Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

P4 = [ 0 1 1 1 0 0 1 ]
Compute the next instances of each pattern by using the rules of binary
Hopfield nets, set threshold = 0.
Repeat the above process by replacing 0 in the patterns by –1 ; do you get
any changes in the results?
Can you call these 4 patterns stable states (states that do not change)? If
so, in which of the two cases?
Take any other arbitrary patterns, comprising of 1 and 0s. Are they also
stable states?
2. Suppose the 4 patterns are only given. Can you compute the weights in
the
network by using the formula given in the text?
3. Show that the learning rule in Widrow-Hoff’s model, given by the
following expression, is stable, when 0 < α < 2, unstable for α > 2 and
oscillatory when α = 2.
Learning rule:
∈
k
∆∈k
∆ w = α k X / | X |
k ∈ k k
~
; X = T
d − k k k
= − T
X k ∆w
~ ~
.
= −α
∈
k
= −α
∈
k
X
~
~ ~
w
k
k
/ |
X
~
~
where ∆Wk = change in weight vector, Xk = the input vector, whose
components are x1, x2, …xn.
[ Hints:
So,
Now, ( E –1 + α) ∈k = 0,
or, ∈k = (1 - α) k .
2
|
k
Now, put 0 < α < 2, α > 2 and α = 2 to prove the results.]
4. Derive the gradient descent learning rule for the following error function:
E= (1 / 2) ∑ ( tk – Outk) 2 + ∑ wj i 2
~
2
,