Machine Learning Fundamentals Questions and Answers

Q: The output of two-input logical Exclusive OR function............ :

The XOR output can be separated with two lines.Plot the four input pairs: (0, 0) and (1, 1) give 0, while (0, 1) and (1, 0) give 1. The two classes sit on opposite corners of the square, so no single straight line can put both 1s on one side and both 0s on the other. Two lines, one cutting off (0, 0) and one cutting off (1, 1), leave the two 1s in the band between them.That is why XOR is the classic example of a problem that is not linearly separable, why a single-layer perceptron cannot learn it, and why a hidden layer of two neurons solves it. More than two lines are never needed.

Q: A four input neuron has weights 1, 3, 4, 5 and their inputs are 5, 10, 2, 8 respectively. The transfer function is linear with the constant of proportionality being 3. What is/are its output ?

The output is 249.The neuron first forms the weighted sum of its inputs, then applies the linear transfer function, which multiplies by 3:\[ \begin{aligned} \text{net} &= 1(5) + 3(10) + 4(2) + 5(8) \\ &= 5 + 30 + 8 + 40 = 83 \\ y &= 3 \times 83 = 249 \end{aligned} \]5, 30, 8, 40 are the individual weighted inputs before summing, and 83 is the net input before the transfer function is applied. 860 does not come from any step of the calculation.

The output of two-input logical Exclusive OR function............ :

A.is an example of linearly separable problem
B.can be separated with a single line
C.can be separated with two lines
D.needs more than two lines for separation.

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

The XOR output can be separated with two lines.

Plot the four input pairs: (0, 0) and (1, 1) give 0, while (0, 1) and (1, 0) give 1. The two classes sit on opposite corners of the square, so no single straight line can put both 1s on one side and both 0s on the other. Two lines, one cutting off (0, 0) and one cutting off (1, 1), leave the two 1s in the band between them.

That is why XOR is the classic example of a problem that is not linearly separable, why a single-layer perceptron cannot learn it, and why a hidden layer of two neurons solves it. More than two lines are never needed.

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A four input neuron has weights 1, 3, 4, 5 and their inputs are 5, 10, 2, 8 respectively. The transfer function is linear with the constant of proportionality being 3. What is/are its output ?

A.5, 30, 8, 40
B.83
C.249
D.860

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

The output is 249.

The neuron first forms the weighted sum of its inputs, then applies the linear transfer function, which multiplies by 3:

\[ \begin{aligned} \text{net} &= 1(5) + 3(10) + 4(2) + 5(8) \\ &= 5 + 30 + 8 + 40 = 83 \\ y &= 3 \times 83 = 249 \end{aligned} \]

5, 30, 8, 40 are the individual weighted inputs before summing, and 83 is the net input before the transfer function is applied. 860 does not come from any step of the calculation.

Discuss in Forum

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Machine Learning Fundamentals Questions and Answers

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