Thought experiment - timesseries prediction/trading

[Lawrence]

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?