[Neural network] How does neural network calculate output from net.IW, net.LW, net.b ?

Example I have a trained neural network as following

clear all
clc
[ x, t ] = simplefit_dataset;
net      = feedforwardnet;

rng('default')
net = configure(net,x,t);
[net,tr,y,e] = train(net,x,t);

After training finished, weights will be save to net.IW, net.LW, net.b

How does the network calculate output from these weights ?

If output can be calculated as :

y=[ones(Ns,1) tansig([ones(Ns,1) x]*W1')] * W2'

Where Ns is number of training samples.

How can W1 and W2 be formed from net.IW, net.LW and net.b ?

Answer 1

[Greg Heath]

I will let you figure out how to do it when the default normalization and de-normalization are not removed:

 clear all, clc
[ x, t ] = simplefit_dataset;
[ I  N ] = size(x) %[ 1 94 ]
[ O  N ] = size(t) %[ 1 94 ]
net     = fitnet;  % H=10 default
rng('default')     % For repeatability

% net = configure(net,x,t); % For multiple designs

 A = net.input.processFcns  % see below
 B = net.output.processFcns % see below
% processFcns = {'removeconstantrows' 'mapminmax'}

 net.input.processFcns = { }; % Remove normalization
 net.output.processFcns= { };  

 [net,tr,y,e] = train(net,x,t); 
 R2           = 1-mse(e)/var(t,1) % 0.99998

 IW = net.IW{1,1} 
 b1 = net.b{1}
 b2 = net.b{2}
 LW = net.LW{2,1}

y1 = b2 + LW * tansig( b1 * ones(1,N) + IW * x );

 dy = max(abs(y1-y))    %2.6645e-15

Hope this helps.

Thank you for formally accepting my answer

Greg

[Son Nguyen]

Appreciate very much, this really helps. Could you please do me a favor ? How can I know and control the initial weights of training ? Example, how do I set initial weights as an given weights matrix ?

[Greg Heath]

It is better to just use the random weights assigned by the program.

Otherwise, reverse the above assignment statements. For example

 net.IW{1,1}= 0.01*randn(H,I);

for I input nodes and H hidden nodes.

[Asaduz Zaman]

Helped me a lot. Couldn't find why

sim(net,input)

and

classify(net,input)

wasn't producing same response as I'm new in NNTool. Now I got it. Thanks again.

Answer 2

[Greg Heath]

You did not consider

 net.input.processFcns

and

 net.output.processFcns

Search in ANSWERS and

 comp.soft-sys.matlab

Hope this helps.

Greg