Neuron Model and Network Architectures

1. Neuron Model and Network Architectures

2. Biological Inspiration

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0 t為神經元輸出

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)

5. Single-Input Neuron 例1：w=3,p=2 and b=-1.5then a=f(3(2)-1.5)=f(4.5)

6. Transfer Functions a=0 n<0 a=1 n>=0 例2：w=3, p=2 and b=-1.5then a=hardlim(3(2)-1.5)=hardlim(4.5)=1

7. Transfer Functions 例3：w=3, p=2 and b=-1.5then a=purelin(3(2)-1.5)=purelin(4.5)=4.5

8. Transfer Functions 例4：w=3, p=2 and b=-1.5then a=logsig(3(2)-1.5)=logsig(4.5)=

9. Transfer Functions

10. 0<=a<=1 -1<=a<=1

11. Multiple-Input Neuron Abbreviated Notation Neuron With R Inputs

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)= -1 ii. a=satlin(-1.8)= 0 iii. a=tansig(-1.8)=

13. Layer of S Neurons R Input S Output i.e.,R≠S Layer of S Neurons

14. Abbreviated Notation w w ¼ w 1 , 1 1 , 2 1 , R w w ¼ w W 2 , 1 2 , 2 2 , R = w w ¼ w S , 1 S , 2 S , R p b a 1 1 1 p b a p a b 2 2 2 = = = p b a R S S

15. Multiple Layers of Neurons Three-Layer Network

16. Abbreviated Notation Hidden Layers Output Layer

17. Delays and Integrators a(0)=a(0) a(1)=u(0)

18. Recurrent Network