DRDO CSE 2022 Paper 2 | Question: 32

Question

A perceptron consists of weights $\left[w_{1}, w_{2}, w_{3}, w_{4}\right]=[0.5,2,1,-3]$. The activation function is provided as $y=f(z)=1$ if $z \geq 2$ otherwise $0,$ where $z= \sum(w . d)$. What is the output $y$ for the following four data samples $d?$

$$\begin{array}{|c|c|c|c|c|}
\hline & p_{1} & p_{2} & p_{3} & p_{4} \\
\hline \hline d_{1} & 1 & -1  & 0 & 1 \\
d_{2} & 1 & -1 & 1 & 1 \\
d_{3} & 0 & 0 & 1 & -1 \\
d_{4} & 1 & 0 & 1 & -1  \\
\hline
\end {array}$$

Answer 1

In a perceptron model, the output y is calculated using the weighted sum of inputs z, where z = $\sum_{i} (w_{i} *d_{i}),$ and then applying an activation function to the z value. weights [0.5,2,1,−3], the activation function y = 1 if z ≥ 2 and y = 0 otherwise.

Let's calculate the output y for each data sample d using the provided weights:

For $d_{1}$:

z=(0.5×1)+(2×−1)+(1×0)+(−3×1)= −3.5
∵ z < 2, y = 0.

for same as:

$d_{2}$ → -2.5 at z < 2, y = 0
$d_{3}$ → 4 at z >= 2, y = 1
$d_{4}$ → 2.5 at z >= 2, y = 1

So, the outputs y for the four data samples $d_{1}$, $d_{2}$, $d_{3}$, and $d_{4}$​ are 0,0,1, and 1 respectively.