5.9. EXERCISES AND PROJECTS 193
- What is a good size for the training set? As in statistics, such a question
only makes sense when we specify some degree of accuracy of the classi-
fication. There is some rule of thumb relating to the number of training
samples, the number of weights in a neural network, and the degree of
accuracy.
5.9 Exercisesandprojects ........................
- Design an artificial neuron to implement the Boolean function AND whose
truth table is
g(x 1 ,x 2 )=
Ω
1 ifx 1 =x 2 =1
0 otherwise
- Consider the logical Boolean function ìAand notB,î symbolicallyA∩B^0 ,
with truth function
g(x 1 ,x 2 )=
Ω
1 ifx 1 =1andx 2 =0
0 otherwise
Design an artificial neuron to implementg.
- Using your answer to Exercise 2 and(wAC,wBC,bC)=(2, 2 ,2)from Ex-
ample 5.1, as values for the two-layer neural network depicted in Example
5.1, show that the network implements the XOR function by verifying
that the four possible inputs give the desired outputs.
- Using your answer to Exercise 2 and(wAC,wBC,bC)=(1,− 2 ,− 0 .5),as
values for the two-layer neural network depicted in Example 5.1, show
that the network also implements the XOR function by verifying that the
four possible inputs give the desired outputs.
- Design an artificial neuron to implement the material implication operator
in Boolean logic:AimpliesB=A^0 ORBwhosetruthtableisasfollows
x 1 \x 2 01
0 11
1 01
or in other words,
g(x 1 ,x 2 )=
Ω
0 ifx 1 =1andx 2 =0
0 otherwise
- Refer to Example 5.3.Verify that the linex 1 +x 2 =^32 in thex 1 - x 2 plane
partitions the inputsxq,q=1, 2 , 3 , 4 , into two subsets corresponding to
output targets− 1 ,+1, respectively.
