move

my $obj = $Measure->new($wn);
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before the for loop (Update: suaveant already mentioned this, sorry).

Check your word list. Does it contain duplicated lines (you should never have to use Memoize)? Try this to spot errors:

sub similarity {
   my ( $w1, $w2 ) = @_;
   warn "'$w1' vs '$w2'";
   return $obj->getRelatedness($w1, $w2);
}
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