d2（c，a）-4-4-2-（2*k）,k∈{0,1}
d2（c，fa）-4-4-2-（2*k）,k∈{0,1}
d2（p，a）-4-4-2-（2*k）,k∈{0,1}
d2（p，fa）-4-4-2-（2*k）,k∈{0,1}
d2（a，fa）-4-4-2-（2*k）,k∈{0,1}
本次實驗構造了6個網絡分別二分類cp,ca,cfa,pa,pfa,afa。
實驗過程
以二分類吸引子和排斥子為例子
d2（c，p）-4-4-2-（2*k）,k∈{0,1}
制作一個4*4*2的網絡向這個的左側輸入吸引子，并讓左側網絡向1，0收斂；向右側網絡輸入排斥子讓右側向0，1收斂，并讓4*4*2部分權重共享，，前面大量實驗表明這種效果相當于將兩個彈性系數為k1，k2的彈簧并聯成一個彈性系數為k的彈簧，并且讓k1=k2=k/2的過程。
?
這個網絡的收斂標準是
if (Math.abs(f2[0]-y[0])< δ? &&? Math.abs(f2[1]-y[1])< δ?? )
因為對應每個收斂標準δ都有一個特征的迭代次數n與之對應因此可以用迭代次數曲線n(δ)來評價網絡性能。
本文嘗試了δ從0.5到1e-6在內的26個值.
| 具體進樣順序 | ? | ? |
| 進樣順序 | 迭代次數 | ? |
| δ=0.5 | ? | ? |
| c | 1 | 判斷是否達到收斂 |
| p | 2 | 判斷是否達到收斂 |
| 梯度下降 | ? | ? |
| c | 3 | 判斷是否達到收斂 |
| p | 4 | 判斷是否達到收斂 |
| 梯度下降 | ? | ? |
| …… | ? | ? |
| 達到收斂標準測量準確率,記錄迭代次數，將這個過程重復199次 | ? | |
| δ=0.4 | ? | ? |
| … | ? | ? |
| δ=1e-6 | ? | ? |
將這個網絡簡寫成
d2（c，p）-4-4-2-（2*k）,k∈{0,1}
得到的數據
| cp | ? | ? | ? | ? | ? | ? | ? | ? |
| 測試集 | 0.3 | c | ? | ? | ? | ? | ? | ? |
| ? | 0.7 | p | ? | ? | ? | ? | ? | ? |
| f2[0] | f2[1] | 迭代次數n | 平均準確率p-ave | δ | 耗時ms/次 | 耗時ms/199次 | 耗時 min/199 | 最大準確率p-max |
| 0.499499 | 0.52977 | 149.2864 | 0.700283 | 0.5 | 2.050251 | 408 | 0.0068 | 0.736737 |
| 0.60013 | 0.404593 | 6191.251 | 0.978929 | 0.4 | 13.31156 | 2665 | 0.044417 | 0.993994 |
| 0.711649 | 0.293137 | 10058.88 | 0.991353 | 0.3 | 18.55779 | 3725 | 0.062083 | 1 |
| 0.810707 | 0.191481 | 15794.96 | 0.996972 | 0.2 | 27.67337 | 5507 | 0.091783 | 1 |
| 0.907472 | 0.09366 | 24295.35 | 0.993979 | 0.1 | 41.65829 | 8290 | 0.138167 | 1 |
| 0.99134 | 0.008736 | 59370.36 | 0.86567 | 0.01 | 98.75879 | 19653 | 0.32755 | 1 |
| 0.999168 | 8.37E-04 | 116218.8 | 0.632869 | 0.001 | 193.5276 | 38512 | 0.641867 | 0.978979 |
| 0.999918 | 8.26E-05 | 213160.8 | 0.534097 | 1.00E-04 | 353.3568 | 70318 | 1.171967 | 0.928929 |
| 0.999926 | 7.41E-05 | 212890.8 | 0.540621 | 9.00E-05 | 353.4271 | 70332 | 1.1722 | 0.891892 |
| 0.999934 | 6.58E-05 | 216429.1 | 0.55042 | 8.00E-05 | 359.8945 | 71635 | 1.193917 | 0.905906 |
| 0.999944 | 5.66E-05 | 227994 | 0.534218 | 7.00E-05 | 379.3015 | 75512 | 1.258533 | 0.933934 |
| 0.999952 | 4.87E-05 | 238336.1 | 0.521904 | 6.00E-05 | 393.8492 | 78376 | 1.306267 | 0.863864 |
| 0.99996 | 4.05E-05 | 256301.7 | 0.507533 | 5.00E-05 | 423.5678 | 84291 | 1.40485 | 0.84985 |
| 0.999967 | 3.32E-05 | 272096.3 | 0.523715 | 4.00E-05 | 451.9347 | 89935 | 1.498917 | 0.850851 |
| 0.999976 | 2.46E-05 | 283245.7 | 0.505737 | 3.00E-05 | 391.5779 | 77941 | 1.299017 | 0.800801 |
| 0.999984 | 1.62E-05 | 320385.5 | 0.491366 | 2.00E-05 | 533.608 | 106188 | 1.7698 | 0.798799 |
| 0.999992 | 7.92E-06 | 362938.1 | 0.499625 | 1.00E-05 | 602.6432 | 119942 | 1.999033 | 0.828829 |
| 0.999993 | 7.22E-06 | 379786.3 | 0.492769 | 9.00E-06 | 631.7085 | 125710 | 2.095167 | 0.757758 |
| 0.999994 | 6.41E-06 | 391093.6 | 0.485304 | 8.00E-06 | 650.3668 | 129439 | 2.157317 | 0.747748 |
| 0.999994 | 5.58E-06 | 396418.2 | 0.48787 | 7.00E-06 | 667.5075 | 132850 | 2.214167 | 0.722723 |
| 0.999995 | 4.71E-06 | 401244.4 | 0.494746 | 6.00E-06 | 678.4372 | 135009 | 2.25015 | 0.813814 |
| 0.999996 | 3.97E-06 | 439625.5 | 0.484474 | 5.00E-06 | 743.7889 | 148014 | 2.4669 | 0.754755 |
| 0.999997 | 3.16E-06 | 480586.6 | 0.472216 | 4.00E-06 | 810.5377 | 161297 | 2.688283 | 0.765766 |
| 0.999998 | 2.37E-06 | 482990.6 | 0.483745 | 3.00E-06 | 810.3819 | 161266 | 2.687767 | 0.762763 |
| 0.999998 | 1.59E-06 | 555404.6 | 0.469817 | 2.00E-06 | 933.8191 | 185831 | 3.097183 | 0.724725 |
| 0.999999 | 7.75E-07 | 621276.4 | 0.467452 | 1.00E-06 | 1045.342 | 208023 | 3.46705 | 0.712713 |
| ? | ? | ? | ? | ? | ? | ? | ? | ? |
| 0.943057 | 0.058565 | 268626.3 | 0.604142 | 0.058138 | 446.5611 | 88871.88 | 1.481198 | 0.851005 |
這個網絡的測試集有30%的c和70%的p
從數值上觀察很明顯準確率的平均值和最大值都沒有隨著收斂標準的減小而增大。平均值趨向于50%。
第二個網絡
d2（c，a）-4-4-2-（2*k）,k∈{0,1}
| ca | ? | ? | ? | ? | ? | ? | ? | ? |
| 測試集 | 0.3 | c | ? | ? | ? | ? | ? | ? |
| ? | 0.7 | a | ? | ? | ? | ? | ? | ? |
| f2[0] | f2[1] | 迭代次數n | 平均準確率p-ave | δ | 耗時ms/次 | 耗時ms/199次 | 耗時 min/199 | 最大準確率p-max |
| 0.499584 | 0.515973 | 181.6482 | 0.700867 | 0.5 | 2.165829 | 431 | 0.007183 | 0.88989 |
| 0.605006 | 0.400648 | 4185.683 | 0.936233 | 0.4 | 9.201005 | 1847 | 0.030783 | 0.972973 |
| 0.719815 | 0.284929 | 4950.729 | 0.914266 | 0.3 | 9.592965 | 1910 | 0.031833 | 0.942943 |
| 0.819668 | 0.185906 | 5621.844 | 0.898466 | 0.2 | 10.68844 | 2127 | 0.03545 | 0.936937 |
| 0.91303 | 0.089101 | 6358.879 | 0.879789 | 0.1 | 12.24121 | 2436 | 0.0406 | 0.923924 |
| 0.991778 | 0.008487 | 9141.543 | 0.860177 | 0.01 | 16.79397 | 3342 | 0.0557 | 0.906907 |
| 0.999184 | 8.34E-04 | 13441.74 | 0.852918 | 0.001 | 23.22111 | 4621 | 0.077017 | 0.918919 |
| 0.999918 | 8.29E-05 | 21858.25 | 0.856253 | 1.00E-04 | 37.16583 | 7413 | 0.12355 | 0.911912 |
| 0.999926 | 7.49E-05 | 22514.33 | 0.854769 | 9.00E-05 | 38.0804 | 7594 | 0.126567 | 0.907908 |
| 0.999935 | 6.62E-05 | 22933.27 | 0.85485 | 8.00E-05 | 38.64824 | 7691 | 0.128183 | 0.907908 |
| 0.999942 | 5.90E-05 | 23904.65 | 0.861882 | 7.00E-05 | 40.0804 | 8023 | 0.133717 | 0.921922 |
| 0.999951 | 4.98E-05 | 25076.15 | 0.858165 | 6.00E-05 | 42.8392 | 8525 | 0.142083 | 0.91992 |
| 0.999959 | 4.12E-05 | 25666.67 | 0.85815 | 5.00E-05 | 44.90452 | 8941 | 0.149017 | 0.913914 |
| 0.999968 | 3.19E-05 | 27387.46 | 0.856746 | 4.00E-05 | 46.67337 | 9288 | 0.1548 | 0.914915 |
| 0.999976 | 2.40E-05 | 30215.88 | 0.856283 | 3.00E-05 | 52.1206 | 10372 | 0.172867 | 0.90991 |
| 0.999984 | 1.63E-05 | 32900.33 | 0.857496 | 2.00E-05 | 56.1407 | 11173 | 0.186217 | 0.915916 |
| 0.999992 | 7.91E-06 | 40569.4 | 0.853557 | 1.00E-05 | 68 | 13532 | 0.225533 | 0.90991 |
| 0.999993 | 7.27E-06 | 41823.16 | 0.854558 | 9.00E-06 | 69.82412 | 13910 | 0.231833 | 0.914915 |
| 0.999993 | 6.55E-06 | 43123.77 | 0.852541 | 8.00E-06 | 72.23618 | 14375 | 0.239583 | 0.914915 |
| 0.999994 | 5.59E-06 | 45766.82 | 0.851057 | 7.00E-06 | 76.51759 | 15243 | 0.25405 | 0.924925 |
| 0.999995 | 4.84E-06 | 47956.51 | 0.851751 | 6.00E-06 | 80.61307 | 16057 | 0.267617 | 0.901902 |
| 0.999996 | 3.89E-06 | 51933.27 | 0.843939 | 5.00E-06 | 87.17085 | 17362 | 0.289367 | 0.908909 |
| 0.999997 | 3.26E-06 | 58216.54 | 0.840373 | 4.00E-06 | 96.90955 | 19285 | 0.321417 | 0.897898 |
| 0.999998 | 2.39E-06 | 67257.81 | 0.83659 | 3.00E-06 | 112.0503 | 22313 | 0.371883 | 0.906907 |
| 0.999998 | 1.60E-06 | 93343.57 | 0.823105 | 2.00E-06 | 155.2864 | 30902 | 0.515033 | 0.898899 |
| 0.999999 | 7.52E-07 | 136177.5 | 0.805584 | 1.00E-06 | 225.0302 | 44781 | 0.74635 | 0.892893 |
| ? | ? | ? | ? | ? | ? | ? | ? | ? |
| 0.944138 | 0.057168 | 34711.82 | 0.852706 | 0.058138 | 58.62292 | 11672.85 | 0.194547 | 0.914953 |
這個網絡的測試集有30%的c，70%的a
這個網路的準確率的平均值和最大值要比較第一個網絡高些，但也不是隨著δ的減小增加的。明顯的趨于一個定值。
第三個網絡
d2（c，fa）-4-4-2-（2*k）,k∈{0,1}
| cfa | ? | ? | ? | ? | ? | ? | ? | ? |
| 測試集 | 0.3 | c | ? | ? | ? | ? | ? | ? |
| ? | 0.7 | fa | ? | ? | ? | ? | ? | ? |
| f2[0] | f2[1] | 迭代次數n | 平均準確率p-ave | δ | 耗時ms/次 | 耗時ms/199次 | 耗時 min/199 | 最大準確率p-max |
| 0.499631 | 0.516258 | 181.5377 | 0.701043 | 0.5 | 2.040201 | 406 | 0.006767 | 0.736737 |
| 0.593787 | 0.409867 | 4247.367 | 0.932686 | 0.4 | 9.844221 | 1959 | 0.03265 | 0.962963 |
| 0.720905 | 0.28509 | 5066.859 | 0.914236 | 0.3 | 9.763819 | 1959 | 0.03265 | 0.955956 |
| 0.820136 | 0.183989 | 5560.809 | 0.895433 | 0.2 | 10.47236 | 2099 | 0.034983 | 0.935936 |
| 0.914333 | 0.088609 | 6510.085 | 0.882838 | 0.1 | 12.05025 | 2398 | 0.039967 | 0.926927 |
| 0.991791 | 0.008448 | 9125.794 | 0.860982 | 0.01 | 16.23116 | 3230 | 0.053833 | 0.910911 |
| 0.999171 | 8.42E-04 | 13343.48 | 0.856148 | 0.001 | 22.82412 | 4542 | 0.0757 | 0.912913 |
| 0.999918 | 8.28E-05 | 21923.32 | 0.856535 | 1.00E-04 | 37.12563 | 7388 | 0.123133 | 0.917918 |
| 0.999927 | 7.43E-05 | 22779.75 | 0.858783 | 9.00E-05 | 39.04523 | 7770 | 0.1295 | 0.903904 |
| 0.999935 | 6.55E-05 | 23230.09 | 0.858472 | 8.00E-05 | 39.28141 | 7817 | 0.130283 | 0.911912 |
| 0.999944 | 5.70E-05 | 23991.33 | 0.858366 | 7.00E-05 | 40.61809 | 8115 | 0.13525 | 0.90991 |
| 0.99995 | 5.04E-05 | 24863.7 | 0.860816 | 6.00E-05 | 42.32161 | 8422 | 0.140367 | 0.91992 |
| 0.999959 | 4.12E-05 | 25851.49 | 0.856007 | 5.00E-05 | 44.35678 | 8827 | 0.147117 | 0.906907 |
| 0.999966 | 3.39E-05 | 27462.18 | 0.856807 | 4.00E-05 | 46.85427 | 9325 | 0.155417 | 0.915916 |
| 0.999976 | 2.46E-05 | 29699.94 | 0.855977 | 3.00E-05 | 50.56784 | 10063 | 0.167717 | 0.905906 |
| 0.999984 | 1.66E-05 | 33061.28 | 0.857667 | 2.00E-05 | 55.63317 | 11086 | 0.184767 | 0.911912 |
| 0.999992 | 8.15E-06 | 41189.6 | 0.854307 | 1.00E-05 | 69.30653 | 13823 | 0.230383 | 0.908909 |
| 0.999993 | 7.18E-06 | 41336.82 | 0.85077 | 9.00E-06 | 70.16583 | 13979 | 0.232983 | 0.906907 |
| 0.999994 | 6.43E-06 | 42669.6 | 0.853567 | 8.00E-06 | 72.1608 | 14360 | 0.239333 | 0.912913 |
| 0.999994 | 5.57E-06 | 45067.12 | 0.850061 | 7.00E-06 | 76.80402 | 15284 | 0.254733 | 0.905906 |
| 0.999995 | 4.78E-06 | 48391.38 | 0.846173 | 6.00E-06 | 81.25628 | 16186 | 0.269767 | 0.905906 |
| 0.999996 | 3.99E-06 | 53587.13 | 0.851012 | 5.00E-06 | 90.59296 | 18028 | 0.300467 | 0.906907 |
| 0.999997 | 3.19E-06 | 58254.92 | 0.841902 | 4.00E-06 | 98.29146 | 19577 | 0.326283 | 0.905906 |
| 0.999998 | 2.38E-06 | 66089.84 | 0.836304 | 3.00E-06 | 110.9497 | 22079 | 0.367983 | 0.904905 |
| 0.999998 | 1.55E-06 | 89193.42 | 0.823919 | 2.00E-06 | 149.0804 | 29699 | 0.494983 | 0.905906 |
| 0.999999 | 7.50E-07 | 138352.1 | 0.807783 | 1.00E-06 | 231.1508 | 45999 | 0.76665 | 0.883884 |
| ? | ? | ? | ? | ? | ? | ? | ? | ? |
| 0.943818 | 0.057446 | 34655.04 | 0.853023 | 0.058138 | 58.79957 | 11708.46 | 0.195141 | 0.907484 |
?
?這個網絡的值與第二個網路的值高度近似， 這體現了a和fa相對c的對稱性。
兩個網絡的迭代次數是高度重合的。
兩個網絡的平均準確率是高度重合的。
兩個網絡的最大準確率也是高度重合的。
第四個網絡
d2（p，a）-4-4-2-（2*k）,k∈{0,1}
| pa | ? | ? | ? | ? | ? | ? | ? | ? |
| 測試集 | 0.3 | p | ? | ? | ? | ? | ? | ? |
| ? | 0.7 | a | ? | ? | ? | ? | ? | ? |
| f2[0] | f2[1] | 迭代次數n | 平均準確率p-ave | δ | 耗時ms/次 | 耗時ms/199次 | 耗時 min/199 | 最大準確率p-max |
| 0.514668 | 0.499679 | 177.8141 | 0.299395 | 0.5 | 2.045226 | 408 | 0.0068 | 0.334334 |
| 0.401314 | 0.604127 | 4073.583 | 0.909694 | 0.4 | 9.477387 | 1902 | 0.0317 | 0.961962 |
| 0.288585 | 0.716915 | 4806.276 | 0.920051 | 0.3 | 9.768844 | 1960 | 0.032667 | 0.967968 |
| 0.189818 | 0.814494 | 5306.126 | 0.922138 | 0.2 | 10.1608 | 2022 | 0.0337 | 0.954955 |
| 0.090113 | 0.912569 | 6021.729 | 0.924754 | 0.1 | 11.19095 | 2227 | 0.037117 | 0.953954 |
| 0.008526 | 0.991673 | 8323.387 | 0.927475 | 0.01 | 16.87437 | 3358 | 0.055967 | 0.952953 |
| 8.46E-04 | 0.999167 | 11739.58 | 0.926927 | 0.001 | 20.72362 | 4124 | 0.068733 | 0.954955 |
| 8.61E-05 | 0.999915 | 17633.54 | 0.928542 | 1.00E-04 | 30.29648 | 6029 | 0.100483 | 0.950951 |
| 7.76E-05 | 0.999923 | 18116.37 | 0.928753 | 9.00E-05 | 30.89447 | 6148 | 0.102467 | 0.954955 |
| 6.86E-05 | 0.999932 | 18777.39 | 0.928506 | 8.00E-05 | 32.18593 | 6405 | 0.10675 | 0.950951 |
| 6.01E-05 | 0.999941 | 19536.37 | 0.927918 | 7.00E-05 | 32.57286 | 6482 | 0.108033 | 0.953954 |
| 5.19E-05 | 0.999949 | 20382.09 | 0.928376 | 6.00E-05 | 34.92462 | 6966 | 0.1161 | 0.952953 |
| 4.27E-05 | 0.999958 | 21002.82 | 0.927234 | 5.00E-05 | 35.69347 | 7119 | 0.11865 | 0.952953 |
| 3.48E-05 | 0.999966 | 21406.57 | 0.928894 | 4.00E-05 | 36.90955 | 7360 | 0.122667 | 0.947948 |
| 2.62E-05 | 0.999974 | 23201.12 | 0.929372 | 3.00E-05 | 40.37688 | 8035 | 0.133917 | 0.951952 |
| 1.73E-05 | 0.999983 | 25067.48 | 0.929502 | 2.00E-05 | 42.63819 | 8517 | 0.14195 | 0.950951 |
| 8.51E-06 | 0.999991 | 29899.49 | 0.930946 | 1.00E-05 | 51.58794 | 10266 | 0.1711 | 0.94995 |
| 7.81E-06 | 0.999992 | 30046.65 | 0.929558 | 9.00E-06 | 51.07035 | 10178 | 0.169633 | 0.948949 |
| 6.88E-06 | 0.999993 | 30608.13 | 0.930352 | 8.00E-06 | 52.32161 | 10412 | 0.173533 | 0.958959 |
| 5.91E-06 | 0.999994 | 32460.66 | 0.929185 | 7.00E-06 | 55.56281 | 11057 | 0.184283 | 0.954955 |
| 5.16E-06 | 0.999995 | 33155.83 | 0.92992 | 6.00E-06 | 55.96482 | 11138 | 0.185633 | 0.951952 |
| 4.25E-06 | 0.999996 | 34170.82 | 0.930559 | 5.00E-06 | 57.47236 | 11452 | 0.190867 | 0.952953 |
| 3.41E-06 | 0.999997 | 36493.76 | 0.931565 | 4.00E-06 | 61.8593 | 12310 | 0.205167 | 0.953954 |
| 2.59E-06 | 0.999997 | 38369.11 | 0.931801 | 3.00E-06 | 65.30151 | 12995 | 0.216583 | 0.954955 |
| 1.71E-06 | 0.999998 | 42692.81 | 0.932339 | 2.00E-06 | 71.24623 | 14178 | 0.2363 | 0.952953 |
| 8.76E-07 | 0.999999 | 47401.5 | 0.932028 | 1.00E-06 | 80.39698 | 15999 | 0.26665 | 0.94995 |
| ? | ? | ? | ? | ? | ? | ? | ? | ? |
| 0.057476 | 0.943774 | 22341.19 | 0.903684 | 0.058138 | 38.44298 | 7655.654 | 0.127594 | 0.92993 |
這網絡的平均準確率和最大準確率都要高些，但更加趨于一個恒定值。
第5個網絡
d2（p，fa）-4-4-2-（2*k）,k∈{0,1}
| pfa | ? | ? | ? | ? | ? | ? | ? | ? |
| 測試集 | 0.3 | p | ? | ? | ? | ? | ? | ? |
| ? | 0.7 | fa | ? | ? | ? | ? | ? | ? |
| f2[0] | f2[1] | 迭代次數n | 平均準確率p-ave | δ | 耗時ms/次 | 耗時ms/199次 | 耗時 min/199 | 最大準確率p-max |
| 0.515643 | 0.499664 | 174.9799 | 0.300491 | 0.5 | 2.120603 | 422 | 0.007033 | 0.375375 |
| 0.412515 | 0.594208 | 4135.432 | 0.909045 | 0.4 | 10.20603 | 2031 | 0.03385 | 0.964965 |
| 0.285641 | 0.718931 | 4765.95 | 0.923763 | 0.3 | 9.61809 | 1914 | 0.0319 | 0.96997 |
| 0.184718 | 0.818123 | 5357.095 | 0.923582 | 0.2 | 10.32663 | 2055 | 0.03425 | 0.950951 |
| 0.089264 | 0.912503 | 6056.724 | 0.925413 | 0.1 | 11.27136 | 2243 | 0.037383 | 0.956957 |
| 0.008684 | 0.991461 | 8337.327 | 0.926016 | 0.01 | 15.36683 | 3090 | 0.0515 | 0.951952 |
| 8.56E-04 | 0.999158 | 11779.91 | 0.928612 | 0.001 | 21.0402 | 4187 | 0.069783 | 0.956957 |
| 8.61E-05 | 0.999915 | 18232.5 | 0.929085 | 1.00E-04 | 31.31156 | 6231 | 0.10385 | 0.94995 |
| 7.69E-05 | 0.999924 | 18278.48 | 0.9274 | 9.00E-05 | 31.9397 | 6356 | 0.105933 | 0.945946 |
| 6.86E-05 | 0.999932 | 18963.28 | 0.928703 | 8.00E-05 | 32.08543 | 6385 | 0.106417 | 0.953954 |
| 6.05E-05 | 0.99994 | 19460.16 | 0.92826 | 7.00E-05 | 33.40704 | 6649 | 0.110817 | 0.954955 |
| 5.17E-05 | 0.999949 | 19832.13 | 0.928687 | 6.00E-05 | 33.72362 | 6712 | 0.111867 | 0.95996 |
| 4.31E-05 | 0.999958 | 21033.61 | 0.928632 | 5.00E-05 | 36.23618 | 7227 | 0.12045 | 0.94995 |
| 3.38E-05 | 0.999966 | 21792.55 | 0.927908 | 4.00E-05 | 37.32161 | 7427 | 0.123783 | 0.951952 |
| 2.59E-05 | 0.999974 | 22954.92 | 0.928672 | 3.00E-05 | 39.19095 | 7829 | 0.130483 | 0.956957 |
| 1.69E-05 | 0.999983 | 25568.18 | 0.92992 | 2.00E-05 | 44.03015 | 8764 | 0.146067 | 0.950951 |
| 8.65E-06 | 0.999991 | 29570.57 | 0.930066 | 1.00E-05 | 53.71859 | 10692 | 0.1782 | 0.951952 |
| 7.73E-06 | 0.999992 | 30655.57 | 0.929784 | 9.00E-06 | 52.04523 | 10357 | 0.172617 | 0.950951 |
| 6.79E-06 | 0.999993 | 30476.99 | 0.930292 | 8.00E-06 | 51.45729 | 10256 | 0.170933 | 0.94995 |
| 6.09E-06 | 0.999994 | 31881.28 | 0.930458 | 7.00E-06 | 54.45729 | 10853 | 0.180883 | 0.955956 |
| 5.12E-06 | 0.999995 | 33848.89 | 0.930614 | 6.00E-06 | 57.75879 | 11494 | 0.191567 | 0.953954 |
| 4.34E-06 | 0.999996 | 34395.23 | 0.930262 | 5.00E-06 | 57.96985 | 11536 | 0.192267 | 0.956957 |
| 3.42E-06 | 0.999997 | 35777.86 | 0.930951 | 4.00E-06 | 60.78392 | 12096 | 0.2016 | 0.950951 |
| 2.57E-06 | 0.999997 | 37674.54 | 0.930755 | 3.00E-06 | 64.0201 | 12740 | 0.212333 | 0.955956 |
| 1.74E-06 | 0.999998 | 42115.04 | 0.931117 | 2.00E-06 | 71.68342 | 14265 | 0.23775 | 0.954955 |
| 8.64E-07 | 0.999999 | 48476.45 | 0.931846 | 1.00E-06 | 81.79397 | 16292 | 0.271533 | 0.960961 |
| ? | ? | ? | ? | ? | ? | ? | ? | ? |
| 0.057609 | 0.943598 | 22369.06 | 0.903859 | 0.058138 | 38.6494 | 7696.269 | 0.128271 | 0.932471 |
將這個網絡和第4個網絡比較
迭代次數曲線是高度重合的。
平均準確率是高度重合的。兩個網絡的平均準確率的平均值分別是0.903684和0.903859表明這種算法的精度是有保證的。
兩個網絡的最大準確率也是高度重合的。
第六個網絡
d2（a，fa）-4-4-2-（2*k）,k∈{0,1}
| afa | ? | ? | ? | ? | ? | ? | ? | ? |
| 測試集 | 0.3 | a | ? | ? | ? | ? | ? | ? |
| ? | 0.7 | fa | ? | ? | ? | ? | ? | ? |
| f2[0] | f2[1] | 迭代次數n | 平均準確率p-ave | δ | 耗時ms/次 | 耗時ms/199次 | 耗時 min/199 | 最大準確率p-max |
| 0.503493 | 0.503889 | 212.603 | 0.574263 | 0.5 | 2.150754 | 443 | 0.007383 | 1 |
| 0.508644 | 0.49533 | 2235.704 | 0.997681 | 0.4 | 5.351759 | 1065 | 0.01775 | 1 |
| 0.491317 | 0.513018 | 2640.658 | 0.998672 | 0.3 | 5.512563 | 1097 | 0.018283 | 1 |
| 0.561021 | 0.442177 | 2962.291 | 0.998788 | 0.2 | 6.150754 | 1224 | 0.0204 | 1 |
| 0.489822 | 0.510905 | 3503.392 | 0.998461 | 0.1 | 7.567839 | 1521 | 0.02535 | 1 |
| 0.527219 | 0.472919 | 5312.216 | 0.998798 | 0.01 | 11.19095 | 2227 | 0.037117 | 1 |
| 0.472417 | 0.527593 | 9557.186 | 0.999251 | 0.001 | 18.66332 | 3714 | 0.0619 | 1 |
| 0.522609 | 0.477392 | 20758.42 | 0.999512 | 1.00E-04 | 35.34171 | 7033 | 0.117217 | 1 |
| 0.502513 | 0.497488 | 21057.2 | 0.999406 | 9.00E-05 | 35.68342 | 7132 | 0.118867 | 1 |
| 0.437195 | 0.562805 | 21819.72 | 0.999371 | 8.00E-05 | 36.69347 | 7302 | 0.1217 | 1 |
| 0.507537 | 0.492463 | 23084.82 | 0.999447 | 7.00E-05 | 39.15075 | 7808 | 0.130133 | 1 |
| 0.497488 | 0.502513 | 25048.22 | 0.999502 | 6.00E-05 | 42.43216 | 8444 | 0.140733 | 1 |
| 0.417093 | 0.582907 | 26331.89 | 0.999532 | 5.00E-05 | 44.44724 | 8845 | 0.147417 | 1 |
| 0.54271 | 0.45729 | 28623.57 | 0.999633 | 4.00E-05 | 48.15578 | 9599 | 0.159983 | 1 |
| 0.462314 | 0.537686 | 31665.49 | 0.999567 | 3.00E-05 | 53.46231 | 10639 | 0.177317 | 1 |
| 0.537687 | 0.462313 | 37038.34 | 0.999567 | 2.00E-05 | 62.22111 | 12397 | 0.206617 | 1 |
| 0.522613 | 0.477387 | 47352.31 | 0.999593 | 1.00E-05 | 79.39698 | 15801 | 0.26335 | 1 |
| 0.462312 | 0.537688 | 50876.94 | 0.999733 | 9.00E-06 | 85.59799 | 17034 | 0.2839 | 1 |
| 0.512563 | 0.487437 | 53048.54 | 0.999638 | 8.00E-06 | 88.94472 | 17715 | 0.29525 | 1 |
| 0.502513 | 0.497487 | 55641.3 | 0.999517 | 7.00E-06 | 92.98492 | 18519 | 0.30865 | 1 |
| 0.532663 | 0.467337 | 59971.42 | 0.999683 | 6.00E-06 | 100.0653 | 19913 | 0.331883 | 1 |
| 0.507538 | 0.492462 | 64722.1 | 0.999668 | 5.00E-06 | 108.0854 | 21509 | 0.358483 | 1 |
| 0.477387 | 0.522613 | 68794.14 | 0.999688 | 4.00E-06 | 115.1759 | 22936 | 0.382267 | 1 |
| 0.492462 | 0.507538 | 79341.16 | 0.999743 | 3.00E-06 | 132.4171 | 26352 | 0.4392 | 1 |
| 0.477387 | 0.522613 | 88647.71 | 0.999658 | 2.00E-06 | 147.8995 | 29447 | 0.490783 | 1 |
| 0.442211 | 0.557789 | 118332.5 | 0.999723 | 1.00E-06 | 196.2814 | 39075 | 0.65125 | 1 |
| ? | ? | ? | ? | ? | ? | ? | ? | ? |
| 0.496567 | 0.504194 | 36483.84 | 0.983004 | 0.058138 | 61.57789 | 12261.19 | 0.204353 | 1 |
?
這個網絡的平均準確率和最大準確率都高度的接近1.
6組數據綜合
| ? | cp | ca | cfa | pa | pfa | afa |
| δ | 迭代次數n | 迭代次數n | 迭代次數n | 迭代次數n | 迭代次數n | 迭代次數n |
| 0.5 | 149.2864 | 181.6482 | 181.5377 | 177.8141 | 174.9799 | 212.603 |
| 0.4 | 6191.251 | 4185.683 | 4247.367 | 4073.583 | 4135.432 | 2235.704 |
| 0.3 | 10058.88 | 4950.729 | 5066.859 | 4806.276 | 4765.95 | 2640.658 |
| 0.2 | 15794.96 | 5621.844 | 5560.809 | 5306.126 | 5357.095 | 2962.291 |
| 0.1 | 24295.35 | 6358.879 | 6510.085 | 6021.729 | 6056.724 | 3503.392 |
| 0.01 | 59370.36 | 9141.543 | 9125.794 | 8323.387 | 8337.327 | 5312.216 |
| 0.001 | 116218.8 | 13441.74 | 13343.48 | 11739.58 | 11779.91 | 9557.186 |
| 1.00E-04 | 213160.8 | 21858.25 | 21923.32 | 17633.54 | 18232.5 | 20758.42 |
| 9.00E-05 | 212890.8 | 22514.33 | 22779.75 | 18116.37 | 18278.48 | 21057.2 |
| 8.00E-05 | 216429.1 | 22933.27 | 23230.09 | 18777.39 | 18963.28 | 21819.72 |
| 7.00E-05 | 227994 | 23904.65 | 23991.33 | 19536.37 | 19460.16 | 23084.82 |
| 6.00E-05 | 238336.1 | 25076.15 | 24863.7 | 20382.09 | 19832.13 | 25048.22 |
| 5.00E-05 | 256301.7 | 25666.67 | 25851.49 | 21002.82 | 21033.61 | 26331.89 |
| 4.00E-05 | 272096.3 | 27387.46 | 27462.18 | 21406.57 | 21792.55 | 28623.57 |
| 3.00E-05 | 283245.7 | 30215.88 | 29699.94 | 23201.12 | 22954.92 | 31665.49 |
| 2.00E-05 | 320385.5 | 32900.33 | 33061.28 | 25067.48 | 25568.18 | 37038.34 |
| 1.00E-05 | 362938.1 | 40569.4 | 41189.6 | 29899.49 | 29570.57 | 47352.31 |
| 9.00E-06 | 379786.3 | 41823.16 | 41336.82 | 30046.65 | 30655.57 | 50876.94 |
| 8.00E-06 | 391093.6 | 43123.77 | 42669.6 | 30608.13 | 30476.99 | 53048.54 |
| 7.00E-06 | 396418.2 | 45766.82 | 45067.12 | 32460.66 | 31881.28 | 55641.3 |
| 6.00E-06 | 401244.4 | 47956.51 | 48391.38 | 33155.83 | 33848.89 | 59971.42 |
| 5.00E-06 | 439625.5 | 51933.27 | 53587.13 | 34170.82 | 34395.23 | 64722.1 |
| 4.00E-06 | 480586.6 | 58216.54 | 58254.92 | 36493.76 | 35777.86 | 68794.14 |
| 3.00E-06 | 482990.6 | 67257.81 | 66089.84 | 38369.11 | 37674.54 | 79341.16 |
| 2.00E-06 | 555404.6 | 93343.57 | 89193.42 | 42692.81 | 42115.04 | 88647.71 |
| 1.00E-06 | 621276.4 | 136177.5 | 138352.1 | 47401.5 | 48476.45 | 118332.5 |
可以明顯的看到cp的迭代次數是最大的。
由迭代次數可以按從大到小排列
具體順序cp>afa>ca=cfa>pa=pfa
也就是cp的迭代次數是最多的，而pa的迭代次數是最少的。
?
| ? | cp | ca | cfa | pa | pfa | afa |
| δ | 平均準確率p-ave | 平均準確率p-ave | 平均準確率p-ave | 平均準確率p-ave | 平均準確率p-ave | 平均準確率p-ave |
| 0.5 | 0.700283 | 0.700867 | 0.701043 | 0.299395 | 0.300491 | 0.574263 |
| 0.4 | 0.978929 | 0.936233 | 0.932686 | 0.909694 | 0.909045 | 0.997681 |
| 0.3 | 0.991353 | 0.914266 | 0.914236 | 0.920051 | 0.923763 | 0.998672 |
| 0.2 | 0.996972 | 0.898466 | 0.895433 | 0.922138 | 0.923582 | 0.998788 |
| 0.1 | 0.993979 | 0.879789 | 0.882838 | 0.924754 | 0.925413 | 0.998461 |
| 0.01 | 0.86567 | 0.860177 | 0.860982 | 0.927475 | 0.926016 | 0.998798 |
| 0.001 | 0.632869 | 0.852918 | 0.856148 | 0.926927 | 0.928612 | 0.999251 |
| 1.00E-04 | 0.534097 | 0.856253 | 0.856535 | 0.928542 | 0.929085 | 0.999512 |
| 9.00E-05 | 0.540621 | 0.854769 | 0.858783 | 0.928753 | 0.9274 | 0.999406 |
| 8.00E-05 | 0.55042 | 0.85485 | 0.858472 | 0.928506 | 0.928703 | 0.999371 |
| 7.00E-05 | 0.534218 | 0.861882 | 0.858366 | 0.927918 | 0.92826 | 0.999447 |
| 6.00E-05 | 0.521904 | 0.858165 | 0.860816 | 0.928376 | 0.928687 | 0.999502 |
| 5.00E-05 | 0.507533 | 0.85815 | 0.856007 | 0.927234 | 0.928632 | 0.999532 |
| 4.00E-05 | 0.523715 | 0.856746 | 0.856807 | 0.928894 | 0.927908 | 0.999633 |
| 3.00E-05 | 0.505737 | 0.856283 | 0.855977 | 0.929372 | 0.928672 | 0.999567 |
| 2.00E-05 | 0.491366 | 0.857496 | 0.857667 | 0.929502 | 0.92992 | 0.999567 |
| 1.00E-05 | 0.499625 | 0.853557 | 0.854307 | 0.930946 | 0.930066 | 0.999593 |
| 9.00E-06 | 0.492769 | 0.854558 | 0.85077 | 0.929558 | 0.929784 | 0.999733 |
| 8.00E-06 | 0.485304 | 0.852541 | 0.853567 | 0.930352 | 0.930292 | 0.999638 |
| 7.00E-06 | 0.48787 | 0.851057 | 0.850061 | 0.929185 | 0.930458 | 0.999517 |
| 6.00E-06 | 0.494746 | 0.851751 | 0.846173 | 0.92992 | 0.930614 | 0.999683 |
| 5.00E-06 | 0.484474 | 0.843939 | 0.851012 | 0.930559 | 0.930262 | 0.999668 |
| 4.00E-06 | 0.472216 | 0.840373 | 0.841902 | 0.931565 | 0.930951 | 0.999688 |
| 3.00E-06 | 0.483745 | 0.83659 | 0.836304 | 0.931801 | 0.930755 | 0.999743 |
| 2.00E-06 | 0.469817 | 0.823105 | 0.823919 | 0.932339 | 0.931117 | 0.999658 |
| 1.00E-06 | 0.467452 | 0.805584 | 0.807783 | 0.932028 | 0.931846 | 0.999723 |
將平均準確率從大到小排列afa>pfa=pa>ca=cfa>cp
其中afa的平均準確率接近1，cp的平均準確率接近50%。
但這6個網絡的平均準確率都是趨向一個恒定值的，也就是這6個二分類網絡的準確率和δ是無關的。
| ? | cp | Ca | cfa | pa | pfa | afa |
| δ | 最大準確率p-max | 最大準確率p-max | 最大準確率p-max | 最大準確率p-max | 最大準確率p-max | 最大準確率p-max |
| 0.5 | 0.736737 | 0.88989 | 0.736737 | 0.334334 | 0.375375 | 1 |
| 0.4 | 0.993994 | 0.972973 | 0.962963 | 0.961962 | 0.964965 | 1 |
| 0.3 | 1 | 0.942943 | 0.955956 | 0.967968 | 0.96997 | 1 |
| 0.2 | 1 | 0.936937 | 0.935936 | 0.954955 | 0.950951 | 1 |
| 0.1 | 1 | 0.923924 | 0.926927 | 0.953954 | 0.956957 | 1 |
| 0.01 | 1 | 0.906907 | 0.910911 | 0.952953 | 0.951952 | 1 |
| 0.001 | 0.978979 | 0.918919 | 0.912913 | 0.954955 | 0.956957 | 1 |
| 1.00E-04 | 0.928929 | 0.911912 | 0.917918 | 0.950951 | 0.94995 | 1 |
| 9.00E-05 | 0.891892 | 0.907908 | 0.903904 | 0.954955 | 0.945946 | 1 |
| 8.00E-05 | 0.905906 | 0.907908 | 0.911912 | 0.950951 | 0.953954 | 1 |
| 7.00E-05 | 0.933934 | 0.921922 | 0.90991 | 0.953954 | 0.954955 | 1 |
| 6.00E-05 | 0.863864 | 0.91992 | 0.91992 | 0.952953 | 0.95996 | 1 |
| 5.00E-05 | 0.84985 | 0.913914 | 0.906907 | 0.952953 | 0.94995 | 1 |
| 4.00E-05 | 0.850851 | 0.914915 | 0.915916 | 0.947948 | 0.951952 | 1 |
| 3.00E-05 | 0.800801 | 0.90991 | 0.905906 | 0.951952 | 0.956957 | 1 |
| 2.00E-05 | 0.798799 | 0.915916 | 0.911912 | 0.950951 | 0.950951 | 1 |
| 1.00E-05 | 0.828829 | 0.90991 | 0.908909 | 0.94995 | 0.951952 | 1 |
| 9.00E-06 | 0.757758 | 0.914915 | 0.906907 | 0.948949 | 0.950951 | 1 |
| 8.00E-06 | 0.747748 | 0.914915 | 0.912913 | 0.958959 | 0.94995 | 1 |
| 7.00E-06 | 0.722723 | 0.924925 | 0.905906 | 0.954955 | 0.955956 | 1 |
| 6.00E-06 | 0.813814 | 0.901902 | 0.905906 | 0.951952 | 0.953954 | 1 |
| 5.00E-06 | 0.754755 | 0.908909 | 0.906907 | 0.952953 | 0.956957 | 1 |
| 4.00E-06 | 0.765766 | 0.897898 | 0.905906 | 0.953954 | 0.950951 | 1 |
| 3.00E-06 | 0.762763 | 0.906907 | 0.904905 | 0.954955 | 0.955956 | 1 |
| 2.00E-06 | 0.724725 | 0.898899 | 0.905906 | 0.952953 | 0.954955 | 1 |
| 1.00E-06 | 0.712713 | 0.892893 | 0.883884 | 0.94995 | 0.960961 | 1 |
?
?
最大準確率排序afa>pa=pfa>ca=cfa>cp
而且afa，pa，pfa，ca，cfa的最大準確率都趨向恒定。
也就表明并不是所有的二分類網路的最大分類準確都是100%。
實驗參數
學習率 0.1
權重初始化方式
Random rand1 =new Random();
int ti1=rand1.nextInt(98)+1;
tw[a][b]=xx*((double)ti1/100);
總結
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