In my Class/Exam there are a lot tasks where the goal is to draw the decision boundary of a Heaviside based Neural Network.
An example of this is:
Problem:
For the given neural Network, sketch the decision boundary (the area of Points in R^2 that is classified as 1).
$ W_1 = \begin{bmatrix} 1 & 1 \\ 1 & -1 \\ -1 & 1 \\ -1 & -1 \\ 1 & 1 \\ 1 & -1 \\ -1 & 1 \\ -1 & -1 \\ \end{bmatrix}, b_1 = \begin{bmatrix} 2 \\ 2 \\ 2 \\ 2 \\ 0 \\ 2 \\ 0 \\ 2 \\ \end{bmatrix} , W_2 = \begin{bmatrix} 1 & 1 & 1 & 1& 0 & 0& 0& 0 \\ 0 & 0 & 0 & 0 & 1& 1 &1 &1 \end{bmatrix}, b_2 = \begin{bmatrix} -4 \\ -4 \end{bmatrix}, W_3 = \begin{bmatrix} 1 & -1 \end{bmatrix}, b_3 = 0 $
If I put it into a graphing calculator i get the result:
But obviously doing this is trivial.
My first approach at doing this by-hand would just be to do the forward-pass/evaluation on-paper for a bunch of points, but that seems like alot of 'dumb' work. Is there a trick involved that im unaware of?
Any help is appreciated !
