受限玻尔兹曼机RBM实现及能量值思考——matlab实现

一、三元因子玻尔兹曼机

这个是我正在写的一篇论文的部分代码，用了一个三元因子RBM，大家只需要看采样部分和权重与偏置的更新部分就行了

%第一层RBM训练：数据before-数据current-隐单元1numbatches = length(minibatch);numdims = size(batchdata,2);%学习率的设置%权重的学习率epsilonvisfac=single(1e-2);  %可见层到因子层的学习率epsilonhidfac=single(1e-2);  %隐藏层到因子层epsilonpastfac=single(1e-3);%过去到因子层的学习率%偏置学习率epsilonvisbias=single(1e-2);  %可见层偏置学习率0.01epsilonhidbias=single(1e-2);  %隐含层偏置学习率0.01%所有权重的的衰减wdecay = single(0.0002);mom = single(0.9);       %动量学习率，每五个周期用一次if restart==1,    restart=0;    epoch=1;        %初始化权重    visfac = single(0.01*randn(numdims,numfac));%可见层到因子层权重    hidfac = single(0.01*randn(numhid,numfac));%隐藏层到因子层之间的权重    pastfac= single(0.01*randn(nt*numdims,numfac));%隐藏层到因子层之间的权重        %初始化偏置    visbiases = zeros(1,numdims,'single');  %可见层偏置1*58    hidbiases = zeros(1,numhid,'single');   %隐藏层偏置1*600        clear posdataprod pospastprod poshidprod posvishidprod posvisact poshidact    clear negdataprod negpastprod neghidprod negvishidprod negvisact neghidact        %keep previous updates around for momentum  %为当前状态保存前面的更新信息    visfacinc = zeros(size(visfac),'single');   %可见层到因子层的信息    hidfacinc = zeros(size(hidfac),'single');   %隐藏层到因子层的信息    pastfacinc = zeros(size(pastfac),'single'); %过去层到因子层        visbiasinc = zeros(size(visbiases),'single');   %可见层偏置    hidbiasinc = zeros(size(hidbiases),'single');   %隐藏层偏置        %动态绘制误差曲线    x=1:maxepoch;    h=plot(0,0);    annotation('arrow',[0.132 0.132],[0.8,1]);    annotation('arrow',[0.8 1],[0.108,0.108]);    errorrecord=[];end%Main loopfor epoch = epoch:maxepoch,  %1到200 训练周期    errsum=0; %重构数据与原始数据的误差    for batch = 1:numbatches,     %对每一批数据都进行处理                %%%%%%%%% START POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                numcases = length(minibatch{batch});   %每一批数据的大小        mb = minibatch{batch}; %caches the indices  找到对应批次的内容，里面存的是随机数，前面定义过                past = zeros(numcases,nt*numdims,'single'); %初始化过去层的数据，帧数*15帧总共的感兴趣数据                data = single(batchdata(mb,:));%把随机数对应的那个帧的数据取出来一般来说是100*58维的(每批100帧，每帧58个维度)                for hh=nt:-1:1 %100个随机帧的前面15个帧信息的综合，即100*(12*58维)            past(:,numdims*(nt-hh)+1:numdims*(nt-hh+1)) = batchdata(mb-hh,:) + randn(numcases,numdims);        end                yvis = data*visfac;        ypast=past*pastfac;        ypastvis=yvis.*ypast;        poshidprobs = 1./(1 + exp(-ypastvis*hidfac' - repmat(hidbiases,numcases,1)));        batchposhidprobs{batch}=poshidprobs;        %Activate the hidden units    激活隐单元        hidstates = single(poshidprobs > rand(numcases,numhid)); %全是0和1                yhid = hidstates*hidfac;     %找到激活的单元，把权重保留，其他的权重置零        yhid_ = poshidprobs*hidfac;  %概率乘以隐藏层到因子层的权值                        %Calculate statistics needed for gradient update        %Gradients are taken w.r.t neg energy        %Note that terms that are common to positive and negative stats        %are left out        posvisprod = data'*(ypast.*yhid_); %smoothed        pospastprod = past'*(yvis.*yhid_); %smoothed        poshidprod = poshidprobs'*(ypast.*yvis); %smoothed                posvisact = sum(data,1);        poshidact = sum(poshidprobs,1);  %smoothed                %%%%%%%%% END OF POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                %%%%%%%%% START NEGATIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%        %10步对比散度算法        for cdn = 1:cdsteps            negdata =(ypast.*yhid)*visfac' + repmat(visbiases,numcases,1);    %重构数据                        yvis = negdata*visfac;            ypastvis=yvis.*ypast;            neghidprobs = 1./(1 + exp(-ypastvis*hidfac'- repmat(hidbiases,numcases,1)));                        if cdn == 1                %Calculate reconstruction error计算重构误差                err= sum(sum( (data(:,:,1)-negdata).^2 ));                errsum = err + errsum;            end                        if cdn == cdsteps                                yhid_ = neghidprobs*hidfac; %smoothed version                yvishid_ = yvis.*yhid_;                                negvisprod = negdata'*(ypast.*yhid_); %smoothed                negpastprod = past'*(yvishid_); %smoothed                neghidprod = neghidprobs'*(ypast.*yvis); %smoothed                                %negvishidprod = data'*neghidprobs;                negvisact = sum(negdata,1);                neghidact = sum(neghidprobs,1);  %smoothed                            else                %Stochastically sample the hidden units                hidstates = single(neghidprobs > rand(numcases,numhid));                yhid = hidstates*hidfac;            end        end                        %%%%%%%%% END NEGATIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%        if epoch > 5 %use momentum            momentum=mom;        else %no momentum            momentum=0;        end                %%%%%%%%% UPDATE WEIGHTS AND BIASES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                visfacinc = momentum*visfacinc + ...            epsilonvisfac*( ( posvisprod - negvisprod)/numcases - wdecay*visfac);                hidfacinc = momentum*hidfacinc + ...            epsilonhidfac*( (poshidprod - neghidprod)/numcases - wdecay*hidfac);   %前面一个参数应该是学习率，后面那个wdecay应该是权重衰减率                pastfacinc = momentum*pastfacinc + ...            epsilonpastfac*( (pospastprod - negpastprod)/numcases - wdecay*pastfac);                %两个偏置        visbiasinc = momentum*visbiasinc + ...            (epsilonvisbias/numcases)*(posvisact - negvisact);        hidbiasinc = momentum*hidbiasinc + ...            (epsilonhidbias/numcases)*(poshidact - neghidact);                        visfac = visfac + visfacinc;        pastfac = pastfac + pastfacinc;        hidfac = hidfac + hidfacinc;                visbiases = visbiases + visbiasinc;        hidbiases = hidbiases + hidbiasinc;                %%%%%%%%%%%%%%%% END OF UPDATES  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%            end        %%%动态绘制误差曲线    title('第一层误差折线图')    errorrecord=[errorrecord errsum];    set(h,'xData',x(1:epoch),'yData',errorrecord(1:epoch))    fprintf(1, 'epoch %4i error %6.1f  \n', epoch, errsum);        %Checkpoint models    %最终得到的就是可见层-因子层权重、特征曾-因子层权重、隐藏层-因子层权重、过去-因子层A(或者称为m)的权重、可见层-因子层A的权重    %过去-因子层B的权重、隐藏层-因子层B的权重、标签-特征的权重；可见层偏置，隐藏层偏置、k步采样、隐藏层单元个数、周期数、训练帧数    if ~isnan(errsum)        snapshot_file = [snapshot_path '1.mat'];        save(snapshot_file, 'pastfac','visfac','hidfac', 'visbiases','hidbiases', ...            'cdsteps', 'numhid','numfac','epoch', 'nt','n1','batchposhidprobs');    else        break;    end       drawnow; %update any plots你可以理解为把当前需要画的东西都画到屏幕上。一般用于循环内，显示动画效果。看看文档的例子吧http://cn.mathworks.com/help/matlab/ref/drawnow.htmlend%%         snapshot_file = [snapshot_path '1.mat'];%         save(snapshot_file, 'pastfac','visfac','hidfac', 'visbiases','hidbiases', ...%             'cdsteps', 'numhid','numfac','epoch', 'nt','n1');

二、Hinton主页上的标准RBM代码

网址：http://www.cs.toronto.edu/~hinton/MatlabForSciencePaper.html

这个代码主要是在mnist上做手写数字识别的代码，贴出来的目的主要是想研究一下在迭代过程中能量的变化情况。

2.1标准能量函数

标准的能量函数的表达式为：

那么就将这个表达式放在每一批次迭代的末尾，然后将所有批次迭代一次的结果累加就是当前迭代次数的能量值。

我写的表达式如下：

  energy=energy-sum(sum(negdata*vishid.*poshidstates))-...      sum(sum(negdata.*repmat(visbiases,size(negdata,1),1)))-...      sum(sum(poshidstates.*repmat(hidbiases,size(poshidstates,1),1)));

具体位置截图如下

【注】肯能还有更高效简洁的写法，只要保重RBM对应的二部图中的每一条连接线都有计算入能量函数中去就行。

第一层迭代了五十次的结果如下

Pretraining Layer 1 with RBM: 784-500 epoch 1epoch    1 error 906233.0 energy -11099587.215172 epoch 2epoch    2 error 557528.5 energy -30047032.045595 epoch 3epoch    3 error 496027.4 energy -53112598.240393 epoch 4epoch    4 error 468267.6 energy -78539687.671057 epoch 5epoch    5 error 452678.9 energy -105299865.601975 epoch 6epoch    6 error 478165.1 energy -129373309.014318 epoch 7epoch    7 error 454438.2 energy -152106055.038886 epoch 8epoch    8 error 438489.1 energy -174308595.910380 epoch 9epoch    9 error 428747.2 energy -195910590.668272 epoch 10epoch   10 error 421810.9 energy -217028311.853859 epoch 11epoch   11 error 416392.9 energy -237610724.670849 epoch 12epoch   12 error 411178.5 energy -257759919.144502 epoch 13epoch   13 error 408115.5 energy -277438854.842965 epoch 14epoch   14 error 405091.1 energy -296657959.425424 epoch 15epoch   15 error 403533.2 energy -315397871.648862 epoch 16epoch   16 error 400616.4 energy -333710720.884443 epoch 17epoch   17 error 398482.7 energy -351563160.004860 epoch 18epoch   18 error 396461.9 energy -369009936.125511 epoch 19epoch   19 error 395664.3 energy -386036922.651997 epoch 20epoch   20 error 394134.4 energy -402656725.716640 epoch 21epoch   21 error 392316.9 energy -418988195.512326 epoch 22epoch   22 error 391985.3 energy -435041246.765398 epoch 23epoch   23 error 390845.3 energy -450774503.774346 epoch 24epoch   24 error 389345.9 energy -466241495.153597 epoch 25epoch   25 error 388229.8 energy -481430774.200754 epoch 26epoch   26 error 387980.9 energy -496349569.785631 epoch 27epoch   27 error 386886.4 energy -510986252.435888 epoch 28epoch   28 error 385948.6 energy -525397051.912323 epoch 29epoch   29 error 385386.0 energy -539599081.300994 epoch 30epoch   30 error 385348.8 energy -553574564.640536 epoch 31epoch   31 error 385159.7 energy -567319607.941765 epoch 32epoch   32 error 384260.7 energy -580846734.110570 epoch 33epoch   33 error 383174.4 energy -594214877.616236 epoch 34epoch   34 error 382934.3 energy -607405266.358145 epoch 35epoch   35 error 382697.1 energy -620430109.937463 epoch 36epoch   36 error 382095.5 energy -633260002.931164 epoch 37epoch   37 error 381486.8 energy -645950143.694427 epoch 38epoch   38 error 380661.3 energy -658521662.217831 epoch 39epoch   39 error 379594.0 energy -670919982.496346 epoch 40epoch   40 error 379996.7 energy -683233935.943210 epoch 41epoch   41 error 379679.9 energy -695420009.453536 epoch 42epoch   42 error 379632.1 energy -707458130.547251 epoch 43epoch   43 error 379168.7 energy -719365334.031710 epoch 44epoch   44 error 378787.6 energy -731171831.263565 epoch 45epoch   45 error 378450.0 energy -742883647.550836 epoch 46epoch   46 error 379054.0 energy -754479143.953231 epoch 47epoch   47 error 377713.5 energy -765939049.101519 epoch 48epoch   48 error 377721.1 energy -777334241.922596 epoch 49epoch   49 error 376576.0 energy -788647805.279271 epoch 50epoch   50 error 377725.3 energy -799861904.731226

可以有两点发现：

1、能量是负值

2、能量是不断减少，或者更形象点是逐渐降低的，也就是说绝对值是不断增大的，越来越远离0

这个也就说明了能量越低，模型越稳定

【注】其实我刚开始一直是以为能量值不断趋近于0的，实验结果证明了我的想法是错的。读者有任何想法也可以在评论区讨论讨论。有其他比较有价值的规律谢谢大家一起来完善

为了进一步验证这个结论，下面列出第二层的能量值变化

Pretraining Layer 2 with RBM: 500-500 epoch 1epoch    1 error 987086.0 energy -9062710.051405 epoch 2epoch    2 error 665834.8 energy -22633241.117738 epoch 3epoch    3 error 610662.3 energy -36830053.019285 epoch 4epoch    4 error 572091.6 energy -51281490.520769 epoch 5epoch    5 error 540614.1 energy -65915030.623658 epoch 6epoch    6 error 508557.3 energy -79431130.648043 epoch 7epoch    7 error 434258.1 energy -92467710.762025 epoch 8epoch    8 error 399902.2 energy -105430274.786403 epoch 9epoch    9 error 383352.3 energy -118255093.037551 epoch 10epoch   10 error 374529.1 energy -130904210.951242 epoch 11epoch   11 error 368514.4 energy -143354512.397248 epoch 12epoch   12 error 363563.4 energy -155627227.699558 epoch 13epoch   13 error 360383.7 energy -167717570.110705 epoch 14epoch   14 error 358861.5 energy -179615072.973138 epoch 15epoch   15 error 356927.2 energy -191293665.350483 epoch 16epoch   16 error 354678.5 energy -202753482.269224 epoch 17epoch   17 error 353843.7 energy -214037964.189715 epoch 18epoch   18 error 352791.3 energy -225155932.564075 epoch 19epoch   19 error 351835.7 energy -236104963.909265 epoch 20epoch   20 error 351010.4 energy -246873022.282188 epoch 21epoch   21 error 350847.1 energy -257470705.809567 epoch 22epoch   22 error 349911.6 energy -267900561.925812 epoch 23epoch   23 error 349589.7 energy -278184302.605534 epoch 24epoch   24 error 349400.3 energy -288317945.532343 epoch 25epoch   25 error 349051.0 energy -298312328.865682 epoch 26epoch   26 error 348249.4 energy -308184434.905750 epoch 27epoch   27 error 348383.1 energy -317909079.840016 epoch 28epoch   28 error 347618.3 energy -327508125.959673 epoch 29epoch   29 error 347152.3 energy -336984710.426838 epoch 30epoch   30 error 346707.3 energy -346366295.669933 epoch 31epoch   31 error 347245.8 energy -355642353.726434 epoch 32epoch   32 error 346502.2 energy -364798534.538484 epoch 33epoch   33 error 346450.0 energy -373854688.256938 epoch 34epoch   34 error 346358.1 energy -382818178.531560 epoch 35epoch   35 error 346985.5 energy -391695106.532281 epoch 36epoch   36 error 346818.4 energy -400478029.118356 epoch 37epoch   37 error 346446.7 energy -409183885.047261 epoch 38epoch   38 error 346409.3 energy -417793622.658515 epoch 39epoch   39 error 346342.5 energy -426331454.717778 epoch 40epoch   40 error 345685.5 energy -434801072.747726 epoch 41epoch   41 error 345374.3 energy -443199522.909101 epoch 42epoch   42 error 345590.6 energy -451522224.505664 epoch 43epoch   43 error 345611.4 energy -459769819.711364 epoch 44epoch   44 error 345459.2 energy -467949310.324651 epoch 45epoch   45 error 345785.0 energy -476052215.833106 epoch 46epoch   46 error 345640.1 energy -484099406.063227 epoch 47epoch   47 error 344962.8 energy -492075533.907423 epoch 48epoch   48 error 344727.7 energy -500000744.350654 epoch 49epoch   49 error 345307.3 energy -507865250.165273 epoch 50epoch   50 error 345707.6 energy -515675253.128295 

可以发现能量值依旧遵循上面两条规律。

2.2 自由能量函数

如果看RBM相关论文，经常会提到一个东东叫做自由能量函数(free energy)

这个是一篇关于用玻尔兹曼机做分类的文章中的一个式子，可以去我的CSDN资源中下载

这里面的softplus也是一种函数类型，类似于ReLu、sigmoid等，Softplus函数是Logistic-Sigmoid函数原函数。

按照这个公式，可以抽取一下普通的RBM中的能量函数，在一位作者的博客中有相关解释，这里搬过来

当隐藏层单元值为二值情况时候，很容易证明出

代码书写如下：

energy=energy-sum(sum(negdata.*repmat(visbiases,size(negdata,1),1)))-...    sum(sum( log(1+exp(negdata*vishid+repmat(hidbiases,size(poshidstates,1),1))) ));

迭代第一次的结果：

Pretraining Layer 1 with RBM: 784-500 epoch 1epoch    1 error 905276.0 energy -19881397.779961 epoch 2epoch    2 error 558779.6 energy -47693109.210766 epoch 3epoch    3 error 495834.6 energy -79830190.885475 epoch 4epoch    4 error 468697.6 energy -114398712.137404 epoch 5epoch    5 error 453039.3 energy -150310200.560388 epoch 6epoch    6 error 478686.3 energy -182605142.786704 epoch 7epoch    7 error 451919.2 energy -213180793.202729 epoch 8epoch    8 error 438010.1 energy -242816234.242592 epoch 9epoch    9 error 427760.4 energy -271590223.327619 epoch 10epoch   10 error 420847.2 energy -299660032.178816 epoch 11epoch   11 error 415645.8 energy -326954499.696240 epoch 12epoch   12 error 410386.1 energy -353688087.921110 epoch 13epoch   13 error 408491.9 energy -379773439.302978 epoch 14epoch   14 error 404256.8 energy -405219040.048392 epoch 15epoch   15 error 402607.1 energy -430136766.920731 epoch 16epoch   16 error 398868.0 energy -454524480.565422 epoch 17epoch   17 error 398208.7 energy -478411816.895757 epoch 18epoch   18 error 396493.4 energy -501819653.242841 epoch 19epoch   19 error 394605.5 energy -524762199.874034 epoch 20epoch   20 error 392981.9 energy -547265960.648713 epoch 21epoch   21 error 392338.4 energy -569340099.227584 epoch 22epoch   22 error 390601.4 energy -591085154.512036 epoch 23epoch   23 error 389879.6 energy -612461539.974077 epoch 24epoch   24 error 388782.1 energy -633468451.054830 epoch 25epoch   25 error 388364.5 energy -654125425.131981 epoch 26epoch   26 error 386876.1 energy -674518443.101429 epoch 27epoch   27 error 386544.7 energy -694619635.858860 epoch 28epoch   28 error 385006.0 energy -714467061.612437 epoch 29epoch   29 error 384898.6 energy -734014091.415583 epoch 30epoch   30 error 384137.1 energy -753300736.046747 epoch 31epoch   31 error 383938.5 energy -772303792.788062 epoch 32epoch   32 error 383642.5 energy -791090169.476486 epoch 33epoch   33 error 382299.7 energy -809661333.174433 epoch 34epoch   34 error 381459.4 energy -828056903.650036 epoch 35epoch   35 error 382378.4 energy -846229339.194885 epoch 36epoch   36 error 381321.8 energy -864236457.069615 epoch 37epoch   37 error 380576.9 energy -882130475.692142 epoch 38epoch   38 error 380819.1 energy -899805881.559751 epoch 39epoch   39 error 380575.8 energy -917291008.281778 epoch 40epoch   40 error 380441.0 energy -934597287.769714 epoch 41epoch   41 error 378924.6 energy -951799519.728817 epoch 42epoch   42 error 379242.5 energy -968837996.416408 epoch 43epoch   43 error 378084.0 energy -985763999.393868 epoch 44epoch   44 error 377760.6 energy -1002485955.994587 epoch 45epoch   45 error 378065.3 energy -1019135408.410493 epoch 46epoch   46 error 378113.7 energy -1035609968.466859 epoch 47epoch   47 error 378137.6 energy -1051977206.619751 epoch 48epoch   48 error 377804.7 energy -1068256355.969882 epoch 49epoch   49 error 377078.1 energy -1084361351.832399 epoch 50epoch   50 error 376941.1 energy -1100352833.515859 

迭代第二次的结果

Pretraining Layer 2 with RBM: 500-500 epoch 1epoch    1 error 993889.2 energy -15205761.985310 epoch 2epoch    2 error 676743.8 energy -34794600.316635 epoch 3epoch    3 error 622237.7 energy -54860642.213566 epoch 4epoch    4 error 585614.3 energy -75025441.023491 epoch 5epoch    5 error 555836.9 energy -95270049.773320 epoch 6epoch    6 error 521063.7 energy -113064624.687646 epoch 7epoch    7 error 442315.3 energy -129533185.056863 epoch 8epoch    8 error 407058.7 energy -145427948.901373 epoch 9epoch    9 error 389512.7 energy -160926615.310918 epoch 10epoch   10 error 379349.7 energy -176038677.575432 epoch 11epoch   11 error 372263.0 energy -190819909.913752 epoch 12epoch   12 error 368580.7 energy -205272520.010386 epoch 13epoch   13 error 365315.1 energy -219429209.242861 epoch 14epoch   14 error 363198.0 energy -233282955.187790 epoch 15epoch   15 error 360865.5 energy -246872028.136193 epoch 16epoch   16 error 360440.2 energy -260191385.979074 epoch 17epoch   17 error 358262.1 energy -273277908.363102 epoch 18epoch   18 error 356881.8 energy -286135114.134431 epoch 19epoch   19 error 356049.6 energy -298750619.512386 epoch 20epoch   20 error 356009.3 energy -311137943.591194 epoch 21epoch   21 error 355319.0 energy -323321281.109947 epoch 22epoch   22 error 354783.1 energy -335312699.884763 epoch 23epoch   23 error 354477.3 energy -347119931.104351 epoch 24epoch   24 error 354285.7 energy -358745715.833463 epoch 25epoch   25 error 353366.3 energy -370214880.549267 epoch 26epoch   26 error 352662.9 energy -381532009.670373 epoch 27epoch   27 error 353588.7 energy -392675673.518439 epoch 28epoch   28 error 352470.9 energy -403697030.809657 epoch 29epoch   29 error 353054.5 energy -414589450.592768 epoch 30epoch   30 error 352482.0 energy -425354947.125350 epoch 31epoch   31 error 351719.4 energy -435996803.022372 epoch 32epoch   32 error 351546.8 energy -446524221.283293 epoch 33epoch   33 error 351439.6 energy -456927518.928294 epoch 34epoch   34 error 351518.5 energy -467237727.772437 epoch 35epoch   35 error 351350.9 energy -477451966.520637 epoch 36epoch   36 error 350986.0 energy -487572943.439880 epoch 37epoch   37 error 350939.2 energy -497598679.794740 epoch 38epoch   38 error 350509.6 energy -507538226.850344 epoch 39epoch   39 error 350470.0 energy -517375214.715247 epoch 40epoch   40 error 351177.7 energy -527125526.454195 epoch 41epoch   41 error 350052.4 energy -536812334.692637 epoch 42epoch   42 error 350338.3 energy -546408162.241688 epoch 43epoch   43 error 349897.6 energy -555922938.066808 epoch 44epoch   44 error 350848.5 energy -565355955.788417 epoch 45epoch   45 error 350459.8 energy -574712019.150728 epoch 46epoch   46 error 349903.4 energy -583997810.590286 epoch 47epoch   47 error 350130.9 energy -593219406.465314 epoch 48epoch   48 error 349957.5 energy -602379132.214209 

回顾一下便能发现，判断玻尔兹曼机的参数设置是否合理或者训练是否朝着正常方向的两个可能的判别标准就是：

1、重构误差：一般是均方差，是正值、曲线向X轴逼近

2、能量值或者自由能量值：负值、远离X轴方向收敛

当然如果是判别式的RBM，可以利用CNN的判别方法，观察验证集的分类错误率。

文章代码下载地址：http://download.csdn.net/detail/zb1165048017/9750247

数据集即为：链接：http://pan.baidu.com/s/1pK9YZIb 密码：qw3w

【注】博文是博主自己研究的，可能有错误，如若有任何问题，请在评论区标注，大家一起研究。