implementation of mini-batch stochastic gradient descent

I implemented a mini-batch stochastic gradien descent but counldn't find the bug in my code.

I used this implement to do a classification problem but all my final predictions are 0.

W2 = -1+2*rand(5,2); W3 = -1+2*rand(5,5); 
W4 = -1+2*rand(5,5); W5 = -1+2*rand(1,5);
b2 = -1+2*rand(5,1); b3 = -1+2*rand(5,1); 
b4 = -1+2*rand(5,1); b5 = -1+2*rand(1,1);

eta = 5e-3; % learning rate
iter = 1000; % number of iterations
num_data = length(label);

loss_vec = zeros(1,iter);
tloss_vec = zeros(1,iter);

for it = 1:iter
    % mini-batch method
    batch_size = 50;
    rand_idx = randperm(num_data);
    rand_idx = reshape(rand_idx,[],num_data/batch_size);
    
    for idx = rand_idx
    % forward pass
        a2 = activate([x1(:,idx);x2(:,idx)], W2, b2);
        a3 = activate(a2,W3,b3);
        a4 = activate(a3,W4,b4);
        a5 = activate(a4,W5,b5);
        
    % backward pass (gradient)
        delta5 = a5.*(1-a5).*(a5-label(idx));
        delta4 = a4.*(1-a4).*(W5'*delta5);
        delta3 = a3.*(1-a3).*(W4'*delta4);
        delta2 = a2.*(1-a2).*(W3'*delta3);
        
    % update weights and bias
        W2 = W2 - 1/length(idx)*eta*delta2*[x1(:,idx);x2(:,idx)]';
        W3 = W3 - 1/length(idx)*eta*delta3*a2';
        W4 = W4 - 1/length(idx)*eta*delta4*a3';
        W5 = W5 - 1/length(idx)*eta*delta5*a4';
        b2 = b2 - 1/length(idx)*eta*sum(delta2,2);
        b3 = b3 - 1/length(idx)*eta*sum(delta3,2);
        b4 = b4 - 1/length(idx)*eta*sum(delta4,2);
        b5 = b5 - 1/length(idx)*eta*sum(delta5,2);
        
    % compute train loss and test loss
        loss_vec(it) = 1/(2*num_data)*LossFunc(W2,W3,W4,W5,b2,b3,b4,b5,[x1;x2],label);
        tloss_vec(it) = 1/(2*200)*LossFunc(W2,W3,W4,W5,b2,b3,b4,b5,[tx1;tx2],tlabel);
    end
end

%% cost function
function loss = LossFunc(W2,W3,W4,W5,b2,b3,b4,b5,x,y)
    a2 = activate(x, W2, b2);
    a3 = activate(a2, W3, b3);
    a4 = activate(a3, W4, b4);
    a5 = activate(a4, W5, b5);
    loss = norm(a5-y,2)^2;
end

%% prediction
function pred = predict(W2,W3,W4,W5,b2,b3,b4,b5,x)
    a2 = activate(x, W2, b2);
    a3 = activate(a2, W3, b3);
    a4 = activate(a3, W4, b4);
    a5 = activate(a4, W5, b5);
    pred = round(a5);
end

%% activation function
function y = activate(x,W,b)
    y = 1./(1+exp(-(W*x+b)));
end

Answer 1

[Mahesh Taparia]

Hi

You mentioned that you are implementing a classification network. In your code, you are using square of L2 norm to calculate the loss and loss derivative is also not correct while doing back propagation. Moreover, since it is a classification network, use the classification loss like cross entropy loss, focalcrossentropy, etc instead of norm. May be this is the reason you are getting 0 everytime.

Also, you can use MATLAB inbuilt function to perform back propagation. For this, you can refer the link given below:

Link 1

Link 2

Hope it will help!

[konoha]

the derivative of mes is -(y-f(x))f'(x). I don't follow your suggestions.

Thank you.

Answer 2

[Mohamed Salem]

Write a MATLAB code, that implement Dalta learning rule with mini-batch.

Compare (with graph) your mini-batch algorithm with SGD, Batch algorithm in terms of mean square error.