artificial intelligence

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ARTIFICIAL NEURON
Biological Neuron

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ARTIFICIAL NEURON
Biological Neuron
The brain may be thought of as a
complex computer
It has the following amazing
characteristics:
The ability to perform complex tasks (e.g. pattern
recognition, perception & motor control) much faster than
any computer – even though events occur in the nanosecond
range for silicon gates, and milliseconds for neural systems.
The brain has the ability to solve several problems
simultaneously using distributed parts of the brain

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ARTIFICIAL NEURON
Biological Neuron
The ability to learn, memorize and still generalize
The brain is Fault Tolerant in two respects
- It is able to recognize many input signals that are
somewhat different from any signal we have seen before
(e.g. recognition of person from different pictures)
- It is able to tolerate damage to the neural system itself.
Most of the neurons are not replaced when they die. In
spite of continuous loss of neurons, we continue to learn

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ARTIFICIAL NEURON
Biological Neuron
These characteristics prompted research in algorithmic
modeling of brain (biological neural systems)
Is it possible to truly model the human brain?
Not at the present. Current successes in neural modeling are
for small artificial NNs aimed at solving a specific task

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ARTIFICIAL NEURON
Biological Neuron
The basic building blocks of biological neural systems are
nerve cells, referred to as neurons
About 100 billion neuron in the human brain

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ARTIFICIAL NEURON
Biological Neuron
The neurons are arranged in approximately 1000 main
modules, each having about 500 neural networks

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Biological Neuron
The main body of the cell collects the incoming signals from
the other neurons through its dendrites
The incoming signals are constantly being summed in the cell
body
If the result of the summation crosses a certain threshold, the
cell body emits a signal of its own (called firing of the
neuron)
This signal passes through the neuron’s axon, from where the
dendrites of other neurons pick it up
ARTIFICIAL NEURON

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Biological Neuron
There are 1,000 to 10,000 dendrites in each neuron (few
millimeters long).
There is only one axon (several centimeters long)
The connection between dendrites and axon is
electrochemical and it is called synapse
The synapses modify (enhance or inhibit) the signal while
passing it on to dendrites
ARTIFICIAL NEURON

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Biological Neuron
The human learning is stored in these synapses, and the
connection of neurons with other neurons
If stimulus at a dendrite causes the neuron to fire, then the
connection between that dendrite and axon is strengthened
If the arrival of stimulus does not cause the neuron to fire,
the connection weakens over time
ARTIFICIAL NEURON

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ARTIFICIAL NEURON
Artificial Neuron Model

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Artificial Neuron Model
ARTIFICIAL NEURON

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Artificial Neuron Model
It receives a vector X of I input signals,
X = (x1, x2, …, xI)
either from the environment or from other artificial neurons
Each input signal xi is multiplied by a weight wi to strengthen
or weaken it
The neuron computes the weighted
sum of the input signals
ARTIFICIAL NEURON

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Artificial Neuron Model
The weighted sum is usually called the activation of the
neuron
An activation function is applied on this weighted sum to
produce the output of the neuron
y = f(activation)
If the activation function is the unit step function, we can say
that an artificial neuron implements a nonlinear mapping
from a vector of real numbers to [-1, 1]
ARTIFICIAL NEURON

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ARTIFICIAL NEURON
Implementation of Logic Functions

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Artificial Neuron Model
Implementation of AND
function
Let W1 = W2 = 1
X1 X2 X1W1 + X2W2 Y
0 0 0 F
0 1 1 F  = any value >1 but <=2
1 0 1 F = 1.5 (e.g.)
1 1 2 T
With appropriate value of  of the unit step activation
function, we will get correct results
ARTIFICIAL NEURON

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Artificial Neuron Model
We can graphically show the
AND functions input on a two
coordinate system (X1 and X2)
ARTIFICIAL NEURON

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Artificial Neuron Model
The neuron outputs a 1, if
X1W1 + X2W2 ≥ θ, otherwise
the output is 0
Let θ = 1.5, W1 = W2 = 1
ARTIFICIAL NEURON
At the boundary between the output of 1 and 0 we have
X1 + X2 = 1.5
For plotting this boundary,
We first take X2 = 0, and get X1 = 1.5
And then we put X1 = 0, and get X2 = 1.5

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Artificial Neuron Model
ARTIFICIAL NEURON
The neuron has drawn a line
from (1.5, 0) to (0, 1.5) in the
input plane
Any new data falling on the
left side of the line will result
in an output of zero (F)
and the data on the right side
of the line will result in one (T)

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Artificial Neuron Model
Implementation of OR
function
Let W1 = W2 = 1
X1 X2 X1W1 + X2W2 Y
0 0 0 F
0 1 1 T
1 0 1 T
1 1 2 T
If we make  = 1 (or any value >0 but <=2), we will get
correct results with a unit step activation function
ARTIFICIAL NEURON

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Artificial Neuron Model
If we place the 4 points in a
two coordinate system (X1 and
X2), we have drawn a line
from (1, 0) to (0, 1) in the
resulting plane
Any new data falling on the
left side of the line will give an
output of zero and the data on
the right side of the line will be
classified as one
ARTIFICIAL NEURON

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Artificial Neuron Model
If we want to utilize a unit step function centered at zero for
both AND and OR neurons, we can incorporate another
input X0 constantly set at –1
The weight W0 corresponding to this input would be the ,
calculated previously . It is called bias
ARTIFICIAL NEURON

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Artificial Neuron Model
AND function
W1 = W2 = 1
We have calculated  = 1.5 for this problem, so W0 =  = 1.5
X1 X2 X1W1 + X2W2 + (-1)W0 Y
0 0 0 – 1.5 = -1.5 F With bias
0 1 1 – 1.5 = -0.5 F a unit step
1 0 1 – 1.5 = -0.5 F function
1 1 2 – 1.5 = 0.5 T centered at
0 is used
ARTIFICIAL NEURON

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ARTIFICIAL NEURON
Linearly Separable Problems

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Linearly Separable Problems
Those problems for which the data can be correctly divided
into two categories by a line or hyper-plane
ARTIFICIAL NEURON
Because the equation
for the hyperplane is linear, hence
a single neuron is a linear
classifier

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Linearly Separable Problems
Single neurons can realize linearly separable functions
Linear separation is achieved with the help of an n-
dimensional hyperplane created in the space of n-
dimensional input vectors
The hyperplane forms a boundary between the input vectors
associated with the two output values
ARTIFICIAL NEURON

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Linearly Separable Problems
X1 X2 Y
1.0 1.0 1
9.4 6.4 -1
2.5 2.1 1
8.0 7.7 -1
0.5 2.2 1
7.9 8.4 -1
7.0 7.0 -1
2.8 0.8 1
1.2 3.0 1
7.8 6.1 -1
ARTIFICIAL NEURON

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Linearly Separable Problems
Suppose we set the weight vector [w1, w2, ]
to [-1.3, -1.1, 10.9]
ARTIFICIAL NEURON
The output = f(xiwi)
= f(-1.3x1 –1.1x2 + 10.9)
To draw the boundary
line we take the output
as zero on the boundary
i.e.
-1.3x1 – 1.1x2 + 10.9 = 0

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Linearly Separable Problems
If the data cannot be correctly
separated by a single line or
plane, then it is not linearly
separable
(e.g. exclusive OR problem)
ARTIFICIAL NEURON
A single layered neurons cannot classify the input patterns
that are not linearly separable.
We need more than one neurons arranged in more than one
layers