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@imaginary_truth(虚真 Kyoshin or Kyoma)

2【-】Four Arithmetic by Machine Learning

Last updated at Posted at 2019-06-16

english_a-b.png

深層学習の形式でひき算をする回路を考えてみました。\\
I\ had\ thought\ about\ a\ Perceptron\ that\ Subtraction\  in\  the\  form\  of\  deep\  learning.\\
重りを
\begin{pmatrix}
1\\
-1
\end{pmatrix}
とすればひき算ができます。\\
It\ would\ be\ able\ to\ minus\ if\ weight\ is
\begin{pmatrix}
1\\
-1
\end{pmatrix}
.\\
　\\

\begin{pmatrix}
a & b
\end{pmatrix}
\begin{pmatrix}
1\\
-1
\end{pmatrix}
=a-b\\
　\\
前回と回路自体は同じで活性化関数が無いのでおもしろみに欠けますが\\
Perceptron\ is\ the\ same\ as\ before\ so\ there\ is\ no\ activation\ function,\ since\ are\ lacking\ in\ interest, but\\
それは次回にまわすとして\\
as\ it\ will\ go\ next\ time\\
重りの初期値を乱数で決めてから学習を繰り返すと\\
重りが
\begin{pmatrix}
1\\
-1
\end{pmatrix}
になるのか試してみました。\\
I\ tried\ whether\ weight\ would\ become
\begin{pmatrix}
1\\
-1
\end{pmatrix}\\
if\ the\ initial\ value\ of\ the\ weight\ was\ determined\ by\ random\ numbers\ and\ then\ repeated\ learning.


        string path = @"D:\開発\AI\" + DateTime.Now.ToString("yyyyMMdd") + "差.csv";
        double[] w = new double[2];

        private void button1_Click(object sender, EventArgs e)
        {
            button1.Enabled = false;
            sw.Start();
            Thread th = new Thread(nnw);
            th.Start();
        }

        private void nnw()
        {
            using (StreamWriter sw = new StreamWriter(path, true, Encoding.Unicode))
            {//row index
                sw.Write(
                    "a,b,a-b," +
                    "w[0],w[1]," +
                    "Y,ΔE" +
                    Environment.NewLine);
            }

            // get random number 0.0 ～ 1.0
            Random cRandom = new Random();
            for (int n = 0; n < w.Length; n++)
            {
                w[n] = cRandom.NextDouble();
            }

            //learning
            for (int p = 0; p < 100; p++)
            {
                //input data
                double a = cRandom.NextDouble();
                double b = cRandom.NextDouble();

                double a_sub_b = a - b;

                //forward propagation
                double Y = a * w[0] + b * w[1];

                //least squares error
                double dE = Y - a_sub_b;//value after differentiation of squared error because calculation is omitted

                //record
                using (StreamWriter sw = new StreamWriter(path, true, Encoding.Unicode))
                {
                    sw.Write(
                        a.ToString() + "," + b.ToString() + "," + a_sub_b.ToString() + "," +
                        w[0].ToString() + "," + w[1].ToString() + "," +
                        Y.ToString() + "," + dE.ToString() +
                        Environment.NewLine);
                }

                //back propagation
                w[0] = w[0] - (a * dE);
                w[1] = w[1] - (b * dE);
            }

            //final record
            using (StreamWriter sw = new StreamWriter(path, true, Encoding.Unicode))
            {
                sw.Write(
                    ",,," +
                    w[0].ToString() + "," + w[1].ToString() + "," +
                    "," +
                    Environment.NewLine);
            }

            //read only
            File.SetAttributes(path, FileAttributes.ReadOnly);

            Invoke(new dldl(delegate
            {
                sw.Stop();
                label1.Text = sw.Elapsed.ToString();
                button1.Enabled = true;
            }));
        }

        Stopwatch sw = new Stopwatch();
        private delegate void dldl();

乱数で重みの初期値が
\begin{pmatrix}
0.569274364770052\\
0.031159881982561
\end{pmatrix}
と決定され\\
100回学習させてみましたが最終的には
\begin{pmatrix}
0.999980547941049\\
-0.999987981692304
\end{pmatrix}
と\\
ひき算でも
\begin{pmatrix}
1\\
-1
\end{pmatrix}
まで重みが近似されました。\\
The\ initial\ value\ of\ the\ weight\ was\ determined\ to\ be\
\begin{pmatrix}
0.999980547941049\\
-0.999987981692304
\end{pmatrix}
by\ random\ numbers\\
and\ I\ tried\ to\ make\ it\ learn\ 100\ times\\
also\ in\ subtraction\ finally\ the\ weight\ was\ corrected\ to\\
\begin{pmatrix}
0.999980547941049\\
-0.999987981692304
\end{pmatrix}
gradually,\ to\ an\ approximation\ of
\begin{pmatrix}
1\\
-1
\end{pmatrix}\\
\\
重みの推移グラフを掲載します。\\
I\ will\ post\ the\ transition\ graph\ of\ the\ weight.\

差重み.png

a b a-b w[0] w[1] Y ΔE
1 0.84634401455817 0.680053877029593 0.166290137528577 0.569274364770052 0.031159881982561 0.502992349814563 0.336702212285986
2 0.844342519922341 0.968672198228851 -0.12432967830651 0.284308462713313 -0.197815762886965 0.048435093962572 0.172764772269082
3 0.802462208924099 0.938649923512083 -0.136187714587985 0.138435819541827 -0.365168194617364 -0.231675584402881 -0.095487869814897
4 0.819457468492658 0.605762529003323 0.213694939489334 0.215061226478946 -0.275538512919279 0.009322621797566 -0.204372317691768
5 0.455969781361506 0.699470792291439 -0.243501010929933 0.38253564856462 -0.151737420896043 0.068288802024577 0.31178981295451
6 0.12910706229932 0.387504314718537 -0.258397252419217 0.240368915721007 -0.369825288391734 -0.112275570367012 0.146121682052205
7 0.098039181482996 0.90920312419031 -0.811163942707313 0.221503574613011 -0.426448070660893 -0.366011888999197 0.445152053708117
8 0.430195516641343 0.587986916111776 -0.157791399470433 0.177861231631993 -0.831181708632045 -0.412208865154683 -0.254417465684249
9 0.570975760263845 0.988265416113783 -0.417289655849938 0.287310484724609 -0.68158756757939 -0.50954209864442 -0.092252442794482
10 0.701955172560157 0.366814441684081 0.335140730876075 0.339984393385385 -0.590417668813589 0.022080075980325 -0.31306065489575
11 0.115525251308235 0.5034356971753 -0.387910445867065 0.559738939414528 -0.475582499474751 -0.174761225544575 0.21314922032249
12 0.700535585498687 0.130034404401683 0.570501181097003 0.535114822170618 -0.582889425810175 0.299071295941054 -0.271429885155949
13 0.987057544284993 0.308584319571305 0.678473224713687 0.725261115690182 -0.547594202357104 0.546895471482986 -0.131577753230701
14 0.24559802247472 0.896921643007976 -0.651323620533256 0.855135929676614 -0.506991370905687 -0.244711840107937 0.406611780425319
15 0.879109178613457 0.631550400346308 0.247558778267148 0.755272880489231 -0.871690277071162 0.113450978133631 -0.134107800133518
16 0.349375404114544 0.685859217162178 -0.336483813047634 0.873168278510265 -0.786994442207276 -0.234703871878743 0.101779941168891
17 0.010143078402683 0.323895652929272 -0.31375257452659 0.83760887043363 -0.856801152980185 -0.269018236431479 0.04473433809511
18 0.391793866358601 0.629592209416252 -0.23779834305765 0.837155126535039 -0.871290410625859 -0.220565410902041 0.017232932155609
19 0.456639075398743 0.723705168684807 -0.267066093286064 0.830403369417097 -0.88214013045643 -0.259214745096984 0.00785134818908
20 0.905527679671313 0.754829624087936 0.150698055583377 0.826818137039402 -0.887822191722011 0.078552217908995 -0.072145837674383
21 0.775999036513269 0.024183572281238 0.751815464232031 0.892148190026629 -0.833364376190747 0.672152408259503 -0.079663055972528
22 0.959457012805835 0.269724646243139 0.689732366562696 0.953966644707013 -0.831437838918492 0.691030710271546 0.00129834370885
23 0.695203811253982 0.163878418115842 0.531325393138139 0.952720939730525 -0.831788034216063 0.526023121107121 -0.005302272031018
24 0.921940651220242 0.231822647727943 0.690118003492298 0.956407099454794 -0.8309191062632 0.689124716841344 -0.000993286650955
25 0.987655197730127 0.053042046284788 0.934613151445339 0.957322850796623 -0.830688839921823 0.901443453599718 -0.033169697845621
26 0.804407995103117 0.337735786259983 0.466672208843134 0.990083075280989 -0.828929451273443 0.516471601592417 0.049799392749282
27 0.603756707908472 0.202459923085971 0.401296784822502 0.950024045602186 -0.845748488338891 0.402353216307496 0.001056431484995
28 0.915634630674326 0.34290831738287 0.572726313291456 0.949386218006675 -0.845962373376089 0.579203365068223 0.006477051776767
29 0.979518291530906 0.714308115520658 0.265210176010248 0.943455605095196 -0.848183408302462 0.318267730437684 0.053057554427435
30 0.981614653943858 0.493877889352794 0.487736764591065 0.891484760029627 -0.886082850019658 0.437477776453289 -0.050258988137776
31 0.693051901037363 0.922535825484682 -0.229483924447319 0.940819719278058 -0.861261047037166 -0.142507276007137 0.086976648440182
32 0.726653350389867 0.824419381015198 -0.097766030625331 0.880540387730732 -0.94150012120382 -0.136343324250459 -0.038577293625127
33 0.350095388176895 0.443247845137142 -0.093152456960246 0.908572707392404 -0.909696252672151 -0.085133789044787 0.008018667915459
34 0.377361236315854 0.774143528553724 -0.39678229223787 0.90576540873588 -0.913250509946549 -0.365186217770802 0.031596074467067
35 0.517409257831708 0.800603307225091 -0.283194049393383 0.89384227501226 -0.93771040652293 -0.288251784548944 -0.005057735155561
36 0.131347840713033 0.847270591579038 -0.715922750866005 0.896459194005408 -0.93366116703032 -0.673315669904197 0.042607080961807
37 0.08273773644247 0.947125548472221 -0.864387812029751 0.890862845921989 -0.969760893722286 -0.844777343001349 0.019610469028402
38 0.590815405170813 0.091341679026998 0.499473726143815 0.889240320104004 -0.988334469956609 0.435100750090376 -0.064372976053439
39 0.543978684369465 0.430810939255548 0.113167745113917 0.927272866033068 -0.982454534239923 0.081164513044398 -0.032003232069519
40 0.434830593147702 0.82317912616915 -0.388348533021449 0.944681942109815 -0.96866719177284 -0.386610003248757 0.001738529772691
41 0.386643668351063 0.013775374746777 0.372868293604287 0.943925976177551 -0.970098313191943 0.351599534275712 -0.021268759328575
42 0.909266445277849 0.826067132328668 0.08319931294918 0.952149407305627 -0.969805328061793 0.064633200685129 -0.018566112264051
43 0.827142405243191 0.011639617854562 0.81550278738863 0.96903095020659 -0.954468472945336 0.790416942629663 -0.025085844758966
44 0.082102509253706 0.807683155316712 -0.725580646063006 0.989780516178079 -0.954176483298783 -0.689408808771116 0.03617183729189
45 0.408261022254946 0.048885548975731 0.359375473279215 0.986810717572098 -0.983391866976299 0.354802701052716 -0.004572772226499
46 0.650073917885345 0.742330959878085 -0.092257041992739 0.988677602235827 -0.983168324495666 -0.087122763633662 0.005134278359077
47 0.742090514740949 0.41164979031852 0.330440724422429 0.985339941787428 -0.986979658278241 0.324921455216967 -0.005519269205462
48 0.061777723050573 0.853463211028587 -0.791685487978014 0.989435739113103 -0.984707652267101 -0.779286667761033 0.012398820216981
49 0.297530221891371 0.135037631790637 0.162492590100734 0.988669768231585 -0.995289589182452 0.159757586450159 -0.002735003650575
50 0.919629258066243 0.25195596611684 0.667673291949403 0.989483514474614 -0.994920260766539 0.659281894774416 -0.008391397174987
51 0.786517181799988 0.147797122666518 0.63872005913347 0.997200488832786 -0.992805998184245 0.637581448268642 -0.001138610864828
52 0.714413389896235 0.187051890505036 0.527361499391199 0.998096025841358 -0.992637714774587 0.527378404128099 1.69047369006359E-05
53 0.921694205571755 0.957137403524079 -0.035443197952324 0.998083948870963 -0.992640876837583 -0.030165519139646 0.005277678812678
54 0.254998049817513 0.656631159436252 -0.401633109618739 0.993219542890449 -0.997692340632983 -0.401846831912797 -0.000213722294058
55 0.611644517915158 0.824292951647329 -0.212648433732171 0.993274041658637 -0.997552003915238 -0.214744463361062 -0.002096029628891
56 0.798929633013406 0.548707352275358 0.250222280738048 0.994556066690536 -0.995824261465699 0.248164219531918 -0.002058061206129
57 0.279477522372956 0.158435527774708 0.121041994598248 0.996200312774668 -0.994694988150463 0.120820569778952 -0.000221424819296
58 0.10723422100173 0.679276526290586 -0.572042305288856 0.996262196034556 -0.994659906592356 -0.568815725685336 0.00322657960352
59 0.013269380206833 0.900586218061199 -0.887316837854365 0.995916196284273 -0.996851646377235 -0.884535663516314 0.002781174338051
60 0.997276975772007 0.338455770322334 0.658821205449673 0.99587929182456 -0.999356333656109 0.654929570650683 -0.00389163479899
61 0.361145335883436 0.569678080999143 -0.208532745115707 0.999760329607705 -0.998039187402404 -0.207502269002236 0.001030476113471
62 0.365882506298778 0.468523708855977 -0.102641202557199 0.999388177965586 -0.998626227057242 -0.102221412342292 0.000419790214907
63 0.150529389339746 0.389016880834949 -0.238487491495203 0.999234584069636 -0.998822908725671 -0.238144800711794 0.000342690783409
64 0.105180076838089 0.67108794612395 -0.565907869285861 0.999182999035277 -0.998956221225324 -0.565293334156002 0.000614535129859
65 0.885347825421648 0.737352194142226 0.147995631279422 0.999118362183099 -0.999368628343442 0.147680618431701 -0.00031501284772
66 0.793811457135627 0.408941052578828 0.384870404556799 0.999397258122808 -0.999136352928992 0.384745121891263 -0.000125282665536
67 0.511181681189305 0.182874627030862 0.328307054158443 0.999496708938091 -0.999085119703878 0.32821708938022 -8.9964778222984E-05
68 0.036661944369162 0.238846545684546 -0.202184601315383 0.999542697284671 -0.999068667428615 -0.201978921354534 0.00020567996085
69 0.299361984850542 0.722214554772812 -0.42285256992227 0.999535156657388 -0.99911779337678 -0.422354583884353 0.000497986037918
70 0.904372926756913 0.870005001719112 0.034367925037801 0.999386078568649 -0.999477446141438 0.034267335586749 -0.000100589451052
71 0.756641568037049 0.425471349817454 0.331170218219594 0.999477048944899 -0.999389932815902 0.331034097821553 -0.000136120398041
72 0.196038637401554 0.583968070607618 -0.387929433206063 0.999580043296314 -0.99933201748641 -0.387621680486361 0.000307752719703
73 0.249955915962325 0.101366565609987 0.148589350352338 0.999519711872487 -0.999511735248359 0.148518793214482 -7.0557137856031E-05
74 0.462853437505129 0.583654986966241 -0.120801549461112 0.999537348046508 -0.999504583113615 -0.120726536971789 7.50124893234561E-05
75 0.304415569316789 0.382501196759986 -0.078085627443197 0.999502628257968 -0.999548364527093 -0.078064284036324 2.13434068734308E-05
76 0.840193830821753 0.396944003830172 0.443249826991581 0.999496130992614 -0.999556528405765 0.443002512750234 -0.000247314241348
77 0.13776065601863 0.581173487743909 -0.443412831725279 0.999703922892469 -0.999458358500601 -0.443138831822532 0.000273999902747
78 0.890810630233405 0.216839100800845 0.673971529432559 0.999666176486117 -0.999617599979722 0.673757075174314 -0.000214454258245
79 0.78191461636774 0.245889681040258 0.536024935327482 0.999857214619061 -0.999571097911201 0.536018751948934 -6.1833785475196E-06
80 0.036522501165291 0.532677324736806 -0.496154823571516 0.999862049493126 -0.999569577482222 -0.495930585553787 0.000224238017728
81 0.85195732668599 0.583910103693563 0.268047222992427 0.999853859759862 -0.99968902398961 0.268104299778591 5.70767861639565E-05
82 0.771283334014604 0.874292323772932 -0.103008989758328 0.999805232773706 -0.999722351701737 -0.102916464698101 9.25250602269445E-05
83 0.030481494511702 0.389988580434578 -0.359507085922876 0.999733869736774 -0.99980324565165 -0.359438466022027 6.86199008493316E-05
84 0.037525671086053 0.096602895342094 -0.059077224256041 0.999731778099643 -0.999830006629372 -0.05907086761106 6.35664498074145E-06
85 0.121773583405546 0.868387675317185 -0.746614091911639 0.999731539562274 -0.999830620699682 -0.746499696404294 0.000114395507346
86 0.379914541440045 0.291054825434021 0.088859716006024 0.999717609211419 -0.999929960348373 0.088772817017651 -8.68989883726079E-05
87 0.996213291304285 0.127271974052895 0.86894131725139 0.999750623400739 -0.999904667978481 0.868705018063235 -0.000236299188155
88 0.581814202285285 0.935673986065981 -0.353859783780696 0.999986027792703 -0.999874593714338 -0.353750573610155 0.000109210170541
89 0.373639443597588 0.78191443569116 -0.408274992093572 0.999922487764449 -0.999976778829927 -0.408285796754041 -1.08046604693768E-05
90 0.218567792893652 0.049162823729759 0.169404969163893 0.999926524811775 -0.999968330509933 0.169390466815728 -1.45023481650797E-05
91 0.92616344332982 0.521525089871849 0.404638353457972 0.999929694558005 -0.999967617533546 0.404590127396456 -4.8226061515444E-05
92 0.366672376807161 0.502846628661662 -0.136174251854501 0.999974359773196 -0.99994246643248 -0.136154722856943 1.95289975580826E-05
93 0.897158363320473 0.396867453305455 0.500290910015018 0.999967199029245 -0.999952286523064 0.50028041827586 -1.04917391576809E-05
94 0.271180396560198 0.930008193445396 -0.658827796885198 0.999976611780776 -0.999948122693263 -0.658785892991443 4.19038937550242E-05
95 0.292063996797457 0.819822843568317 -0.52775884677086 0.99996524826625 -0.999987093657793 -0.527758415586946 4.3118391379604E-07
96 0.456931929316806 0.053472303810284 0.403459625506522 0.999965122332953 -0.999987447152215 0.403444360016519 -1.52654900033578E-05
97 0.685692053607522 0.371695602020107 0.313996451587415 0.999972097622752 -0.999986630871296 0.313982288395401 -1.41631920133056E-05
98 0.018047675033122 0.172731464343486 -0.154683789310364 0.99998180921097 -0.999981366475114 -0.154680899015774 2.89029459041301E-06
99 0.654188015802851 0.321746313628622 0.332441702174228 0.999981757047872 -0.999981865719931 0.332435602491336 -6.09968289239093E-06
100 0.553486576095916 0.859967335527748 -0.306480759431832 0.99998574738732 -0.999979903169446 -0.3064713654438 9.39398803168068E-06
0.999980547941049 -0.999987981692304

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