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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).

enter image description here

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?

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  • $\begingroup$ In your neural network diagram, there are no weights on the connections between the $x$ input and the 2 bottom hidden neurons (in the second layer). I assume that those weights are zero. Right? Similarly, I assume that the connections that come from the input $y$ to the top 2 hidden neurons are zero. $\endgroup$
    – nbro
    Jan 2 '21 at 22:53
  • $\begingroup$ I didn't really think about what this neural network does, but this is what comes to my mind in order for that to make sense to me, given that, if you're checking whether $x$ is within the range $[1, 4]$ (which is the $x$ range of the rectangle, you don't need to care about the values of the $y$ range. In any case, even if this reasoning was correct, I don't fully understand what the output of this NN is supposed to be to consider that a point is inside the rectangle. Maybe you need to clarify that. Where did you take this NN from? $\endgroup$
    – nbro
    Jan 2 '21 at 22:53
  • $\begingroup$ Can you provide a link to the resource that claimed that this NN computes whether a point is inside a NN, so that we have more context? $\endgroup$
    – nbro
    Jan 2 '21 at 22:55
  • $\begingroup$ @nbro, regarding your first question, sorry yes the weights not shown are 0, 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. $\endgroup$ Jan 3 '21 at 10:57
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    $\begingroup$ Please, edit your post to include these details. $\endgroup$
    – nbro
    Jan 3 '21 at 11:51

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