neuron model and network architectures
DESCRIPTION
Neuron Model and Network Architectures. Biological Inspiration. Neuron Model. a 1 ~ a n 為輸入向量的各個分量 w 1 ~ w n 為神經元各個突觸的權值 b 為偏差 f 為傳遞函數,通常為非線性函數。 例如: hardlim ( n ) , n 正為 1 ,其餘 0 t 為神經元輸出. Notation. Scalars-small italic letters : a,b,c Vectors-small bold nonitalic letters : a,b,c - PowerPoint PPT PresentationTRANSCRIPT
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Neuron Modeland
Network Architectures
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Biological Inspiration
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Neuron Model
a1~an 為輸入向量的各個分量 w1~wn 為神經元各個突觸的權值 b為偏差f為傳遞函數,通常為非線性函數。例如: hardlim(n) , n正為 1 ,其餘 0t為神經元輸出
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Notation• Scalars-small italic letters : a,b,c• Vectors-small bold nonitalic letters : a,b,c• Matrices-capital BOLD nonitalic letters : A,B,C• Input-p,p,P• Weight-w,w,W• Bias-b,b• Output-a,a,a(t)
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Single-Input Neuron
例 1 : w=3,p=2 and b=-1.5 thena=f(3(2)-1.5)=f(4.5)
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Transfer Functions
例 2 : w=3, p=2 and b=-1.5 thena=hardlim(3(2)-1.5)=hardlim(4.5)=1
a=0 n<0a=1 n>=0
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Transfer Functions
例 3 : w=3, p=2 and b=-1.5 thena=purelin(3(2)-1.5)=purelin(4.5)=4.5
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Transfer Functions
例 4 : w=3, p=2 and b=-1.5 thena=logsig(3(2)-1.5)=logsig(4.5)=
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Transfer Functions
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0<=a<=1
-1<=a<=1
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Multiple-Input Neuron
Abbreviated NotationNeuron With R Inputs
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Example P2.3
Given a two-input neuron with the following parameters: b=1.2, W= [ 3 2 ] and p= [ -5 6 ]T , calculate the neuron output for the following transfer functions:
i. A symmetrical hard limit transfer functionii. A saturating linear transfer function iii. A hyperbolic tangent sigmoid(tansig) transfer function
i. a=hardlims(-1.8)= -1ii. a=satlin(-1.8)= 0iii. a=tansig(-1.8)=
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Layer of S Neurons
R InputS Outputi.e.,R≠SLayer of S Neurons
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Abbreviated Notation
W
w1 1, w1 2, ¼ w1 R,
w2 1, w2 2, ¼ w2 R,
wS 1, wS 2, ¼ wS R,
=
b1
2
S
=
b
b
b
pp1
p2
pR
= a
a1
a2
aS
=
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Multiple Layers of Neurons
Three-Layer Network
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Abbreviated Notation
Hidden Layers Output Layer
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Delays and Integrators
a(0)=a(0)a(1)=u(0)
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Recurrent Network
a 2 satlins Wa 1 b+ =a 1 satlins Wa 0 b+ satlins Wp b+ = =