function bpback1(ny,eta,mini_size,epoch)%ny:隐藏层为1层，神经元数目为ny;eta:学习速率;mini_size:最小采样;eopch：迭代次数%该函数为梯度下降+反向传播%images[numimages,images]=bpimages(‘train-images.idx3-ubyte‘);[n_test,test_data_x]=bpimages(‘t10k-images.idx3-ubyte‘);%labels[numlabels,labels]=bplabels(‘train-labels.idx1-ubyte‘);[n_test,test_data_y]=bplabels(‘t10k-labels.idx1-ubyte‘);%init w/b%rand(‘state‘,sum(100*clock));%ny=30;eta=0.01;mini_size=10;w1=randn(ny,784);b1=randn(ny,1);w2=randn(10,ny);b2=randn(10,1);for epo=1:epochfor nums=1:numimages/mini_size    for num=(nums-1)*mini_size+1:nums*mini_size        x=images(:,num);        y=labels(:,num);    net2=w1*x;               %input of net2                      for i=1:ny    hidden(i)=1/(1+exp(-net2(i)-b1(i)));%output of net2                   end       net3=w2*hidden‘;            %input of net3                  for i=1:10    o(i)=1/(1+exp(-net3(i)-b2(i)));%output of net3    end        %back    for i=1:10    delta3(i)=(y(i)-o(i))*o(i)*(1-o(i));%delta of net3                     end    for i=1:ny    delta2(i)=delta3*w2(:,i)*hidden(i)*(1-hidden(i));%delta of net2        end    %updata w/b    for i=1:10        for j=1:ny    w2(i,j)=w2(i,j)+eta*delta3(i)*hidden(j)/mini_size;                  end    end    for i=1:ny        for j=1:784    w1(i,j)=w1(i,j)+eta*delta2(i)*x(j)/mini_size;                      end    end    for i=1:10    b2(i)=b2(i)+eta*delta3(i);         end    for i=1:ny    b1(i)=b1(i)+eta*delta2(i);        end    end end%calculate sum of error%accuracysum0=0;for i=1:1000    x0=test_data_x(:,i);    y0=test_data_y(:,i);    a1=[];    a2=[];    s1=w1*x0;    for j=1:ny    a1(j)=1/(1+exp(-s1(j)-b1(j)));    end    s2=w2*a1‘;    for j=1:10    a2(j)=1/(1+exp(-s2(j)-b2(j)));    end    a2=a2‘;    [m1,n1]=max(a2);    [m2,n2]=max(y0);    if n1==n2        sum0=sum0+1;    end    %e=o‘-y;    %sigma(num)=e‘*e;    sigma(i)=sumsqr(a2-y0);   %代价为误差平方和endsigmas(epo)=sum(sigma)/(2*1000);fprintf(‘epoch %d:%d/%d\n‘,epo,sum0,1000); endplot(sigmas);xlabel(‘epoch‘);ylabel(‘cost on the training_data‘);end

function bpback2(ny,eta,mini_size,epoch,numda)%ny:隐藏层为1层，神经元数目为ny;eta:学习速率;mini_size:最小采样;eopch：迭代次数%bpback的优化，包括L2规范化、交叉熵代价函数的引入---结果证明该优化非常赞！%images[numimages,images]=bpimages(‘train-images.idx3-ubyte‘);[n_test,test_data_x]=bpimages(‘t10k-images.idx3-ubyte‘);%labels[numlabels,labels]=bplabels(‘train-labels.idx1-ubyte‘);[n_test,test_data_y]=bplabels(‘t10k-labels.idx1-ubyte‘);%init w/b%ny=30;eta=0.05;mini_size=10;epoch=10;numda=0.1;rand(‘state‘,sum(100*clock));w1=randn(ny,784)/sqrt(784);b1=randn(ny,1);w2=randn(10,ny)/sqrt(ny);b2=randn(10,1);for epo=1:epochfor nums=1:numimages/mini_size    for num=(nums-1)*mini_size+1:nums*mini_size        x=images(:,num);        y=labels(:,num);    net2=w1*x;               %input of net2                      hidden=1./(1+exp(-net2-b1));%output of net2                   net3=w2*hidden;            %input of net3                   o=1./(1+exp(-net3-b2));%output of net3    %back    delta3=(y-o);%delta of net3   由于交叉熵代价函数的引入，偏导被消去    delta2=w2‘*delta3.*(hidden.*(1-hidden));%delta of net2        %updata w/b    w2=w2*(1-eta*numda/numimages)+eta*delta3*hidden‘/mini_size;     %L2规范化          w1=w1*(1-eta*numda/numimages)+eta*delta2*x‘/mini_size;                   b2=b2+eta*delta3/mini_size;        b1=b1+eta*delta2/mini_size;        end end%calculate sum of error%accuracysum0=0;for i=1:1000    x0=test_data_x(:,i);    y0=test_data_y(:,i);    a1=[];    a2=[];    a1=1./(1+exp(-w1*x0-b1));    a2=1./(1+exp(-w2*a1-b2));    [m1,n1]=max(a2);    [m2,n2]=max(y0);    if n1==n2        sum0=sum0+1;    end    %e=o‘-y;    %sigma(num)=e‘*e;    sigma(i)=m2*log(m1)+(1-m2)*log(1-m1);   %计算代价costendsigmas(epo)=-sum(sigma)/1000;       %cost求和fprintf(‘epoch %d:%d/%d\n‘,epo,sum0,1000); endplot(sigmas);xlabel(‘epoch‘);ylabel(‘cost on the training_data‘);end