I am reading an exam question about NN (that I cannot publish, for copyright reasons). The question says: 'Construct a rectangle in 2D space. Define the lines, and then define the weights and threshold that will only fire for points inside the rectangle.'
I understand that this is an example of a rectangle drawn as a NN (i.e. this NN will fire, if the point is in the rectangle, where the rectangle is defined by the lines X = 4; X = 1, Y = 2, Y = 5).
In this diagram, since it's a rectangle, the equations of the line in this example are x = 4, x =1, y=2, y=5, so I left the other weights out (as they equal to 0).
I'm now wondering how this could be translated to a 3D structure. For example, if a 3D shape was defined by the points:
(0,0,0), (0,1,0), (0,0,1), (0,1,1), (1,0,0), (1,1,0), (1,0,1), (1,1,1)
I wanted to draw a hyperplane that separates the corner point (1,1,1) from the other points in this cube. Can this 3D shape be drawn similarly to below (maybe it would be easier to understand, if there were other numbers except 1 and 0 in the co-ordinates)?
Would I draw this with 3 nodes in the input layer, still one node in the output layer, I just don't understand what the hidden layer should look like? Would it have 24 nodes? One for each surface of the cube, with relevant X and Y values?