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3. Problem 3(40 pts) I. Given the following perceptron (with weights given on the connections). 1 --- -3 ---> x1 --- -1 ---> y x2 --- 2 ---> Figure-3 a) Fill in the table below to give the output of this perceptron on the following training set. x1 | x2 | target | output 2 | 1 | 1 | -3 | 1 | 0 | 0 | 0 | 1 | What is the accuracy of this perceptron on this training set? b) Write the equation of the separation line defined by this perceptron in slope-intercept form (x2 = mx1 + b). c) Sketch the line on a two-dimensional plot. Also plot the three training examples. d) What is the bias (weight) of this perceptron? What is the threshold? II. a) For the perceptron and training set in (I), apply the perceptron learning rule with gradient descent for one epoch of training. Use a learning rate ? = 1. b) What are the weights after one epoch of training? c) What is the accuracy on the training set after one epoch of training?

          3. Problem 3(40 pts)
I. Given the following perceptron (with weights given on the connections).

1 --- -3 --->
x1 --- -1 ---> y
x2 --- 2 --->

Figure-3

a) Fill in the table below to give the output of this perceptron on the following training set.

x1 | x2 | target | output
2 | 1 | 1 |
-3 | 1 | 0 |
0 | 0 | 1 |

What is the accuracy of this perceptron on this training set?
b) Write the equation of the separation line defined by this perceptron in slope-intercept form (x2 = mx1 + b).
c) Sketch the line on a two-dimensional plot. Also plot the three training examples.
d) What is the bias (weight) of this perceptron? What is the threshold?

II. a) For the perceptron and training set in (I), apply the perceptron learning rule with gradient descent for one epoch of training. Use a learning rate ? = 1.
b) What are the weights after one epoch of training?
c) What is the accuracy on the training set after one epoch of training?

3. Problem 3(40 pts)
I. Given the following perceptron (with weights given on the connections).

1 — -3 —>
x1 — -1 —> y
x2 — 2 —>

Figure-3

a) Fill in the table below to give the output of this perceptron on the following training set.

x1 | x2 | target | output
2 | 1 | 1 |
-3 | 1 | 0 |
0 | 0 | 1 |

What is the accuracy of this perceptron on this training set?
b) Write the equation of the separation line defined by this perceptron in slope-intercept form (x2 = mx1 + b).
c) Sketch the line on a two-dimensional plot. Also plot the three training examples.
d) What is the bias (weight) of this perceptron? What is the threshold?

II. a) For the perceptron and training set in (I), apply the perceptron learning rule with gradient descent for one epoch of training. Use a learning rate ? = 1.
b) What are the weights after one epoch of training?
c) What is the accuracy on the training set after one epoch of training?

Added by Alexander F.

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