1. Neural Networks
V.Saranya
AP/CSE
Sri Vidya College of Engineering and
Technology,
Virudhunagar

2. Neural Networks
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3. Natural Neural Networks
• Signals “move” via electrochemical signals
• The synapses release a chemical transmitter –
the sum of which can cause a threshold to be
reached – causing the neuron to “fire”
• Synapses can be inhibitory or excitatory
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4. Natural Neural Networks
• We are born with about 100 billion neurons
• A neuron may connect to as many as 100,000
other neurons
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5. Natural Neural Networks
• Many of their ideas still used today e.g.
– many simple units, “neurons” combine to give
increased computational power
– the idea of a threshold
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6. Modelling a Neuron
• aj :Activation value of unit j
• wj,i :Weight on link from unit j to unit i
• ini :Weighted sum of inputs to unit i
• ai :Activation value of unit i
• g :Activation function
j
jiji aWin ,
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7. Activation Functions
• Stept(x) = 1 if x ≥ t, else 0 threshold=t
• Sign(x) = +1 if x ≥ 0, else –1
• Sigmoid(x) = 1/(1+e-x)
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8. Building a Neural Network
1. “Select Structure”: Design the way that the
neurons are interconnected
2. “Select weights” – decide the strengths with
which the neurons are interconnected
– weights are selected so get a “good match” to
a “training set”
– “training set”: set of inputs and desired
outputs
– often use a “learning algorithm”
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9. Basic Neural Networks
• Will first look at simplest networks
• “Feed-forward”
– Signals travel in one direction through net
– Net computes a function of the inputs
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10. The First Neural Neural Networks
Neurons in a McCulloch-Pitts network are connected by directed, weighted
paths
-1
2
2X1
X2
X3
Y
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11. The First Neural Neural Networks
If the on weight on a path is positive the path is
excitatory,
otherwise it is inhibitory
-1
2
2X1
X2
X3
Y
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12. The First Neural Neural Networks
The activation of a neuron is binary. That is, the neuron
either fires (activation of one) or does not fire (activation of
zero).
-1
2
2X1
X2
X3
Y
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13. The First Neural Neural Networks
For the network shown here the activation function for unit Y is
f(y_in) = 1, if y_in >= θ else 0
where y_in is the total input signal received
θ is the threshold for Y
-1
2
2X1
X2
X3
Y
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14. The First Neural Neural Networks
Originally, all excitatory connections into a particular neuron have the same
weight, although different weighted connections can be input to different
neurons
Later weights allowed to be arbitrary
-1
2
2X1
X2
X3
Y
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15. The First Neural Neural Networks
Each neuron has a fixed threshold. If the net input into the neuron is
greater than or equal to the threshold, the neuron fires
-1
2
2X1
X2
X3
Y
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16. The First Neural Neural Networks
The threshold is set such that any non-zero inhibitory input will prevent the neuron
from firing
-1
2
2X1
X2
X3
Y
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17. Building Logic Gates
• Computers are built out of “logic gates”
• Use threshold (step) function for activation
function
– all activation values are 0 (false) or 1 (true)
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18. The First Neural Neural Networks
AND Function
1
1
X1
X2
Y
AND
X1 X2 Y
1 1 1
1 0 0
0 1 0
0 0 0
Threshold(Y) = 2
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19. The First Neural Networks
AND FunctionOR Function
2
2X1
X2
Y
OR
X1 X2 Y
1 1 1
1 0 1
0 1 1
0 0 0
Threshold(Y) = 2
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20. Perceptron
• Synonym for Single-Layer,
Feed-Forward Network
• First Studied in the 50’s
• Other networks were known
about but the perceptron
was the only one capable of
learning and thus all research
was concentrated in this area
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21. Perceptron
• A single weight only affects
one output so we can restrict
our investigations to a model
as shown on the right
• Notation can be simpler, i.e.
j
WjIjStepO 0
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22. What can perceptrons represent?
AND XOR
Input 1 0 0 1 1 0 0 1 1
Input 2 0 1 0 1 0 1 0 1
Output 0 0 0 1 0 1 1 0
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23. What can perceptrons represent?
0,0
0,1
1,0
1,1
0,0
0,1
1,0
1,1
AND XOR
• Functions which can be separated in this way are called Linearly Separable
• Only linearly separable functions can be represented by a perceptron
• XOR cannot be represented by a perceptron
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24. XOR
• XOR is not “linearly separable”
– Cannot be represented by a perceptron
• What can we do instead?
1. Convert to logic gates that can be represented by
perceptrons
2. Chain together the gates
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25. Single- vs. Multiple-Layers
• Once we chain together the gates then we have “hidden
layers”
– layers that are “hidden” from the output lines
• Have just seen that hidden layers allow us to represent XOR
– Perceptron is single-layer
– Multiple layers increase the representational power, so
e.g. can represent XOR
• Generally useful nets have multiple-layers
– typically 2-4 layers
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