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 Author Comment/Response Aaron Honecker 10/26/00 06:18am >I'm trying to construct a generalized transfer function for a fully connected neural net. Basically I need to solve these equations for Y[n] in terms of X[n] and the (n+1) x (n+1) array [a] and I can't figure out how to go about it. I make use of the 1-d arrays wout and win but they should drop out if solved correctly. Any suggestions? Thanks!!> >wout[[i]] = win[[i]] g >Y[n] = Sum[wout[j] a[[j,N+1]],{j,1,N}] >win[i] = Sum[wout[j] a[[j,i]] + X[n] a[[N+1,i]],{j,1,N}] > >Here follows the notebook code I think (I'm new to this whole mathematica thing): > >\!\(wout\_\(\(\[LeftDoubleBracket]\)\(i\)\(\[RightDoubleBracket]\)\) = > win\_\(\(\[LeftDoubleBracket]\)\(i\)\(\[RightDoubleBracket]\)\)\ g\) > >\!\(y[n]\ = \ \[Sum]\+\(j = 1\)\%N wout\_\(\(\[LeftDoubleBracket]\)\(j\)\(\ >\[RightDoubleBracket]\)\)\ \[Alpha]\_\(\(\[LeftDoubleBracket]\)\(j, N + 1\)\(\ >\[RightDoubleBracket]\)\)\) > >\!\(win\_\(\(\[LeftDoubleBracket]\)\(i\)\(\[RightDoubleBracket]\)\) = \ >\[Sum]\+\(j = 1\)\%N wout\_\(\(\[LeftDoubleBracket]\)\(j\)\(\ >\[RightDoubleBracket]\)\)\ \[Alpha]\_\(\(\[LeftDoubleBracket]\)\(j, i\)\(\ >\[RightDoubleBracket]\)\) + > X[n]*\ \[Alpha]\_\(\(\[LeftDoubleBracket]\)\(N + 1, i\)\(\ >\[RightDoubleBracket]\)\)\) Your notation is confusing and you didn't fully specify the neural network. It appears that you have two definitions for wout and win. In one you use [[ ]] and another you use [ ] I'm assuming from your discription that you have a fully connected neural network with no hidden layers. The input is X = {x1, x2, ..., xm} and the output is Y = {y1, ..., yn} where m and n are not necessarily equal to each other. If a is the weight matrix then y1 = a11*x1 + a21*x2 + ... + am1*xm ... yn = a1n*x1 + a2n*x2 + ... + amn*xm or in matrix and Matheamtica notation Y = Transpose[A].X Also in your notation you specifed wout[[i]] = win[[i]] g, where I'm assuming g is the gain of the neurons in the output layer. In this case Y = g * Transpose[A].X Note the . is matrix mulitplication in Mathematica URL: ,

 Subject (listing for 'Some help w/ a generalized H for NNs?') Author Date Posted Some help w/ a generalized H for NNs? Jeff Haynes 10/24/00 06:49am Re: Some help w/ a generalized H for NNs? Aaron Honecker 10/26/00 06:18am
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