// http://www.kx.com/listbox/k/msg05688.html
// Subject: Re: small victory: naive neural net 
// From: "Alexander Skomorokhov" <askom2@kaluga.ru> 
// Date: Fri, 17 May 2002 01:01:45 +0400 


sigm:{%1.0 + _exp -x*y}   	/ sigmoid function

train:{[n;i;t]    		/ net;inputs;target
  ih:n[0]       		/ ih: i->hidden weights
  ho:n[1]			/ ho: hidden->output weights
  i:i,1.0               	/ add bias
  h:sigm[0.5;+/i*ih]    	/ process hidden nodes
  o:sigm[0.5;+/h*ho]    	/ process output node(s)
  eo:o*(1-o)*(t-o)       	/ backprop error
  eh:h*(1-h)*+/'eo*/:ho  	/ backprop error
  ho:ho+(0.5*eo*/:h)     	/ adjust hidden->output weights
  ih:ih+(0.5*eh*/:i)     	/ adjust i->hidden weights
  (ih;ho)}

/ predict output for a given nwork and is
eval:{[n;i]
 x:i,'1.0
 y:sigm[0.5;x _mul n[0]]
 sigm[0.5;y _mul n[1]]}

/ set n state and parameters
ih:2*-0.5+3 4#(3*4) _draw 0
ho:2*-0.5+4 1#(4*1) _draw 0

n:(ih;ho)

i:(0 0;0 1;1 0;1 1)
t:4 1#(0 1 1 0)

/ perform network training

do[10000
 k:0
 do[#i;n:train[n;i[k];t[k]]
 k:k+1]]

/ predict outputs and calculate error

p:eval[n;i]

t,'p

err:+/(p-t)^2
(err%#t)^.5