Improving the convergence of the Back-Propagation Algorithm

Untitled.m

clc;
clear;

nure = 2;

w1 = 2*rand(nure,1)-1;
w2 = 2*rand(1,nure)-1;
b1 = 2*rand(nure,1)-1;
b2 = 2*rand(1,1)-1;
w11 = w1;
w22 = w2;
b11 = b1;
b22 = b2;
lr = 0.01;
lr_1 = 0.1;
s = [];
s_1 = [];
time = 1000;

for k=1:time

    sum_e = 0;
    sum_s2 = 0;
    sum_s1 = 0;
    
for p = -2:0.2:2
    t = sin(pi*p/2);
    a1 = logsig(w1*p+b1);
    a2 = w2*a1+b2;
    e = t-a2;
    s2 = -2*e;
    s1 = diag((1-a1).*a1)*w2'*s2;
    
    b1 = b1-lr*s1;
    b2 = b2-lr*s2;
    
    sum_s2 = sum_s2+s2*a1';
    sum_s1 = sum_s1+s1*p;
    sum_e = sum_e + (t-a2)^2;
end
    s = [s sum_e];
    w2 = w2-lr*sum_s2;
    w1 = w1-lr*sum_s1;
end

for k=1:time

    sum_e = 0;
    sum_s2 = 0;
    sum_s1 = 0;
    
for p = -2:0.2:2
    t = sin(pi*p/2);
    a1 = logsig(w11*p+b11);
    a2 = w22*a1+b22;
    e = a2-t;
    s2 = e;
    s1 = diag((1-a1).*a1)*w22'*s2;
    
    b11 = b11-lr_1*s1;
    b22 = b22-lr_1*s2;
    
    sum_s2 = sum_s2+s2*a1';
    sum_s1 = sum_s1+s1*p;
    sum_e = sum_e + (t-a2)^2;
end
    s_1 = [s_1 sum_e];
    w22 = w22-lr_1*sum_s2;
    w11 = w11-lr_1*sum_s1;
end

figure(1);
    for q3 = -2:0.01:2;
    t = sin(pi*q3/2);
    plot(q3,t,'k');
    hold on;
    a1 = logsig(w1*q3+b1);
    a2 = w2*a1+b2;
    plot(q3,a2,'b');
    hold on;
    a3 = logsig(w11*q3+b11);
    a4 = w22*a3+b22;
    plot(q3,a4,'r');
    end
figure(2);
plot(1:length(s),s,'b');
hold on;
plot(1:length(s_1),s_1,'r');
hold on;