#!/usr/bin/perl -w
use strict; use warnings;

my $numberofinputnodes = 2; my $numberofhiddennodes = 2; my $learningr
+ate = .1;
my $maxepochs = 10; my $errormargin = .1; my @weight = (.6,.6,.6);
my @hiddenweight = (.6,.6,.6);
my @data = (["-1","0.000000","0.000000","0"],["-1","0.000000","1.00000
+0","1"],
["-1","1.000000","0.000000","1"],["-1","1.000000","1.000000","0"]);
my $numberofepochs = 1; my $net = 0; my $netk = 0; my $avgrmse = 0; my
+ @outputh = ();
my @outputk = (); my $deltak = 0; my $deltah = 0; my @rmse = (); my $m
+axrmse =0;

while (($numberofepochs <= $maxepochs) && (($avgrmse == 0) || ($avgrms
+e >= $errormargin))){
    $avgrmse = 0;
    for (my $j=0; $j <= $#data; $j++) {
        for (my $k=0; $k < $#{$data[0]}; $k++){
            $net = $net + $weight[$k]*$data[$j][$k];
        }
        $outputh[$j] = 1 / (1 + exp(-$net));
        $net=0;
        for (my $o = 0; $o <= $numberofhiddennodes; $o++){
            if ($o==0){
                $netk = -$hiddenweight[0];    
            }
            $netk = $netk + $hiddenweight[$o]*$outputh[$j];
        }
        $outputk[$j] = 1 / (1 + exp(-$netk)); $netk=0;
        $deltak = $outputk[$j]*(1 - $outputk[$j])*($data[$j][-1] - $ou
+tputk[$j]);
        my @deltah;
        for (my $o = 0; $o < $#{$data[0]}; $o++){
            $deltah[$o] = $outputh[$j]*(1-$outputh[$j])*$weight[$o]*$d
+eltak;
        }
        for (my $m=0; $m < $#{$data[0]}; $m++){
            my $update = $learningrate*$deltah[$m]*$data[$j][$m];
            $weight[$m] = $weight[$m] + $update;
        }
        for (my $n=0; $n <= $numberofhiddennodes; $n++){
            my $update = $learningrate*$deltak*$outputk[$j];
            $hiddenweight[$n] = $hiddenweight[$n] + $update;
        }
        $deltak=0; @deltah = ();
    } 
    for (my $j=0; $j <= $#data; $j++) {
        for (my $k=0; $k < $#{$data[0]}; $k++){
            $net = $net + $weight[$k]*$data[$j][$k];
        }
        $outputh[$j] = 1 / (1 + exp(-$net));
        for (my $o = 1; $o < $numberofhiddennodes; $o++){
            $netk = $netk + $hiddenweight[$o]*$outputh[$j];
        }
        $netk = $netk - $hiddenweight[0]; $outputk[$j] = 1 / (1 + exp(
+-$netk));
        $net = 0; $netk = 0;
    }
    my $totalrmse = 0;
    for my $q (0..$#data){
        $rmse[$q] = sqrt(($data[$q][-1] - $outputk[$q])**2);
        $totalrmse = $totalrmse + $rmse[$q];
    }
    $avgrmse = $totalrmse / ($#data +1); @rmse = sort( {$a <=> $b} @rm
+se); 
    $maxrmse = $rmse[-1];
    if($numberofepochs==$maxepochs){
        print "\n","***** Epoch $numberofepochs *****", "\n";
        print "Maximum RMSE: $maxrmse", "\n";
        print "Average RMSE: $avgrmse", "\n";
    }
    @rmse = (); $totalrmse = 0;    $numberofepochs++;
}
exit;

[download]

The final output looks like this:

***** Epoch 10 *****
Maximum RMSE: 0.570149294921984
Average RMSE: 0.500071929555965

[download]

The output should be this

***** Epoch 10 *****
Maximum RMSE: 0.5432215742673802
Average RMSE: 0.4999911891911738

[download]

Which shows its behaving with some precision, but it isn't accurate and I have no idea why. The values move in the right direction, but something seems wrong with exactly how much the values change.

I'm trying to implement backpropagation with stochastic gradient descent (this example just uses fixed initial weights instead of random ones) for a Machine Learning course.

I've been able to get the final output incrementally closer to the correct answer over several revisions, but I haven't been able to improve it anymore. So I think additional sets of eyes might be useful.

I'd like to think this code shows I understand how the algorithm works and that the problem is boiling down to some sort of scoping issue or aggregate error that I'm not seeing, but I don't know. Thus I humbly seek Perl Wisdom from the Monks! Thank you in advance for any suggestions.

In reply to backpropagation accuracy issue by perlchris

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