hopefully a clearer version of neural network
DESCRIPTION
Hopefully a clearer version of Neural Network. O1. I1. H1. I2. H2. O2. Layers of Weights. We Name Sets of Weights between layers As W1 for weights between input Layer and First Hidden Layer W2 for weights between next 2 layers and - PowerPoint PPT PresentationTRANSCRIPT
Layers of Weights
• We Name Sets of Weights between layersAs W1 for weights between input Layer and
First Hidden LayerW2 for weights between next 2 layers and WN-1 for Weights between N-1th and Nth
Layer(i.e. Output Layer)In our example Net we just have 3 layersInput Hidden and Output So we have just
W1 and W2
Weights along Individual Links
• Convention
• Each Weight is named as follows
• WNij
• N refers to the Layer of Weights
• So Between Input and First Hiden Layer i.e. W2ij is the Reference
• Between Hidden and Output W2ij
Individual Weights within a layer
• Reference WNij
• WN refers to the Weight Layer
• ij refers to the indices of the source and destination nodes.
• So for example the weight between hidden node h1 and output node o2
• It belongs to weight layer 2 so W2
• i = 1 and j = 2 so Weight is W212
Hidden Layer Computation
• Xi =iW1 = • 1 * 1 + 0 * -1 = 1, • 1 * -1 + 0 * 1 = -1 = • { 1 - 1} = {Xi1,Xi2} = Xi
xF
1
1
• h = F(X)• h1 = F(Xi1) = F(1)• h2 = F(Xi2) = F(-1)
27.01
1
1
1)2(
73.01
1
1
1)1(
)1(2
)1(1
xi
xi
XiF
XiF
Output Layer Computation
• X = hW2 = • 0.73 * -1 + 0.27 * 0 = -0.73, • 0.73 * 0 + 0.27 * -1 = -0.27 =• { -0.73 - 0.27} = {X1,X2} = X
xF
1
1
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
• Target T2 = 1 , O2 = 0.433 = 0.43
• d2 = 0.43(1 - 0.43)(1-0.43) = 0.43(0.57)(0.57) = 0.14
Weight Adjustment
• △W2t = α hd + Θ △W2t-1
• where α = 1• Time t = 1 so no previous time
2212
211121
2
1
dhdh
dhdhdd
h
hhd
)14.0*27.0()15.0*27.0(
)14.0*73.0()15.0*73.0(14.015.0
27.0
73.0hd
This equals
• e1 = (h1(1-h1)W11 D1 +W12D2• e2 = (h2(1-h2)) W21 D1 +W22D2• d1 = 0.15 d2 = = 0.14e1 = (0.73(1-0.73))( -1* 0.15 +0*0.14)• e2 =( 0.27(1-0.27)) (0 *0.15 +-1*0.14)
• e1 = (0.73(0.27)( -0.15))• e2 =( 0.27(0.73)) (-0.14)• e1 = -0.03• e2 = -0.028
Weight Adjustment
• △W1t = α Ie + Θ △W2t-1
• where α = 1
2212
211121
2
1
eIeI
eIeIee
I
IIe
)028.0*0()03.0*0(
)028.0*1()03.0*1(028.003.0
0
1Ie