Künstliche Neuronale Netze

12.05.2009
Backpropagation – Illustration
• Feedforward network with
a 1 a 3 a 5
initial weights
w 13
w 35
• Lerning rate α
1 1
3
5
w 14
w 36
• Two inputs and outputs
a 2 a
w 4 a
23
w 6
45
• Compute output for first 1 2
4
6
w 24 w 46
examples
• Compare to desired target
value
1
1
I1 I2 T1 T2
1 1 1 0
0 0 0 1
...
35
Backpropagation – Illustration (2)
• Compute error: Err=T-O
a 1 a 3 a 5 Δ w 5
13
w 35
1 1
3
5
• W j,i = W j,i + α ×a j × Err i × g’(in i )
w 14
w 36
• Error term Δ i = Err i g’(in i )
a 2 a
w 4 a
23
w 6
45
1 2
• W j,i = W j,i + α ×a j ×Δ
4
6
i
w 24 w 46
Δ 6
• Compute error terms for output
units Δ 5 and Δ 6
I1 I2 T1 T2
• Adaptation of weights for
• w 36 and w 46
0 0 0 1
• w 35 and w 45
1 1 1 0
...
36
1
1
18