I was briefly wondering if it was a function of i<2n>.

To be completely technical it's a perceptron is something that divides data in an n-dimension space with an n-dimenstional plane, with all the points of one class on one side of the plane and all other points on the other side. The theory is then that if you give it a data point of an unknown class, you just need to know what side of the plane it is in order to decide what class it is. So 1 means it's on the right side of the tracks, while -1 means it's with all the plebian scum. :P

We're doing an optical character recognition system on 7 characters, so we do 7 perceptrons in a single-layer network. That's what the 1, -1, thing is about. :)

But interesting guess on the i^(2n)