Machine Learning Self-doubt

Question

Please Solve this question with full explanation.

Answer 1

For the Boolean function  A∧B, we only need a single perceptron. The perceptron takes inputs A and  B, applies weights, and produces an output. In this case, we want the perceptron to fire (output 1) only when both A’  and B’ are 1. So, we set the weights to 1 for both inputs and introduce a bias of -1. This way, the perceptron fires when
A=1

and

B=1,

and remains inactive otherwise.

 

 XOR is a bit trickier and requires a two-layer network. We can achieve this with two perceptrons in the first layer and one perceptron in the second layer.

In the first layer:

Perceptron 1:  A’ and  B’ as inputs with weights (-1, 1) and bias -0.5.
Perceptron 2:  A’ and  B’ as inputs with weights (1, -1) and bias -0.5.
The outputs of these two perceptrons in the first layer will be  A∧¬B and  ¬A∧B, respectively.

 

Now, in the second layer, we use another perceptron with these two outputs as inputs. This perceptron has weights (1, 1) and a bias of -1.5. The final output will be A⊕B.

 

This structure works because the first layer detects when A or  B is 1 but not both (due to the bias term), and the second layer combines these conditions to produce an XOR behavior.