Neural Networks and Fuzzy Systems

1. M. Raihan
Email: rianku11@gmail.com

2. Neural Networks

3. 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

4. Neural Networks
21-Sep-17 4

5. The Perceptron Network
21-Sep-17 5

6. 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

7. 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

8. 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

9. 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

10. 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

11. Biases Replace Thresholds
21-Sep-17 11

12. Training a Perceptron
21-Sep-17 12

13. Training a Perceptron
21-Sep-17 13

14. Training a Perceptron
21-Sep-17 14

15. Linear Separability
21-Sep-17 15

16. More Than One Input Neuron
21-Sep-17
The weights for each neuron separately describe a straight line.
16

17. 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

18. Linear Separability
21-Sep-17 18

19. What Can Perceptrons Represent?
21-Sep-17 19

20. Thank You
21-Sep-17 20