1.
Answer
T or F to the following questions (10 points)
F a. AI is field of research
concerned with the development of hardware
T b. A trained STM has a low
entropy value
F c. In CLS, it is necessary
to perform a complex algorithm to obtain the R/P (Reward/Punishment)
compensation
T d. Backprogation is the R/P
mechanism in Neural Networks
F e. Associative Memory is a
slow but very accurate classifier
T f. To select the next option in a CLS, the use
of the maximum assumes better results
T g. In a neural network, the formula ¶d(i,<t>)
= α*ea(j)*a(h)+β*¶(i,<t-1>) includes a correction for the
momentum
F h. It is possible to write STM
files using a Java Applet
F i. The
p = p + § + (1-P)(P) compensates more at the beginning
T k A Neural Network is a slow learning
algorithm, however it produces a classifier than can generalize and extrapolate
well
2. Choose
the correct option (10 points)
j__ The difference between Information and Knowledge
in AI is similar to the difference
between
a. Find and Select
b. Find and
Search c. Search and Select
d. Get and Put
k__ Donald Michie, Peter Bock have
developed algorithms for
a. Neural Networks b. Associative Memory c. Expert Systems d. Collective Learning
l__ Rummelhart is well known for his work on
a. Neural Networks b. Associative
Memory c. Expert Systems d. Collective Learning
m__ The following formula
is generally used to to obtain faster learning at the beginning
a. P = p +
(1-p)(1-p)§
b. p = p + (1-p)p § c. p = p - p§ d. p = p*(1-§)
n__
A non learner random player can be obtained in an STM if you use
a. p = 0
b. § = 0 c. p = 1 d. § = 1
3. Given the
following STM for Exclusive OR Learner (20 points)
|
STM |
0 |
1 |
|
00 |
0.5 |
0.5 |
|
01 |
0.5 |
0.5 |
|
10 |
0.5 |
0.5 |
|
11 |
0.5 |
0.5 |
a) Using
a single steps process using the
following random numbers
(0.56, 0.45, 0.23, .076, 0.12, 0.67) perform the first six iterations with the following
four inputs (00, 01, 10, 11, 00,11) with the following
truth vector ( 0,1,1,0,0,0 ). Show
the result of the STM after the sixth iteration. Use extra paper to
neatly show all your computations (USING BETA = 0.8)
|
STM |
0 |
1 |
|
00 |
0.90 |
0.10 |
|
01 |
0.10 |
0.90 |
|
10 |
0.10 |
0.90 |
|
11 |
0.90 |
0.10 |
b) Selecting the Maximum, again in
single steps, perform the first six iterations with the following four
inputs (00, 01, 10, 11, 00,11) with the same truth vector ( 0,1,1,0,0,0 ). Show the result of the
STM after the sixth iteration. Use extra paper to neatly show all your
computations (USING BETA = 0.8)
|
00 |
0.90 |
0.10 |
|
01 |
0.10 |
0.90 |
|
10 |
0.10 |
0.90 |
|
11 |
0.90 |
0.10 |
c)
Any comments about both methods?
In this both results are the
same since we are using single non collective learning
4.
Consider again the exclusive Or function, using the following Neural
network formulas, perform the first two
iterations (propagation, backpropagation) with the following inputs (00, 01) with the
same truth vector ( 0,1). Assuming
the initial seed values given below, present the final values Use extra
paper to neatly show all your computations
|
|
Propagation |
|
|
|
Backpropagation |
|
|
|
Input
or Intermediate Axon : a(h) |
|
alpha |
0.9 |
|
|||
|
dendritic
weight: d(i) : weight for a(h) in n(j) |
general
output error : e(s) =
(V(s)-a(s)) |
|
|||||
|
neuronal
summation : n(j) = ·d(i)*a(i) |
|
intermediate
error: e(i) = ·(ea(pos)*d(pos)) |
|||||
|
neuronal
threshold u(j) : Fire constant |
|
axon
error : ea(j) = a(j)*(1-a(j))*e(j) |
|
||||
|
Output
axon : a(j) = Round< 1/(1 + exp(-n(j)-u(j) ) |
dendritic
correction: ¶d(i,<t>) = α*ea(j)*a(h)+β*¶(i,<t-1>) |
||||||
|
Output
axon : a(j) : fire if n(j) > - u(j) |
|
new
dendritic value
d(i,<t+1>) =
d(i,<t>) +
¶d(i,<t>) |
|||||
|
|
|
|
Propagation |
|
|
|
|||||
|
|
|
d
(i) |
a(h) |
n(j) |
T(j) |
a(j)
T |
a(j)
Sigmoid |
||||
|
a(1) |
1.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.50 |
|||||
|
a(2) |
1.00 |
1.00 |
1.00 |
0.00 |
1.00 |
0.73 |
|||||
|
|
|
|
|
|
|
|
|
||||
|
d(1) |
-5.05 |
0.00 |
0.00 |
|
|
|
|||||
|
d(2) |
-3.05 |
1.00 |
-3.05 |
|
|
|
|||||
|
T(3) |
4.94 |
1.00 |
4.94 |
|
|
|
|||||
|
a(3) |
|
|
-3.05 |
4.94 |
1.00 |
0.87 |
|||||
|
|
|
|
|
|
|
|
|
||||
|
d(11) |
-3.95 |
0.00 |
0.00 |
|
|
|
|||||
|
d(22) |
-1.95 |
1.00 |
-1.95 |
|
|
|
|||||
|
d(33) |
-8.00 |
1.00 |
-8.00 |
|
|
|
|||||
|
T(4) |
6.06 |
1.00 |
6.06 |
|
|
|
|||||
|
a(4) |
|
|
-9.95 |
6.06 |
0.00 |
0.02 |
|||||
|
|
|
|
Backpropagation |
|
|
|
|||||
|
|
a(j)
f |
e(j)
f |
ea(j) |
¶(i,<t>) |
¶(i,<t-1>) |
d(i,<t+1>) |
|
||||
|
a(4) |
0.54 |
-0.54 |
-1.34E-01 |
|
|
|
|
||||
|
u(4) |
|
|
|
-0.07 |
-0.07 |
6.00 |
|
||||
|
d(33) |
|
|
|
0.00 |
0.00 |
-7.98 |
|
||||
|
d(22) |
|
|
|
-0.05 |
-0.05 |
-1.99 |
|
||||
|
d(11) |
|
|
|
-0.05 |
-0.05 |
-4.01 |
|
||||
|
|
|
|
|
|
|
|
|
||||
|
a(3) |
0.14 |
1.07 |
1.32E-01 |
|
|
|
|
||||
|
u(3) |
|
|
|
0.07 |
0.07 |
5.04 |
|
||||
|
d(2) |
|
|
|
0.05 |
0.05 |
-2.99 |
|
||||
|
d(1) |
|
|
|
0.05 |
0.05 |
-4.96 |
|
||||
|
|
|
|
|
|
|
|
|
||||
|
a(2) |
0.73 |
-0.14 |
-2.79E-02 |
-0.01 |
-0.01 |
0.99 |
|
||||
|
a(1) |
0.73 |
-0.13 |
-2.58E-02 |
-0.01 |
-0.01 |
0.99 |
|
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