![Page 1: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/1.jpg)
2
1
Neuron Modeland
Network Architectures
![Page 2: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/2.jpg)
2
2
Biological Inspiration
![Page 3: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/3.jpg)
2
3
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
![Page 4: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/4.jpg)
2
4
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)
![Page 5: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/5.jpg)
2
5
Single-Input Neuron
例 1 : w=3,p=2 and b=-1.5 thena=f(3(2)-1.5)=f(4.5)
![Page 6: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/6.jpg)
2
6
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
![Page 7: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/7.jpg)
2
7
Transfer Functions
例 3 : w=3, p=2 and b=-1.5 thena=purelin(3(2)-1.5)=purelin(4.5)=4.5
![Page 8: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/8.jpg)
2
8
Transfer Functions
例 4 : w=3, p=2 and b=-1.5 thena=logsig(3(2)-1.5)=logsig(4.5)=
![Page 9: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/9.jpg)
2
9
Transfer Functions
![Page 10: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/10.jpg)
2
10
0<=a<=1
-1<=a<=1
![Page 11: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/11.jpg)
2
11
Multiple-Input Neuron
Abbreviated NotationNeuron With R Inputs
![Page 12: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/12.jpg)
2
12
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)=
![Page 13: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/13.jpg)
2
13
Layer of S Neurons
R InputS Outputi.e.,R≠SLayer of S Neurons
![Page 14: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/14.jpg)
2
14
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
=
![Page 15: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/15.jpg)
2
15
Multiple Layers of Neurons
Three-Layer Network
![Page 16: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/16.jpg)
2
16
Abbreviated Notation
Hidden Layers Output Layer
![Page 17: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/17.jpg)
2
17
Delays and Integrators
a(0)=a(0)a(1)=u(0)
![Page 18: 2 1 Neuron Model and Network Architectures. 2 2 Biological Inspiration](https://reader036.vdocuments.mx/reader036/viewer/2022062313/56649d2c5503460f94a02320/html5/thumbnails/18.jpg)
2
18
Recurrent Network
a 2 satlins Wa 1 b+ =a 1 satlins Wa 0 b+ satlins Wp b+ = =