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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 function

ii. 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

w 1 1, w1 2, ¼ w1 R,

w 2 1, w2 2, ¼ w2 R,

w S 1, wS 2, ¼ wS R,

=

b

1

2

S

=

b

b

b

p

p1

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+ = =