函式MnistConv使用反向傳播演算法訓練網路，獲取神經網路的權重和訓練資料，並返回訓練後的權重。

The function MnistConv, which trains thenetwork using the back-propagation algorithm, takes the neural network’sweights and training data and returns the trained weights.

[W1,W5, Wo] = MnistConv(W1, W5, Wo, X, D)

其中，W1、W5和Wo分別是卷積濾波器矩陣、池化-隱藏層權重矩陣和隱藏-輸出層權重矩陣。

where W1, W5, and Wo are the convolutionfilter matrix, pooling-hidden layer weight matrix, and hidden-output layerweight matrix, respectively.

X和D分別是訓練資料的輸入和正確輸出。

X and D are the input and correct outputfrom the training data, respectively.

下面的清單顯示了MnistConv.m檔案中的程式碼，它實現了MnistConv函式的功能。

The following listing shows the MnistConv.mfile, which implements the MnistConv function.

function [W1, W5, Wo] = MnistConv(W1, W5,Wo, X, D)

alpha = 0.01;

beta = 0.95;

momentum1 = zeros(size(W1));

momentum5 = zeros(size(W5));

momentumo = zeros(size(Wo));

N = length(D);

bsize = 100;

blist = 1:bsize:(N-bsize+1);

% One epoch loop 按照時代進行迴圈

for batch = 1:length(blist)

   dW1= zeros(size(W1));

   dW5= zeros(size(W5));

   dWo= zeros(size(Wo));

   %Mini-batch loop

   begin= blist(batch);

   fork = begin:begin+bsize-1

          %Forward pass = inference

          x= X(:, :, k); % Input, 28x28

          y1 = Conv(x, W1); % Convolution,20x20x20

          y2 = ReLU(y1); %

          y3 = Pool(y2); % Pool, 10x10x20

          y4 = reshape(y3, [], 1); % 2000

          v5 = W5*y4; % ReLU, 360

          y5 = ReLU(v5); %

          v = Wo*y5; % Softmax, 10

          y= Softmax(v); %

          %One-hot encoding

          d= zeros(10, 1);

          d(sub2ind(size(d),D(k), 1)) = 1;

          % Backpropagation 反向傳播

          e = d - y; % Output layer

          delta = e;

          e5= Wo' * delta; % Hidden(ReLU) layer

          delta5= (y5 > 0) .* e5;

          e4= W5' * delta5; % Pooling layer

          e3 = reshape(e4, size(y3));

          e2= zeros(size(y2));

          W3= ones(size(y2)) / (2*2);

          forc = 1:20

                 e2(:, :, c) = kron(e3(:, :,c), ones([2 2])) .* W3(:, :, c);

          end

          delta2= (y2 > 0) .* e2; % ReLU layer

          delta1_x= zeros(size(W1)); % Convolutional layer

          forc = 1:20

                 delta1_x(:,:, c) = conv2(x(:, :), rot90(delta2(:, :, c), 2), 'valid');

          end

          dW1= dW1 + delta1_x;

          dW5= dW5 + delta5*y4';

          dWo= dWo + delta *y5';

   end

   %Update weights 更新權值

   dW1= dW1 / bsize;

   dW5= dW5 / bsize;

   dWo= dWo / bsize;

   momentum1= alpha*dW1 + beta*momentum1;

   W1= W1 + momentum1;

   momentum5= alpha*dW5 + beta*momentum5;

   W5= W5 + momentum5;

   momentumo= alpha*dWo + beta*momentumo;

   Wo= Wo + momentumo;
 

end

end % 函式結束的end標記

這個程式碼看起來比以前的例子要複雜得多。

This code appears to be rather more complexthan the previous examples.

讓我們一部分一部分地看看這段程式碼。

Let’s take a look at it part by part.

函式MnistConv通過小批量方法訓練網路，而前面的示例使用SGD和批量方法。

The function MnistConv trains the networkvia the minibatch method, while the previous examples employed the SGD andbatch methods.

——本文譯自Phil Kim所著的《Matlab Deep Learning》

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