Supervised Learning Questions and Answers

Q: A single layer perception cannot compute the following logical function :

A single layer perceptron cannot compute XOR.A single layer perceptron computes a linear threshold function: it outputs 1 on one side of a straight line (a hyperplane) and 0 on the other. It can therefore represent only linearly separable functions.AND, OR and NOT are linearly separable; for AND, for example, the line \(x_1 + x_2 = 1.5\) separates (1, 1) from the other inputs. XOR outputs 1 for (0, 1) and (1, 0) and 0 for (0, 0) and (1, 1), and no single straight line separates these two pairs. Minsky and Papert's analysis of this limitation is well known, and it is solved by adding a hidden layer.

Q: Which of the following data is linearly separable ?

The linearly separable data is in plot (D).Data are linearly separable when one straight line puts all points of one class on one side and all points of the other class on the other side.In plot (D) all the crossed circles lie towards the lower right, and all the plain circles towards the upper left, so a straight line running from the lower left to the upper right between them separates the two classes.In each of the other plots a point of one class lies between points of the other. In (A) a crossed circle sits between two plain circles on the left, in an XOR-like pattern; in (B) a crossed circle on the right lies between two plain circles; and in (C) the two classes are interleaved in the same quadrant. No single line separates them.

A single layer perception cannot compute the following logical function :

A.AND
B.OR
C.XOR
D.NOT

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: C

A single layer perceptron cannot compute XOR.

A single layer perceptron computes a linear threshold function: it outputs 1 on one side of a straight line (a hyperplane) and 0 on the other. It can therefore represent only linearly separable functions.

AND, OR and NOT are linearly separable; for AND, for example, the line \(x_1 + x_2 = 1.5\) separates (1, 1) from the other inputs. XOR outputs 1 for (0, 1) and (1, 0) and 0 for (0, 0) and (1, 1), and no single straight line separates these two pairs. Minsky and Papert's analysis of this limitation is well known, and it is solved by adding a hidden layer.

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Which of the following data is linearly separable ?

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: D

The linearly separable data is in plot (D).

Data are linearly separable when one straight line puts all points of one class on one side and all points of the other class on the other side.

In plot (D) all the crossed circles lie towards the lower right, and all the plain circles towards the upper left, so a straight line running from the lower left to the upper right between them separates the two classes.

In each of the other plots a point of one class lies between points of the other. In (A) a crossed circle sits between two plain circles on the left, in an XOR-like pattern; in (B) a crossed circle on the right lies between two plain circles; and in (C) the two classes are interleaved in the same quadrant. No single line separates them.

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Back propagation is a learning technique that adjusts weights in the neural network by propagating weight changes.

A.Forward from source to sink
B.Backward from sink to source
C.Forward from source to hidden nodes
D.Backward from since to hidden nodes

Exam Year(s)

UGC NET - 2012,

Answer: B

Back propagation adjusts the weights by propagating the weight changes backward from the sink to the source. The error found at the output layer is passed back through the hidden layers and used to correct the weights of each layer.

Forward propagation passes the inputs through the network from the source to the sink to find the output, and does not change the weights. The option 'Backward from since to hidden nodes' and the option 'Forward from source to hidden nodes' do not describe the full path of the error, which goes from the output right back to the input.

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You are given an OR problem and a XOR problem to solve. Then, which one of the following statements is true ?

A.Both OR and XOR problems can be solved using single layer perception.
B.OR problem can be solved using single layer perception and XOR problem can be solved using self organizing maps.
C.OR problem can be solved using radial basis function and XOR problem can be solved using single layer perception.
D.OR problem can be solved using single layer perception and XOR problem can be solved using radial basis function.

Exam Year(s)

UGC NET - 2012,

Answer: D

The OR function is linearly separable, so a single layer perceptron can solve it. The XOR function is not linearly separable, so a single layer perceptron cannot solve it, but a radial basis function network can, because it maps the inputs into a space where the classes become separable. The statement that both can be solved by a single layer perceptron is therefore false, and so are those that say the XOR problem can be solved by the perceptron or by self organising maps, which are used for clustering. The keyed answer is that the OR problem can be solved by a single layer perceptron and the XOR problem by a radial basis function.

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Identify the following activation function :

\(\phi(V) = Z + \frac{1}{1 + \exp(-x * V + Y)}\), Z, X, Y are parameters

A.Step function
B.Ramp function
C.Sigmoid function
D.Gaussian function

Exam Year(s)

UGC NET - 2012,

Answer: C

The function \(\phi(V) = Z + 1/(1 + \exp(-xV + Y))\) is an S shaped curve built from the logistic expression with a shift Z, a slope parameter x and an offset Y, so it is the sigmoid function. A step function jumps from one value to another, a ramp function rises linearly between two limits, and a Gaussian function is bell shaped with an exponent of a squared term, so none of these has the form given. The keyed answer is the sigmoid function.

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In Delta Rule for error minimization

A.weights are adjusted w.r.to change in the output
B.weights are adjusted w.r.to difference between desired output and actual output
C.weights are adjusted w.r.to difference between input and output
D.none of the above

Exam Year(s)

UGC NET - 2012,

Answer: B

The delta rule is a gradient descent rule for training a single layer of neurons: each weight is changed in proportion to the difference between the desired output and the actual output, multiplied by the input on that line. So the weights are adjusted with respect to the error, the difference between desired and actual output. Adjusting them with respect to the change in output alone, or the difference between input and output, ignores the target, and 'none of the above' is not right because the second option is the rule. The answer is option (B).

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