How to structure the output layer of an MLP that finds the quadrant of an arbitrary point in a rectangle?

Question

I'm trying to write a neural network that outputs the quadrant of a rectangle that an arbitrary point lies in. This rectangle has its upper left at {0, 0} and its lower right at {1, 1} (e.g. point {0.25, 0.25} should return 'upper left', and point {0.75, 0.75} should return 'lower right').

I'm confused about the structure of the output layer.

I've seen examples that suggest two nodes with Boolean "isLeft" and "isTop".

I've also seen examples that suggest four nodes with probabilities for UL, UR, LL and LR.

Is one or the other considered the proper structure in this case? Are both approaches valid?

I want to do this exercise as simply as possible, as I work to learn Multi Layer Perceptron. If there is a subtopic I need to focus on, please direct me to it.

Thanks in advance!

Answer 1

You need only two hyperplanes to solve this. Thus you need two neurons in the hidden layer. You can use two or four neurons in the output layer. Both options result in the correct solution (theoretically).

You can use perceptrons. With perceptrons, the output is a boolean vecotor, not a probability.