Hopefully a clearer version of Neural Network

With Actual Weights

I1 O1 H1 H2I2 W1 W

Inputs 1 and 0 Target output {1}

Hidden Layer Computation Xi =iW1 = 1 * * -1 = 1, 1 * * 1 = -1 = { 1 - 1} = {Xi1,Xi2} = Xi

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

I1 O1 H1 H2I2 W1 W

Next Output

Output Layer Computation X = hW2 = 0.73 * * 0 = -0.73, { } = X

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

I1 O1 H1 H2I2 W1 W

I1 O1 H1 H2I2 W1 W

I1 O1 H1 H2I2 W1 W

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

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

Weight Adjustments

Weight Change

Equals

Putting these new weights in the diagram To get

I1 O1 H1 H2I2 W1 W

Next Calculate Change on W1 layer weights

the next error

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

I1 O1 H1 H2I2 W1 W

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 = e2 = 0

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

Weight Adjustment

Existing W1

Weight Change W1

New W1

Changing Net

I1 O1 H1 H2I2 W1 W