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Homework due Jul 1 7 , 2 0 2 4 1 7 : 2 9 IST completedDecision Boundaries 0 1 point ( graded ) In

Homework due Jul 17,202417:29 IST completedDecision Boundaries
01 point (graded)
In this problem we visualize the "decision boundaries" in x-space, corresponding to the four hidden units.
These are the lines in x-space where the values of z1,z2,z3,z4 are exactly zero. Plot the decision boundaries
of the four hidden units using the parameters of W provided above.
Enter below the area of the region of your plot that corresponds to a negative (0) value for all of the four
hidden units.
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In this problem we will analyze a simple neural network to understand its classification properties. Consider the
neural network given in the figure below, with ReLU activation functions (denoted by f) on all neurons, and a
softmax activation function in the output layer:
Given an input x=[x1,x2]T, the hidden units in the network are activated in stages as described by the
following equations:
z1=x1W11+x2W11+W01,f(z1)-max{z1,0}
z2-x1W18+x2W22+W02,f(z2)=max{z2,0}
z2=x1W13+x2W23+W03,f(z3)=max{z3,0}
z4=x1W14+x3W24+W04,f(z4)-max{x1,0}
u1=f(x1)V11+f(z2)V21+f(x3)V31+f(z4)V41+V01,f(u1)=max{u1,0}
u2=f(x1)V12+f(z2)V22+f(x3)V02+f(x4)Ve2+V02,f(x2)=max{u9,0}.
The final output of the network is obtained by applying the softmax function to the last hidden layer,
o1=ef(u1)ef(u1)+ef(3)
o2=ef(3)ef(1)+ef(3).
In this problem, we will consider the following setting of parameters:
[W12W22W01W12W23W02W13W23W03W14W44W04]=[10-101-1-10-10-1-1],
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