1. Hopefully a clearer version of Neural Network

2. With Actual Weights

3. I1 O1 H1 H2I2 W1 W2 0 0 1 1

4. Inputs 1 and 0 Target output {1}

5. Hidden Layer Computation Xi =iW1 = 1 * 1 + 0 * -1 = 1, 1 * -1 + 0 * 1 = -1 = { 1 - 1} = {Xi1,Xi2} = Xi

6. h = F(X) h1 = F(Xi1) = F(1) h2 = F(Xi2) = F(-1)

7. I1 O1 H1 H2I2 W1 W2 0 0 1 1 1 0 0.73 0.27

8. Next Output

9. Output Layer Computation X = hW2 = 0.73 * -1 + 0.27 * 0 = -0.73, { -0.73 } = X

10. O = F(X) O1 = F(X1) O2 = F(X2)

11. I1 O1 H1 H2I2 W1 W2 0 0 1 1 1 0 0.73 0.27

12. I1 O1 H1 H2I2 W1 W2 0 0 1 1 1 0 0.73 0.27

13. I1 O1 H1 H2I2 W1 W2 0 0 1 1 1 0 0.73 0.27 0.325

14. Error D= Output(1 – Output)(Target – Output) Target T1 = 1, O1 = 0.325 = 0.33 d1 = 0.33( 1 -0.33)(1 -0.33 ) = 0.33 (0.67)(0.67) = 0.148

15. Weight Adjustment △ W2t = α hd + Θ △ W2t-1 where α = 1 Time t = 1 so no previous time

16. Weight Adjustments

17. Weight Change

18. Equals

20. Putting these new weights in the diagram To get

21. I1 O1 H1 H2I2 W1 W2 0.04 -0.891 0 1 1 1 0 0.73 0.27 0.325

22. Next Calculate Change on W1 layer weights

23. the next error

24. What is this Output is O1 So k = {1} So if i = 1

26. I1 O1 H1 H2I2 W1 W2 0.04 -0.891 0 1 1 1 0 0.73 0.27 0.325

27. This equals e1 = (h1(1-h1)W11 D1 e2 = (h2(1-h2)) W21 D1 d1 = 0.15 e1 = (0.73(1-0.73))( -1* 0.15 ) e2 =( 0.27(1-0.27)) (0 *0.15 ) e1 = (0.73(0.27)( -0.15)) e2 =( 0.27(0.73)) (0) e1 = -0.03 e2 = 0

28. Weight Adjustment △ W1t = α Ie + Θ △ W2t-1 where α = 1

29. Weight Adjustment

30. Existing W1

31. Weight Change W1

32. New W1

33. Changing Net

34. I1 O1 H1 H2I2 W1 W2 0.04 -0.891 0 0.97 1 1 0 0.73 0.27 0.325