Hopefully a clearer version of Neural Network. I1 O2 O1 H1 H2I2.
Hopefully a clearer version of Neural Network. With Actual Weights.
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Hopefully a clearer version of Neural Network
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22-Dec-2015 -
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Transcript of Hopefully a clearer version of Neural Network. With Actual Weights.
Hopefully a clearer version of Neural Network
With Actual Weights
I1
O1
H1
H2I2
W1 W2
-1 0
-10
1
1
Inputs
• 1 and 0
• Target output {1}
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
I1
O1
H1
H2I2
W1 W2
-10
-10
1
1
1
0
0.73
0.27
Next Output
Output Layer Computation
• X = hW2 = • 0.73 * -1 + 0.27 * 0 = -0.73, • { -0.73 } = X
xF
1
1
• O = F(X)• O1 = F(X1)• O2 = F(X2)
325.01
1
1
1)(
)73.0(
x
XF
I1
O1
H1
H2I2
W1 W2
-10
-10
1
1
1
0
0.73
0.27
I1
O1
H1
H2I2
W1 W2
-10
-10
1
1
1
0
0.73
0.27
I1
O1
H1
H2I2
W1 W2
-10
-10
1
1
1
0
0.73
0.27
0.325
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
Weight Adjustment
• △W2t = α hd + Θ △W2t-1
• where α = 1• Time t = 1 so no previous time
�
dh
dhd
h
hhd
22
111
2
1
)15.0*27.0(
)15.0*73.0(15.0
27.0
73.0hd
Weight Adjustments
)04.0(
)109.0(
Weight Change
)04.02(
)109.02(
21
11
W
W
Equals
)04.00(
)109.01(
Equals
)04.0(
)891.0(
Putting these new weights in the diagram
• To get
I1
O1
H1
H2I2
W1 W2
-10.04
-0.8910
1
1
1
0
0.73
0.27
0.325
Next
• Calculate Change on W1 layer weights
the next error
outputsk
kikiih dWhhe )1(
What is this
• Output is O1 • So k = {1}• So if i = 1
outputsk
kikdW
summation
1111,1
dWdWdWki
kikoutputsk
kik
I1
O1
H1
H2I2
W1 W2
-10.04
-0.8910
1
1
1
0
0.73
0.27
0.325
This equals
• e1 = (h1(1-h1)W11 D1• e2 = (h2(1-h2)) W21 D1 • d1 = 0.15e1 = (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
Weight Adjustment
• △W1t = α Ie + Θ △W2t-1
• where α = 1
2212
211121
2
1
eIeI
eIeIee
I
IIe
)0*0()03.0*0(
)0*1()03.0*1(003.0
0
1Ie
Weight Adjustment
)0()0(
)0()03.0(
Existing W1
10
11
11
11
2221
1211
WW
WW
Weight Change W1
)0(1)0(0
)0(1)03.0(1
New W1
10
197.0
• Changing Net
I1
O1
H1
H2I2
W1 W2
-10.04
-0.8910
0.97
1
1
0
0.73
0.27
0.325
