1. Network Architectures
Neuron Model
and
Network Architectures

2. Single-Input Neuron Inputs General Neuron Adjustable a = f(wp+b)
Example:
Suppose w = 3, p = 2, and b = -1.5, then
a = f( 3(2) – 1.5) = f(4.5)

3. Transfer Functions a = hardlim(n) a = hardlim(wp+b) a = purlin(wp+b)
hardlim transfer function
a = hardlim(wp+b)
Single neuron hardlim network
a = purlin(wp+b)
Single neuron purlin network
a = purlin(n)
linear transfer function

4. Transfer Functions a = logsig(wp+b) a = logsig(n) Demo: nnd2n1
Single neuron logsig network
a = logsig(n)
logsig transfer function
Demo: nnd2n1

5. Multiple-Input Neuron
n = w1,1 p1 + w1,2 p2 + …+w1,R pR + b
We will show this in matrix form as:
n = Wp + b
Then, a can be written as: f(Wp + b)
Abbreviated Notation
Demo: nnd2n2

6. Layer of Neurons
Number of inputs to a layer can be different from the number of neurons.
Neurons in a layer may have different transfer functions.
f(Wp + b)

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

8. Multilayer Network

9. a3 = f3(W3f2( W2f1(W1p+ b1)+b2)+b3)
Abbreviated Notation
Hidden Layers
Output Layer
a1 = f1(W1p + b1)
a2 = f2(W2a1 + b2)
a3 = f3(W3a2 + b3)
a3 = f3(W3f2( W2f1(W1p+ b1)+b2)+b3)
Layer number
Neuron Number
Input number

10. Delays and Integrators

11. Recurrent Network