Consider again the same $10$ instances.

$P_1=(4,1)$

$P_2=(2,-1)$

$P_3=(2,2)$

$P_4=(5,5)$

$P_5=(3,-2)$

$N_1=(-3,4)$

$N_2=(-1,1)$

$N_3=(3,6)$

$N_4=(-3,-1)$

$N_5=(-2,3)$

A neural network comprising of $2$ input neurons $($for $x$ and $y$ values$),2$ hidden layer neurons $(h_1$ and

$h_2),$ and a single output neuron, was trained to classify the data. The hidden and output neurons use

the threshold activation function, which outputs either $0($for a negative instance$)$ or $1$ for a positive

instance.

Figure $3$: Three$-$layer neural network with weights and bias values.

i$)$ Calculate the output for each of the three neurons $h_1,h_2,$ and $o_1$ when $N_3$ is given as input to

the network. Use the weights and bias values as shown in Figure $3.$

ii$)$ Does the network classify $N_3$ correctly?

iii$)$ What do you observe about the outputs of $h_1$ and $h_2$ when $N_3$ is given as input? Could the

network still correctly classify $N_3?$ Explain in detail.

iv$)$ Draw the decision boundaries for each of the three neurons, $h_1,h_2,$ and $o_1.$ Show all your

steps and calculations. Explain what you did to arrive at the diagram for $o_1.$