how do i construct neural network

how do i construct neural network that has two layers, four weights linking the input-to-hidden layer with no biases, and two weights linking the hidden-to-output layer with a 1 bias at the output neuron

Answer 1

[Greg Heath]

What you are asking doesn't make much sense. For a standard universal approximation I-H-O net the number of weights are

 Nw = (I+1)*H+(H+1)*O

where the 1s correspond to biases. If either bias node is removed, the net is no longer a universal approximator.

It looks like you want

 Nw = I*H+(H+1)*O

with

 I*H = 4
 H*O = 2
   O = 1

Consequently, O=1, H=2, I = 2 and

 size(input)  = [ 2 N ]
 size(target) = [ 1 N ]

Since you don't specify regregression or classification, lets try classification with the exclusive or function. Typically, I desire the explained target variance = coefficient of variation, = Rsquared (See Wikipeia) to be >= 0.99.

clear all, clc
x     = [1 1 -1 -1 ; -1 1 1 -1 ];
t     = [ 0 1 0 1 ];
MSE00 = var(t)                  % 0.33333 Reference MSE

net            = patternnet(2);
net.biasConnect = [ 0;1];        % No input bias
net.divideFcn   = 'dividetrain'; % No validation or test subsets
rng(0)
for i = 1:10
   net                = configure(net,x,t);
   [net tr y(i,:) e]  = train(net,x,t);
   R2(i,:)            = 1-mse(e)/MSE00;
end

 y  = y      % y  = 0.5*ones(10,4)
 R2 = R2     % R2 = 0.25*ones(10,1), (far from 0.99!!!)

Obviously, can get negligible error with the input bias.

Hope this helps.

Thank you for formally accepting my answer

Greg

[Thirunavukkarasu]

[Greg Heath]

You have designated 3 node layers which makes intuitive sense.

HOWEVER, THE CONVENTION IS TO DESIGNATE WEIGHT LAYERS OF WHICH YOU HAVE 2:

A hidden weight layer and an output weight layer.

Therefore, this is considered a 2-layer net!

I don't like this convention. However, it is what it is.

The nodes you have labeled as being in the Input Layer are considered FAN-IN-UNITS. Whereas the nodes in the other two layers are considered NEURONS.

Nevertheless, without a bias weight for the first weight layer (as I have illustrated with the XOR) you do not have a universal approximator.

Do you have any questions?

Greg