I'm struggling to differentiate that from how we use coinflips normally. We can pretty easily create arbitrary mappings and then sample from the binomial in a way that has meaning far beyond just heads or tails. Maybe I'm not quite understanding.
Which part are you confused about? Symbols are meaningless until someone imposes semantics on them. There is nothing meaningful about arithmetic in a neural network other than whatever conventions are imposed on the binary sequences, same way 97 has no meaning other than the conventional agreement that it is the ascii code point for "a".
