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M. Raihan
Email: rianku11@gmail.com
Neural Networks
Neural Networks
21-Sep-17
Can put lots of McCulloch & Pitts neurons
together.
Connect them up in any way we like.
In fact, assemblies of the neurons are capable of
universal computation.
Can perform any computation that a normal computer can.
Just have to solve for all the weights wij
3
Neural Networks
21-Sep-17 4
The Perceptron Network
21-Sep-17 5
Training Neurons
21-Sep-17
Adapting the weights is learning
How does the network know it is right?
How do we adapt the weights to make the network
right more often?
Training set with target outputs.
Learning rule.
6
A Simple Perceptron
21-Sep-17
It’s a single-unit network
Change the weight by an
amount proportional to
the difference between
the desired output and
the actual output.
7
Updating the Weights
21-Sep-17
 Wij Wij+ Wij
We want to change the values of the weights
Aim: minimize the error at the output
If E = t-y, want E to be 0
Use:
8
The Learning Rate
21-Sep-17
ɳ controls how much to change by weights.
If we could miss it, ɳ = 1.
Weight change a lot, whenever the answer is wrong.
Makes the network unstable.
Small ɳ
Weights need to see the inputs more often before they change
significantly.
Network takes longer to learn.
But, more stable network.
9
Bias Input
21-Sep-17
 What happens when all the inputs to a neuron is zero?
It doesn’t matter what the weights are
The only way that we can control whether neuron fires or not is
through the threshold.
That’s why threshold should be adjustable.
Changing the threshold requires an extra parameter that we need to
write code for.
We can add an extra input weight to the neuron, with
the values of the input to that weight always being fixed.
h = 𝒊=𝟏
𝒎
𝒙𝒊 𝒘𝒊 10
Biases Replace Thresholds
21-Sep-17 11
Training a Perceptron
21-Sep-17 12
Training a Perceptron
21-Sep-17 13
Training a Perceptron
21-Sep-17 14
Linear Separability
21-Sep-17 15
More Than One Input Neuron
21-Sep-17
The weights for each neuron separately describe a straight line.
16
Perceptron Limitations
21-Sep-17
A single layer perceptron can only learn
linearly separable problems.
Boolean AND function is linearly separable, whereas
Boolean XOR function (and the parity problem in
general) is not.
17
Linear Separability
21-Sep-17 18
What Can Perceptrons Represent?
21-Sep-17 19
Thank You
21-Sep-17 20
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Lecture 2

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