1. Example, perceptron learning function AND
Training samples
Initial weights W(0)
Learning rate = 1
Present p1
net = (0, 2, 0)(1, -1, 1) = -2
no learning occurs
in_0
in_1
in_2 d p0 1 -1 p1 p2 p3
Present p2
net = (0, 2, 0)(1, 1, -1) = 2
x = (-1)(1, 1, -1) = (-1, -1, 1)
W(2) = (0, 2, 0) + (-1, -1, 1)
= (-1, 1, 1) w0 w1 w2 1 -1
Present p3
net = (-1, 1, 1)(1, 1, 1) = 1
no learning occurs
Present p0
net = W(0)p0 = (1, 1, -1)(1, -1, -1) =1
p0 misclassified, learning occurs
x =d p0 = (-1, 1, 1)
W(1) = W(0) + x = (0, 2, 0)
New net = W(1)p0 = -2 is closer to target (d = -1)
Present p0, p1, p2, p3
All correctly classified with W(2)
Learning stops with W(2)

2. x o
W(0) = (1, 1, -1) x o
W(1) = (0, 2, 0) x o
W(0) = (-1, 1, 1)

3. Example, learning function AND by delta rule
Training samples
Initial weights W(0)
Learning rate = 0.3
Present p0
net = (1, 1, -1)(1, -1, -1) = 1
∆W = 0.3(d – net) p0
= (-0.6, 0.6, 0.6)
W(1) = W(0) + ∆W
=(0.4, 1.6, -0.4)
New net = W(1)p0 = -0.8 is closer to target (d = -1) than before
in_0
in_1
in_2 d p0 1 -1 p1 p2 p3 w0 w1 w2 1 -1

4. W(k) w0 w1 w2
net1
d_out
d - net 1 -1 -2
0.4
1.6
-0.4
-1.6
0.6 2
0.58
1.42
-0.22
2.22
-3.22 3
-0.386
0.454
0.746
0.814
0.186 4
0.5098
0.8018
0.6418 5 6 7 8
0.6383 9 10 11 12 13 14 15

5. W(0) = (1, 1, -1) W(1) = (04, 1.6, -0.4) W(15) = (-77, 0.36, 0.5) x xo
W(0) = (1, 1, -1) x o
W(1) = (04, 1.6, -0.4) x o
W(15) = (-77, 0.36, 0.5)