# Back propagation algorithm of Neural Network : XOR training

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Ashikur on 22 Jan 2012
Commented: sultana albanhar on 15 Apr 2022
c=0;
wih = .1*ones(nh,ni+1);
who = .1*ones(no,nh+1);
while(c<3000)
c=c+1;
for i = 1:length(x(1,:))
for j = 1:nh
netj(j) = wih(j,1:end-1)*double(x(:,i))+wih(j,end)*1;
outj(j) = 1./(1+exp(-1*netj(j)));
end
% hidden to output layer
for k = 1:no
netk(k) = who(k,1:end-1)*outj'+who(k,end)*1;
outk(k) = 1./(1+exp(-1*netk(k)));
delk(k) = outk(k)*(1-outk(k))*(t(k,i)-outk(k));
end
% back proagation for j = 1:nh s=0; for k = 1:no s = s+who(k,j)*delk(k); end
delj(j) = outj(j)*(1-outj(j))*s;
s=0;
end
for k = 1:no
for l = 1:nh
who(k,l)=who(k,l)+.5*delk(k)*outj(l);
end
who(k,l+1)=who(k,l+1)+1*delk(k)*1;
end
for j = 1:nh
for ii = 1:ni
wih(j,ii)=wih(j,ii)+.5*delj(j)*double(x(ii,i));
end
wih(j,ii+1)=wih(j,ii+1)+1*delj(j)*1;
end
end
end
// The code above, I have written it to implement back propagation neural network, x is input , t is desired output, ni , nh, no number of input, hidden and output layer neuron. I am testing this for different functions like AND, OR, it works fine for these. But XOR is not working.
// Training x = [0 0 1 1; 0 1 0 1] // Training t = [0 1 1 0]
// who -> weight matrix from hidden to output layer
// wih -> weight matrix from input to hidden layer
// Can you help ?
sultana albanhar on 15 Apr 2022
how this code work XOR?

Greg Heath on 25 Jan 2012
close all, clear all, clc
x = [0 0 1 1; 0 1 0 1]
t = [0 1 1 0]
[ni N] = size(x)
[no N] = size(t)
nh = 2
% wih = .1*ones(nh,ni+1);
% who = .1*ones(no,nh+1);
wih = 0.01*randn(nh,ni+1);
who = 0.01*randn(no,nh+1);
c = 0;
while(c < 3000)
c = c+1;
% %for i = 1:length(x(1,:))
for i = 1:N
for j = 1:nh
netj(j) = wih(j,1:end-1)*x(:,i)+wih(j,end);
% %outj(j) = 1./(1+exp(-netj(j)));
outj(j) = tansig(netj(j));
end
% hidden to output layer
for k = 1:no
netk(k) = who(k,1:end-1)*outj' + who(k,end);
outk(k) = 1./(1+exp(-netk(k)));
delk(k) = outk(k)*(1-outk(k))*(t(k,i)-outk(k));
end
% back propagation
for j = 1:nh
s=0;
for k = 1:no
s = s + who(k,j)*delk(k);
end
delj(j) = outj(j)*(1-outj(j))*s;
% %s=0;
end
for k = 1:no
for l = 1:nh
who(k,l) = who(k,l)+.5*delk(k)*outj(l);
end
who(k,l+1) = who(k,l+1)+1*delk(k)*1;
end
for j = 1:nh
for ii = 1:ni
wih(j,ii) = wih(j,ii)+.5*delj(j)*x(ii,i);
end
wih(j,ii+1) = wih(j,ii+1)+1*delj(j)*1;
end
end
end
h = tansig(wih*[x;ones(1,N)])
y = logsig(who*[h;ones(1,N)])
e = t-round(y)
Hope this helps.
Greg
Greg Heath on 10 Sep 2020
1. I ALWAYS use the bipolar tanh in hidden layers. It ALWAYS works.
2. What are x and t for 3 input XOR???
Greg

Greg Heath on 27 Jan 2012
It is well known that successful deterministic training depends on a lucky choice of initial weights. The most common approach is to use a loop and create Ntrial (e.g., 10 or more) nets from different random initial weights. Then choose the best net.
It is also well known that an odd bounded monotonically increasing activation function like TANSIG is the choice of preference for hidden layers because it does not restrict the polarity of the layer variables. It works even better when the input is shifted to have zero mean.
You can check the superiority of TANSIG and zero-mean yourself. You can also search the comp.ai.neural-nets FAQ and archives to find both agreement and numerical experiments.
For most real world problems the best choice for number of hidden nodes, H, is not known apriori. That is why I have posted many examples using a double loop: An outer loop over H and an inner loop over Ntrials random weight initializations. For examples, search the newsgroup using the keywords
heath clear Ntrials
Hope this helps.
Greg
Havot Albeyboni on 9 Dec 2020
Edited: Havot Albeyboni on 9 Dec 2020
can anyone please explain this line ???
netj(j) = wih(j,1:end-1)*x(:,i)+wih(j,end);
shouldnt it be i.e ->> Y3=sigmoid(X1W13+ X2W23 - θ3 )
rgrds

Imran Babar on 8 May 2013
Dear sir I want to use the same code for the following data set
Input dataset=[1 1 1 2;1 1 2 2;1 2 2 2; 2 2 2 2] Output=[5 6 7 8]
but it is always generating output as given below
1 1 1 1
I tried my best but unable to understand how may I get these results
Greg Heath on 10 May 2013
Your outputs are not within the range of logsig.
Either normalize your outputs to fit in {0,1)
or
change your output activation function (e.g., 'purelin')

Sohel Ahammed on 4 Jul 2015
Ok. If i Want to test it, how i have to change. Ex: input : 1 0 expected output : 1 (From learing).

dsmalenb on 17 Oct 2018
Am I missing something here but I don't see any bias neurons. Maybe this is why you are getting some inputs to work and others not?
Greg Heath on 9 Nov 2018
The 1 is a placeholder which is multiplied by a learned weight.
Hmm, I've been using that notation for decades and this is the 1st question re that that I can remember.
Greg

sultana albanhar on 14 Apr 2022 