PORT SAID UNIVERSITY
FACULTY OF ENGINEERI
NG
DEPARTMENT OF ELECTR
ICAL ENGINEERING
PROGRAM/
YEAR
ELECTRONOICS AND
COMMUNICATIONS
DIVISION
201
2

1
3
SEMESTER
SECOND
COURSE TITLE:
Neural Networks
ةيبصعلا تاكبشلا
COURSE CODE:
EC
E3
54
DATE:
13

5

201
3
T
OTAL ASSESSMENT MARK
S:
20
TIME
ALLOWED:
1
HOUR
FRESH
Question (1)
(
10
marks)
(1)(4 marks) For each question, select
the correct answer.
Show all your work
(a)
(2 marks)
The following network is a multilayer perceptron.
A. AND
B. OR
C. XOR
D. NOR
E. None of the above answers
(b)
(2 marks)
A perceptron with a unipolar step function has two inputs with weights
w
1
= 0.5
and
w
2
=
−
0.2
, and
a threshold
= 0.3
(
can be considered as a weight for an ext
ra input which is always set to

1)
. T
he network is trained using the learning rule
Δw =
(d

y) x
,
where x is the input vector,
is the
learning rate,
w
is the weight vector,
d
is
the desired output, and
y
is the actual output.
What are the
new values of the weights and threshold after one step of training with the input vector
x
= [0, 1]
T
and
desired output 1, using a learning rate
= 0.5
?
A.
w
1
= 1.0, w
2
= −0.2,
= −0.2.
B.
w
1
=
0.5, w
2
= 0.3,
= 0.7.
C.
w
1
= 0.5, w
2
= 0.3,
=

0.
2
.
D.
w
1
= 0.5, w
2
= 0.3,
= 0.
3
.
E.
w
1
= 0.5, w
2
= −0.2,
= 0.3.
(2
) (
4 marks)
State
whether each of the following statements is true or false by checking the
appropriate box.
Statement
True
Fals
e
A three

layer back
propagation neural network with 5 neurons in each
layer has a total of 50 connections and 50 weights.
(3
) (
2
mark
s
) Why is it not a good idea to have step activation functions in the hidd
en units of a
multi

layer feedforward network?
What are the preferred activation functions and why?
Q
uestion (
2
) (1
0
marks)
(a) (5 marks)
For
the
neural network
shown, the network have the following weight vectors:
and
that each unit has a bias
= 0
. If the network is tested with an input vector
x
=
[2, 3, 1]
T
,
(i)(2 marks)
c
alculate the output of the first hidden layer
y
1
.
A multi

layer network should have the same number of units in the
input layer and the output layer.
For effective training
of a neural network, the network should have at
least 5

10 times as many weights as there are training samples.
A single perceptron can compute the XOR function.
(ii) (3 marks)
calculate
the output of the third output neuron
z
3
.
(
b
)
(5 marks)
Consider a neural net for a binary classiﬁcation
,
which has one hidden layer as shown in
the ﬁgure. We
use a linear act
ivation function at hidden layers
an
d a sigmoid activation function at the
output layer,
where
x = (x
1
, x
2
)
and
w = (w
1
, w
2
,
. . . , w
9
).
(i)(3 marks)
What
is the output
y
from the above neural net? Express it in terms of
x
i
weights
w
i
.
(ii)(2 marks)
Draw a neural net with no hidden layer which is equivalent to the given neural net,
and
write weights
w
of this new
neural net in terms of
c
and
w
i
.
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