Neural nets require a LOT of reinforcing training time. If you have a child, you understand this process intuitively. People can learn simple things by rote, but they can extrapolate and understand things only if they are shown enough examples to reinforce their forming theory about a governing rule.
A 2- or 3-year old kid needs to be exposed to a rule hundreds of times before they really can apply it (unless it somehow sparks their imagination and interest). A 10-year old probably only needs a few dozen math problems before they can start to apply the method on similar problems. An adult should be able to recognize and extrapolate on a pattern after a few examples.
In the case of your neural net that learns even/odd number rules, you are hoping to train the network to do two things: develop a direct 1:1 relationship between the lowest binary bit input and the output answer bit, while simultaneously completely burning out or dismissing all value from every other binary input bit. Seems simple to you, but not to a 3-year old.
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