LSTM简单例子(MATLAB code)_lstm是python代码还是matlab

最近在学习RNN和LSTM，

(1)： http://magicly.me/2017/03/09/iamtrask-anyone-can-code-lstm/

(2):  https://zybuluo.com/hanbingtao/note/581764

(3): http://blog.sina.com.cn/s/blog_a5fdbf010102w7y8.html

在资料1中给出了RNN的python代码，广为流传，并且被(3)翻译成了matlab代码。网址(2)是个很好的理论推导的网站，强烈推荐。想学习的可以缘木求鱼，根据上述资料进行学习。

但是在(1)中提及到的python源码作者说过段时间在twitter上更新LSTM代码，目前还未更新;(3)的作者想根据RNN写LSTM，但是发现并未运行成功，于是我在(2)的基础上对其进行修改，并运行成功，下面是指出作者(2)中的错误：

1：作者在求H_t_diff时有问题，不应该乘以那么导数，因为从后面传过来的误差是输出层(不是输出门)的误差乘以权值矩阵就可以了。

2：求各个门的误差都不用成乘激活函数

3：各个门中均未加偏置

如果你运行成功，还望点个赞。哈哈！

以上错误可以根据我下面给出的源码和(3)中的源码进行比较。

下面是我修改后的源代码：

%接下来就是LSTM的Matlab代码，我也进行了注释，用英文注释的，也比较容易懂：
% implementation of LSTM
clc
% clear
close all


%% training dataset generation
binary_dim     = 8;


largest_number = 2^binary_dim - 1;
binary         = cell(largest_number, 1);


for i = 1:largest_number + 1
    binary{i}      = dec2bin(i-1, binary_dim);
    int2binary{i}  = binary{i};
end


%% input variables
alpha      = 0.1;
input_dim  = 2;
hidden_dim = 32;
output_dim = 1;
allErr = [];
%% initialize neural network weights
% in_gate     = sigmoid(X(t) * X_i + H(t-1) * H_i)    ------- (1)
X_i = 2 * rand(input_dim, hidden_dim) - 1;
H_i = 2 * rand(hidden_dim, hidden_dim) - 1;
X_i_update = zeros(size(X_i));
H_i_update = zeros(size(H_i));
bi = 2*rand(1,1) - 1;
bi_update = 0;


% forget_gate = sigmoid(X(t) * X_f + H(t-1) * H_f)    ------- (2)
X_f = 2 * rand(input_dim, hidden_dim) - 1;
H_f = 2 * rand(hidden_dim, hidden_dim) - 1;
X_f_update = zeros(size(X_f));
H_f_update = zeros(size(H_f));
bf = 2*rand(1,1) - 1;
bf_update = 0;
% out_gate    = sigmoid(X(t) * X_o + H(t-1) * H_o)    ------- (3)
X_o = 2 * rand(input_dim, hidden_dim) - 1;
H_o = 2 * rand(hidden_dim, hidden_dim) - 1;
X_o_update = zeros(size(X_o));
H_o_update = zeros(size(H_o));
bo = 2*rand(1,1) - 1;
bo_update = 0;
% g_gate      = tanh(X(t) * X_g + H(t-1) * H_g)       ------- (4)
X_g = 2 * rand(input_dim, hidden_dim) - 1;
H_g = 2 * rand(hidden_dim, hidden_dim) - 1;
X_g_update = zeros(size(X_g));
H_g_update = zeros(size(H_g));
bg = 2*rand(1,1) - 1;
bg_update = 0;


out_para = 2 * rand(hidden_dim, output_dim) - 1;
out_para_update = zeros(size(out_para));
% C(t) = C(t-1) .* forget_gate + g_gate .* in_gate    ------- (5)
% S(t) = tanh(C(t)) .* out_gate                       ------- (6)
% Out  = sigmoid(S(t) * out_para)                     ------- (7)
% Note: Equations (1)-(6) are cores of LSTM in forward, and equation (7) is
% used to transfer hiddent layer to predicted output, i.e., the output layer.
% (Sometimes you can use softmax for equation (7))


%% train 
iter = 99999; % training iterations
for j = 1:iter
    % generate a simple addition problem (a + b = c)
    a_int = randi(round(largest_number/2));   % int version
    a     = int2binary{a_int+1};              % binary encoding
    
    b_int = randi(floor(largest_number/2));   % int version
    b     = int2binary{b_int+1};              % binary encoding
    
    % true answer
    c_int = a_int + b_int;                    % int version
    c     = int2binary{c_int+1};              % binary encoding
    
    % where we'll store our best guess (binary encoded)
    d     = zeros(size(c));
    if length(d)<8
        pause;
    end
    
    % total error
    overallError = 0;
    
    % difference in output layer, i.e., (target - out)
    output_deltas = [];
    
    % values of hidden layer, i.e., S(t)
    hidden_layer_values = [];
    cell_gate_values    = [];
    % initialize S(0) as a zero-vector
    hidden_layer_values = [hidden_layer_values; zeros(1, hidden_dim)];
    cell_gate_values    = [cell_gate_values; zeros(1, hidden_dim)];
    
    % initialize memory gate
    % hidden layer
    H = [];
    H = [H; zeros(1, hidden_dim)];
    % cell gate
    C = [];
    C = [C; zeros(1, hidden_dim)];
    % in gate
    I = [];
    % forget gate
    F = [];
    % out gate
    O = [];
    % g gate
    G = [];
    
    % start to process a sequence, i.e., a forward pass
    % Note: the output of a LSTM cell is the hidden_layer, and you need to 
    % transfer it to predicted output
    for position = 0:binary_dim-1
        % X ------> input, size: 1 x input_dim
        X = [a(binary_dim - position)-'0' b(binary_dim - position)-'0'];
        
        % y ------> label, size: 1 x output_dim
        y = [c(binary_dim - position)-'0']';
        
        % use equations (1)-(7) in a forward pass. here we do not use bias
        in_gate     = sigmoid(X * X_i + H(end, :) * H_i + bi);  % equation (1)
        forget_gate = sigmoid(X * X_f + H(end, :) * H_f + bf);  % equation (2)
        out_gate    = sigmoid(X * X_o + H(end, :) * H_o + bo);  % equation (3)
        g_gate      = tan_h(X * X_g + H(end, :) * H_g + bg);    % equation (4)
        C_t         = C(end, :) .* forget_gate + g_gate .* in_gate;    % equation (5)
        H_t         = tan_h(C_t) .* out_gate;                          % equation (6)
        
        % store these memory gates
        I = [I; in_gate];
        F = [F; forget_gate];
        O = [O; out_gate];
        G = [G; g_gate];
        C = [C; C_t];
        H = [H; H_t];
        
        % compute predict output
        pred_out = sigmoid(H_t * out_para);
        
        % compute error in output layer
        output_error = y - pred_out;
        
        % compute difference in output layer using derivative
        % output_diff = output_error * sigmoid_output_to_derivative(pred_out);
        output_deltas = [output_deltas; output_error];%*sigmoid_output_to_derivative(pred_out)];
%         output_deltas = [output_deltas; output_error*(pred_out)];
        % compute total error
        % note that if the size of pred_out or target is 1 x n or m x n,
        % you should use other approach to compute error. here the dimension 
        % of pred_out is 1 x 1
        overallError = overallError + abs(output_error(1));
        
        % decode estimate so we can print it out
        d(binary_dim - position) = round(pred_out);
    end
    
    % from the last LSTM cell, you need a initial hidden layer difference
    future_H_diff = zeros(1, hidden_dim);
    
    % stare back-propagation, i.e., a backward pass
    % the goal is to compute differences and use them to update weights
    % start from the last LSTM cell
    for position = 0:binary_dim-1
        X = [a(position+1)-'0' b(position+1)-'0'];
        
        % hidden layer
        H_t = H(end-position, :);         % H(t)
        % previous hidden layer
        H_t_1 = H(end-position-1, :);     % H(t-1)
        C_t = C(end-position, :);         % C(t)
        C_t_1 = C(end-position-1, :);     % C(t-1)
        O_t = O(end-position, :);
        F_t = F(end-position, :);
        G_t = G(end-position, :);
        I_t = I(end-position, :);
        
        % output layer difference
        output_diff = output_deltas(end-position, :);
        
        % hidden layer difference
        % note that here we consider one hidden layer is input to both
        % output layer and next LSTM cell. Thus its difference also comes
        % from two sources. In some other method, only one source is taken
        % into consideration.
        % use the equation: delta(l) = (delta(l+1) * W(l+1)) .* f'(z) to
        % compute difference in previous layers. look for more about the
        % proof at http://neuralnetworksanddeeplearning.com/chap2.html
%         H_t_diff = (future_H_diff * (H_i' + H_o' + H_f' + H_g') + output_diff * out_para') ...
%                    .* sigmoid_output_to_derivative(H_t);


        H_t_diff = output_diff * (out_para');% .* sigmoid_output_to_derivative(H_t);
%         H_t_diff = output_diff * (out_para') .* sigmoid_output_to_derivative(H_t);
%         future_H_diff = H_t_diff;
%         out_para_diff = output_diff * (H_t) * sigmoid_output_to_derivative(out_para);
        out_para_diff =  (H_t') * output_diff;%输出层权重


        % out_gate diference
        O_t_diff = H_t_diff .* tan_h(C_t) .* sigmoid_output_to_derivative(O_t);
        
        % C_t difference
        C_t_diff = H_t_diff .* O_t .* tan_h_output_to_derivative(C_t);
        
%         % C(t-1) difference
%         C_t_1_diff = C_t_diff .* F_t;
        
        % forget_gate_diffeence
        F_t_diff = C_t_diff .* C_t_1 .* sigmoid_output_to_derivative(F_t);
        
        % in_gate difference
        I_t_diff = C_t_diff .* G_t .* sigmoid_output_to_derivative(I_t);
        
        % g_gate difference
        G_t_diff = C_t_diff .* I_t .* tan_h_output_to_derivative(G_t);
        
        % differences of X_i and H_i
        X_i_diff =  X' * I_t_diff;% .* sigmoid_output_to_derivative(X_i);
        H_i_diff =  (H_t_1)' * I_t_diff;% .* sigmoid_output_to_derivative(H_i);
        
        % differences of X_o and H_o
        X_o_diff = X' * O_t_diff;% .* sigmoid_output_to_derivative(X_o);
        H_o_diff = (H_t_1)' * O_t_diff;% .* sigmoid_output_to_derivative(H_o);
        
        % differences of X_o and H_o
        X_f_diff = X' * F_t_diff;% .* sigmoid_output_to_derivative(X_f);
        H_f_diff = (H_t_1)' * F_t_diff;% .* sigmoid_output_to_derivative(H_f);
        
        % differences of X_o and H_o
        X_g_diff = X' * G_t_diff;% .* tan_h_output_to_derivative(X_g);
        H_g_diff = (H_t_1)' * G_t_diff;% .* tan_h_output_to_derivative(H_g);
        
        % update
        X_i_update = X_i_update + X_i_diff;
        H_i_update = H_i_update + H_i_diff;
        X_o_update = X_o_update + X_o_diff;
        H_o_update = H_o_update + H_o_diff;
        X_f_update = X_f_update + X_f_diff;
        H_f_update = H_f_update + H_f_diff;
        X_g_update = X_g_update + X_g_diff;
        H_g_update = H_g_update + H_g_diff;
        bi_update = bi_update + I_t_diff;
        bo_update = bo_update + O_t_diff;
        bf_update = bf_update + F_t_diff;
        bg_update = bg_update + G_t_diff;                        
        out_para_update = out_para_update + out_para_diff;
    end
    
    X_i = X_i + X_i_update * alpha; 
    H_i = H_i + H_i_update * alpha;
    X_o = X_o + X_o_update * alpha; 
    H_o = H_o + H_o_update * alpha;
    X_f = X_f + X_f_update * alpha; 
    H_f = H_f + H_f_update * alpha;
    X_g = X_g + X_g_update * alpha; 
    H_g = H_g + H_g_update * alpha;
    bi = bi + bi_update * alpha;
    bo = bo + bo_update * alpha;
    bf = bf + bf_update * alpha;
    bg = bg + bg_update * alpha;
    out_para = out_para + out_para_update * alpha;
    
    X_i_update = X_i_update * 0; 
    H_i_update = H_i_update * 0;
    X_o_update = X_o_update * 0; 
    H_o_update = H_o_update * 0;
    X_f_update = X_f_update * 0; 
    H_f_update = H_f_update * 0;
    X_g_update = X_g_update * 0; 
    H_g_update = H_g_update * 0;
    bi_update = 0;
    bf_update = 0;
    bo_update = 0;
    bg_update = 0;
    out_para_update = out_para_update * 0;
    
    if(mod(j,1000) == 0)
        if 1%overallError > 1
            err = sprintf('Error:%s\n', num2str(overallError)); fprintf(err);
        end
        allErr = [allErr overallError];
%         try
            d = bin2dec(num2str(d));
%         catch
%             disp(d);
%         end
        if 1%overallError>1
        pred = sprintf('Pred:%s\n',dec2bin(d,8)); fprintf(pred);
        Tru = sprintf('True:%s\n', num2str(c)); fprintf(Tru);
        end
        out = 0;
        tmp = dec2bin(d,8);
        for i = 1:8           
            out = out + str2double(tmp(8-i+1)) * power(2,i-1);
        end
        if 1%overallError>1
        fprintf('%d + %d = %d\n',a_int,b_int,out);
        sep = sprintf('-------%d------\n', j); fprintf(sep);
        end
    end
end
figure;plot(allErr);
function output = sigmoid(x)
    output = 1./(1+exp(-x));
end


function y = sigmoid_output_to_derivative(output)
    y = output.*(1-output);
end


function y = tan_h_output_to_derivative(x)
    y = (1-x.^2);
end


function y=tan_h(x)
y=(exp(x)-exp(-x))./(exp(x)+exp(-x));
end