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1. Knowledge base Systems
Neural Networks

2. What are Artificial Neural Networks?
Neural Networks Composed of many “neurons”. Each neuron has
one or more inputs. Each input is associated weight which
modifies the strength of each input. The neuron simply adds
together all the inputs and calculates an output to be passed on.

3. Neural Networks (con…)
 The activation of a neuron is binary. That is, the
neuron either fires (activation of one) or does not
fire (activation of zero).
 Each neuron has a fixed threshold. If the output
is greater than or equal to the threshold, the
neuron fires else not fire

4. Example:
If the inputs: x1= 2, x2= 0, x3= 3, weights w1=
0.5, w2= 0,2 , w3= 0.8, and bias is -1. What is
the output?
Output = 2 * 0.5 + 0 * 0.2 + 3 * 0.8 +
(-1) = 2.4
Assuming Output Threshold = 2.2
2.4 > 2.2

5. Example 2:
• Example calculation: x1=-1, x2=1, x3=1, x4=-1
– S = 0.25*(-1) + 0.25*(1) + 0.25*(1) + 0.25*(-1) = 0
• 0 > -0.1, so the output from the ANN is +1
– So the image is categorised as “bright”

6. A single-layer neural network
A single-layer net has one layer of connection weights

7. A multilayer neural network
 Multilayer net is a net with one or more layers (or
levels) of nodes (the so-called hidden units) between the
input units and output units. Typically, there is a layer of
weights between two adjacent levels of units ( input,
hidden, or output)

8. Example :
The input x1=0.6, x2=0.1 , and the weights are set
as in the picture, Calculate the output o6 and o7?

9.  Activations of the hidden units:
net3= x1 *w11+ x2*w21+b3=0.6*0.1+0.1*(-0.2)+0.1=0.14
ox3= 1/(1+e-net3) =0.53.
net4= x1 *w12+ x2*w22+b4=0.6*0+0.1*0.2+0.2=0.22
ox4= 1/(1+e-net4) =0.55
net5= x1 *w13+ x2*w23+b5=0.6*0.3+0.1*(-0.4)+0.5=0.64
ox5= 1/(1+e-net5) =0.65

10.  Activations of the output units:
net6= x3 *w31+ x4*w41+ x5*w51 +b6=
0.53*(-0.4)+0.55*0.1+0.65*0.6-0.1=0.13
oo6= 1/(1+e-net6) =0.53
net7= x3 *w32+ x4*w42+ x5*w52 +b7=
0.53*0.2+0.55*(-0.1)+0.65*(-0.2)+0.6=0.52
oo7= 1/(1+e-net7) =0.63

11. Exercise:
Try calculating the output of this network.

12. Hot and Cold Model:
 If we touch something cold we perceive heat
 If we keep touching something cold we will
perceive cold
 If we touch something hot we will perceive
heat

13.  To model this we will assume that time is
discrete
 If cold is applied for one time step then heat
will be perceived
 If a cold stimulus is applied for two time steps
then cold will be perceived
 If heat is applied then we should perceive heat
Hot and Cold Model:

14. It takes time for the stimulus (applied at X1 and X2) to
make its way to Y1 and Y2 where we perceive either heat
or cold
Hot and Cold Model:

15. • Neurons X1 and X2 represent heat and cold
• Neurons Z1 and Z2 auxiliary units needed
for the problem.
Hot and Cold Example: