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Previous Year Question (PYQs)
Consider the following table defining the sample inputs and corresponding target values for a perceptron model.
| Sample No | x1 | x2 | target | w1 | w2 |
|---|---|---|---|---|---|
| S1 | 0 | 0 | 0 | 0 | 0 |
| S2 | 0 | 1 | 1 | ||
| S3 | 1 | 0 | 1 | ||
| S4 | 1 | 1 | 1 |
What shall be the value of updated weights after applying all the samples S1 to S4 (in the order S1, S2, S3, S4) to this model. Given that the initial weights w1=0, w2=0, learning rate=0.1 and no bias is involved in the perceptron. The activation function for this perceptron is given below:
yobserved =
{ 1 if yin > 0
0 if yin < 0 }
- w1 = 0.1, w2 = 0.1
- w1 = 0.0, w2 = 0.2
- w1 = 0.0, w2 = 0.1
- w1 = 0.2, w2 = 0.2
Solution
Using perceptron learning rule: Δw = η (t − y) x, where y = 1 if yin > 0 else 0.
S1 (0,0,t=0): yin=0 ⇒ y=0 ⇒ no change ⇒ (w1,w2)=(0,0)
S2 (0,1,t=1): yin=0 ⇒ y=0 ⇒ Δw=0.1(1−0)(0,1) ⇒ (w1,w2)=(0,0.1)
S3 (1,0,t=1): yin=0 ⇒ y=0 ⇒ Δw=0.1(1−0)(1,0) ⇒ (w1,w2)=(0.1,0.1)
S4 (1,1,t=1): yin=0.1+0.1=0.2>0 ⇒ y=1 ⇒ no change
Final Weights: w1=0.1, w2=0.1
Answer: (1)
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