Here is a "thought experiment". I am trying to predict the future price change FPC of a stock.

If I supply the FPC as an input, then the NN uses this information and makes pretty-much perfect predictions. No surprise there.

BUT now I want to see whether the NN can find a hidden relationship. So I have created 2 new inputs (InputA and InputB) like this:

for (int i = 0; i <=NumRowsOfData; i++)

{

if (IsEven(i))

{

InputA = Math.Abs(FPC);

InputB = Math.Sign(FPC);

}

else

{

InputA = -Math.Abs(FPC);

InputB = -Math.Sign(FPC);

}

}

Note that InputA * InputB = FPC. i.e. The FPC can be worked out from this simple relationship.

If I give my NN ONLY InputA and InputB, do people think it will be able to discover the relationship and make perfect predictions again?