I have taken your recommendations into consideration. Yet now I am having problem with handling the output of the test set of examples on the network. It appears that the network returns an array of values, but all the values are the same.

 use strict;
 use AI::NNFlex::Backprop;
 use AI::NNFlex::Dataset;
 use Data::Dumper;
 
 my $n = 0.4;
 my $num_epochs = 100;
 
 my $network = AI::NNFlex::Backprop->new(learningrate=>.9,
                bias=>1,
 );
 
 $network->add_layer(nodes=>3,activationfunction=>'tanh');
 #$network->add_layer(nodes=>3,activationfunction=>'tanh');
 #$network->add_layer(nodes=>2,activationfunction=>'tanh');
 #$network->add_layer(nodes=>3,activationfunction=>'tanh');
 $network->add_layer(nodes=>5,activationfunction=>'tanh');
 $network->add_layer(nodes=>2,activationfunction=>'sigmoid');
 $network->init();
 
 my $test_set = AI::NNFlex::Dataset->new([
     [6.28318,1.570795,0], [1,0],
    [6.28318,1.570795,1.570795], [0,-1],
    [6.28318,1.570795,3.14159], [-1,0],
    [6.28318,1.570795,4.712385], [0,1],
    [6.28318,1.570795,6.28318], [1,0],
    [6.28318,1.570795,7.853975], [0,-1],
    [6.28318,3.14159,0], [0,-1],
    [6.28318,3.14159,1.570795], [-1,0],
    [6.28318,3.14159,3.14159], [0,1],
    [6.28318,3.14159,4.712385], [1,0],
    [6.28318,3.14159,6.28318], [0,-1],
    [6.28318,3.14159,7.853975], [-1,0],
    [6.28318,4.712385,0], [-1,0],
    [6.28318,4.712385,1.570795], [0,1],
    [6.28318,4.712385,3.14159], [1,0],
    [6.28318,4.712385,4.712385], [0,-1],
    [6.28318,4.712385,6.28318], [-1,0],
    [6.28318,4.712385,7.853975], [0,1],
    [6.28318,6.28318,0], [0,1],
    [6.28318,6.28318,1.570795], [1,0],
    [6.28318,6.28318,3.14159], [0,-1],
    [6.28318,6.28318,4.712385], [-1,0],
    [6.28318,6.28318,6.28318], [0,1],
    [6.28318,6.28318,7.853975], [1,0],
    [6.28318,7.853975,0], [1,0],
    [6.28318,7.853975,1.570795], [0,-1],
    [6.28318,7.853975,3.14159], [-1,0],
    [6.28318,7.853975,4.712385], [0,1],
    [6.28318,7.853975,6.28318], [1,0],
    [6.28318,7.853975,7.853975], [0,-1],
    [7.853975,0,0], [1,0],
    [7.853975,0,1.570795], [0,-1],
    [7.853975,0,3.14159], [-1,0],
    [7.853975,0,4.712385], [0,1],
    [7.853975,0,6.28318], [1,0],
    [7.853975,0,7.853975], [0,-1],
    [7.853975,1.570795,0], [0,-1],
    [7.853975,1.570795,1.570795], [-1,0],
    [7.853975,1.570795,3.14159], [0,1],
    [7.853975,1.570795,4.712385], [1,0],
    [7.853975,1.570795,6.28318], [0,-1],
    [7.853975,1.570795,7.853975], [-1,0],
    [7.853975,3.14159,0], [-1,0],
    [7.853975,3.14159,1.570795], [0,1],
    [7.853975,3.14159,3.14159], [1,0],
    [7.853975,3.14159,4.712385], [0,-1],
    [7.853975,3.14159,6.28318], [-1,0],
    [7.853975,3.14159,7.853975], [0,1],
    [7.853975,4.712385,0], [0,1],
    [7.853975,4.712385,1.570795], [1,0],
    [7.853975,4.712385,3.14159], [0,-1],
    [7.853975,4.712385,4.712385], [-1,0],
    [7.853975,4.712385,6.28318], [0,1],
    [7.853975,4.712385,7.853975], [1,0],
    [7.853975,6.28318,0], [1,0],
    [7.853975,6.28318,1.570795], [0,-1],
    [7.853975,6.28318,3.14159], [-1,0],
    [7.853975,6.28318,4.712385], [0,1],
    [7.853975,6.28318,6.28318], [1,0],
    [7.853975,6.28318,7.853975], [0,-1],
    [7.853975,7.853975,0], [0,-1],
    [7.853975,7.853975,1.570795], [-1,0],
    [7.853975,7.853975,3.14159], [0,1],
    [7.853975,7.853975,4.712385], [1,0],
    [7.853975,7.853975,6.28318], [0,-1],
    [7.853975,7.853975,7.853975], [-1,0]
]);

 my $train_set = AI::NNFlex::Dataset->new([
    [0,0,0], [0,1],
    [0,0,1.570795], [1,0],
    [0,0,3.14159], [0,-1],
    [0,0,4.712385], [-1,0],
    [0,0,6.28318], [0,1],
    [0,0,7.853975], [1,0],
    [0,1.570795,0], [1,0],
    [0,1.570795,1.570795], [0,-1],
    [0,1.570795,3.14159], [-1,0],
    [0,1.570795,4.712385], [0,1],
    [0,1.570795,6.28318], [1,0],
    [0,1.570795,7.853975], [0,-1],
    [0,3.14159,0], [0,-1],
    [0,3.14159,1.570795], [-1,0],
    [0,3.14159,3.14159], [0,1],
    [0,3.14159,4.712385], [1,0],
    [0,3.14159,6.28318], [0,-1],
    [0,3.14159,7.853975], [-1,0],
    [0,4.712385,0], [-1,0],
    [0,4.712385,1.570795], [0,1],
    [0,4.712385,3.14159], [1,0],
    [0,4.712385,4.712385], [0,-1],
    [0,4.712385,6.28318], [-1,0],
    [0,4.712385,7.853975], [0,1],
    [0,6.28318,0], [0,1],
    [0,6.28318,1.570795], [1,0],
    [0,6.28318,3.14159], [0,-1],
    [0,6.28318,4.712385], [-1,0],
    [0,6.28318,6.28318], [0,1],
    [0,6.28318,7.853975], [1,0],
    [0,7.853975,0], [1,0],
    [0,7.853975,1.570795], [0,-1],
    [0,7.853975,3.14159], [-1,0],
    [0,7.853975,4.712385], [0,1],
    [0,7.853975,6.28318], [1,0],
    [0,7.853975,7.853975], [0,-1],
    [1.570795,0,0], [1,0],
    [1.570795,0,1.570795], [0,-1],
    [1.570795,0,3.14159], [-1,0],
    [1.570795,0,4.712385], [0,1],
    [1.570795,0,6.28318], [1,0],
    [1.570795,0,7.853975], [0,-1],
    [1.570795,1.570795,0], [0,-1],
    [1.570795,1.570795,1.570795], [-1,0],
    [1.570795,1.570795,3.14159], [0,1],
    [1.570795,1.570795,4.712385], [1,0],
    [1.570795,1.570795,6.28318], [0,-1],
    [1.570795,1.570795,7.853975], [-1,0],
    [1.570795,3.14159,0], [-1,0],
    [1.570795,3.14159,1.570795], [0,1],
    [1.570795,3.14159,3.14159], [1,0],
    [1.570795,3.14159,4.712385], [0,-1],
    [1.570795,3.14159,6.28318], [-1,0],
    [1.570795,3.14159,7.853975], [0,1],
    [1.570795,4.712385,0], [0,1],
    [1.570795,4.712385,1.570795], [1,0],
    [1.570795,4.712385,3.14159], [0,-1],
    [1.570795,4.712385,4.712385], [-1,0],
    [1.570795,4.712385,6.28318], [0,1],
    [1.570795,4.712385,7.853975], [1,0],
    [1.570795,6.28318,0], [1,0],
    [1.570795,6.28318,1.570795], [0,-1],
    [1.570795,6.28318,3.14159], [-1,0],
    [1.570795,6.28318,4.712385], [0,1],
    [1.570795,6.28318,6.28318], [1,0],
    [1.570795,6.28318,7.853975], [0,-1],
    [1.570795,7.853975,0], [0,-1],
    [1.570795,7.853975,1.570795], [-1,0],
    [1.570795,7.853975,3.14159], [0,1],
    [1.570795,7.853975,4.712385], [1,0],
    [1.570795,7.853975,6.28318], [0,-1],
    [1.570795,7.853975,7.853975], [-1,0],
    [3.14159,0,0], [0,-1],
    [3.14159,0,1.570795], [-1,0],
    [3.14159,0,3.14159], [0,1],
    [3.14159,0,4.712385], [1,0],
    [3.14159,0,6.28318], [0,-1],
    [3.14159,0,7.853975], [-1,0],
    [3.14159,1.570795,0], [-1,0],
    [3.14159,1.570795,1.570795], [0,1],
    [3.14159,1.570795,3.14159], [1,0],
    [3.14159,1.570795,4.712385], [0,-1],
    [3.14159,1.570795,6.28318], [-1,0],
    [3.14159,1.570795,7.853975], [0,1],
    [3.14159,3.14159,0], [0,1],
    [3.14159,3.14159,1.570795], [1,0],
    [3.14159,3.14159,3.14159], [0,-1],
    [3.14159,3.14159,4.712385], [-1,0],
    [3.14159,3.14159,6.28318], [0,1],
    [3.14159,3.14159,7.853975], [1,0],
    [3.14159,4.712385,0], [1,0],
    [3.14159,4.712385,1.570795], [0,-1],
    [3.14159,4.712385,3.14159], [-1,0],
    [3.14159,4.712385,4.712385], [0,1],
    [3.14159,4.712385,6.28318], [1,0],
    [3.14159,4.712385,7.853975], [0,-1],
    [3.14159,6.28318,0], [0,-1],
    [3.14159,6.28318,1.570795], [-1,0],
    [3.14159,6.28318,3.14159], [0,1],
    [3.14159,6.28318,4.712385], [1,0],
    [3.14159,6.28318,6.28318], [0,-1],
    [3.14159,6.28318,7.853975], [-1,0],
    [3.14159,7.853975,0], [-1,0],
    [3.14159,7.853975,1.570795], [0,1],
    [3.14159,7.853975,3.14159], [1,0],
    [3.14159,7.853975,4.712385], [0,-1],
    [3.14159,7.853975,6.28318], [-1,0],
    [3.14159,7.853975,7.853975], [0,1],
    [4.712385,0,0], [-1,0],
    [4.712385,0,1.570795], [0,1],
    [4.712385,0,3.14159], [1,0],
    [4.712385,0,4.712385], [0,-1],
    [4.712385,0,6.28318], [-1,0],
    [4.712385,0,7.853975], [0,1],
    [4.712385,1.570795,0], [0,1],
    [4.712385,1.570795,1.570795], [1,0],
    [4.712385,1.570795,3.14159], [0,-1],
    [4.712385,1.570795,4.712385], [-1,0],
    [4.712385,1.570795,6.28318], [0,1],
    [4.712385,1.570795,7.853975], [1,0],
    [4.712385,3.14159,0], [1,0],
    [4.712385,3.14159,1.570795], [0,-1],
    [4.712385,3.14159,3.14159], [-1,0],
    [4.712385,3.14159,4.712385], [0,1],
    [4.712385,3.14159,6.28318], [1,0],
    [4.712385,3.14159,7.853975], [0,-1],
    [4.712385,4.712385,0], [0,-1],
    [4.712385,4.712385,1.570795], [-1,0],
    [4.712385,4.712385,3.14159], [0,1],
    [4.712385,4.712385,4.712385], [1,0],
    [4.712385,4.712385,6.28318], [0,-1],
    [4.712385,4.712385,7.853975], [-1,0],
    [4.712385,6.28318,0], [-1,0],
    [4.712385,6.28318,1.570795], [0,1],
    [4.712385,6.28318,3.14159], [1,0],
    [4.712385,6.28318,4.712385], [0,-1],
    [4.712385,6.28318,6.28318], [-1,0],
    [4.712385,6.28318,7.853975], [0,1],
    [4.712385,7.853975,0], [0,1],
    [4.712385,7.853975,1.570795], [1,0],
    [4.712385,7.853975,3.14159], [0,-1],
    [4.712385,7.853975,4.712385], [-1,0],
    [4.712385,7.853975,6.28318], [0,1],
    [4.712385,7.853975,7.853975], [1,0],
    [6.28318,0,0], [0,1],
    [6.28318,0,1.570795], [1,0],
    [6.28318,0,3.14159], [0,-1],
    [6.28318,0,4.712385], [-1,0],
    [6.28318,0,6.28318], [0,1],
    [6.28318,0,7.853975], [1,0]
]);

my $epoch = 1;
my $err = 1;
while($err > .001 && $epoch < 100) {
    $err = $train_set->learn($network);
    my $outputsRef = $test_set->run($network);
    print Dumper($outputsRef);
    print "Error: $err\n";
    $epoch++;
}
[download]

The output of the network with the test set gives the following.

$ perl test1.pl
$VAR1 = [
          [
            '2.22776546277668e-07',
            '0.011408329955622'
          ],
          [
            '2.22776546277668e-07',
            '0.011408329955622'
          ],
          [
            '2.22776546277668e-07',
            '0.011408329955622'
          ],
          [
            '2.22776546277668e-07',
            '0.011408329955622'
          ],
          [
            '2.22776546277668e-07',
            '0.011408329955622'
          ],
          [
            '2.22776546277668e-07',
            '0.011408329955622'
          ],
....
....
[download]

Am I handling the output of the network in correctly? The module says that Runs the dataset through the network and returns a reference to an array of output patterns. I guess I am not handling the reference array correctly.

Thanks for all the help.

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