++Very nice. I had been thinking about brushing up on my neural net skills (they're 20years rusty), and I've bookmarked this this will be a good starting point for using PDL to do so.
My one minor nitpick: the sigmoid function you chose, the "logistic function", has a derivative that's f(x) * (1-f(x)), not x * (1-x), so you should replace your nonlin() sub with
sub nonlin {
my ( $x, $deriv ) = @_;
my $f = 1 / ( 1 + exp( -$x ) );
return $f * ( 1 - $f ) if defined $deriv;
return $f;
}
... It still trains with your slope, but with my slope, it gets there faster, so 10k training loops gives better results:
Output After Training:
[
[ 0.0007225057]
[0.00048051061]
[ 0.999593]
[ 0.999388]
]