FWIW I've finally had a bit of time to revisit this. Sorry its taken so long. The following code works fairly nicely - it learns very quickly, and generalises rather nicely. The problem appears to be that with a small learning constant (needed for large numbers) the network takes for ever to learn. With a large learning constant, the numbers rapidly get out of range.

In addition, bias should not be used (this is only needed for networks where zero activation levels may require true outputs) and the starting weights have been fixed to 1, to keep them as positive numbers.

use AI::NNFlex::Backprop;
use AI::NNFlex::Dataset;

my $network = AI::NNFlex::Backprop->new(
                learningrate=>.00001,
                fahlmanconstant=>0,
                fixedweights=>1,
                momentum=>0.3,
                bias=>0);


$network->add_layer(    nodes=>2,
            activationfunction=>"linear");


$network->add_layer(    nodes=>2,
            activationfunction=>"linear");

$network->add_layer(    nodes=>1,
            activationfunction=>"linear");


$network->init();

# Taken from Mesh ex_add.pl
my $dataset = AI::NNFlex::Dataset->new([
[ 1,   1   ], [ 2    ],
[ 1,   2   ], [ 3    ],
[ 2,   2   ], [ 4    ],
[ 20,  20  ], [ 40   ],
[ 10,  10  ], [ 20   ],
[ 15,  15  ], [ 30   ],
[ 12,  8   ], [ 20   ],

]);

my $err = 10;
# Stop after 4096 epochs -- don't want to wait more than that
for ( my $i = 0; ($err > 0.0001) && ($i < 4096); $i++ ) {
    $err = $dataset->learn($network);
    print "Epoch = $i error = $err\n";
}

foreach (@{$dataset->run($network)})
{
    foreach (@$_){print $_}
    print "\n";
}

print "this should be 4000 - ";
$network->run([2000,2000]);
foreach ( @{$network->output}){print $_."\n";}

 foreach my $a ( 1..10 ) {
     foreach my $b ( 1..10 ) {
     my($ans) = $a+$b;
     my($nnans) = @{$network->run([$a,$b])};
     print "[$a] [$b] ans=$ans but nnans=$nnans\n" unless $ans == $nna
+ns;
     }
 }
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