introduction to artificial intelligence (g51iai)

Introduction to Artificial Intelligence (G51IAI)

Dr Matthew HydeNeural Networks

More precisely: “Artificial Neural Networks”Simulating, on a computer, what we understand about neural networks in the brain

G51IAI – Introduction to AI

Lecture Outline

Biology History Perceptrons Multi-Layer Networks The Neuron’s Activation Function Linear Separability Learning / Training Time Steps

Lecture 1

Lecture 2

Biology



Neural Networks


Neural Networks

We have between 15-33 billion neurons A neuron may connect to as many as 10,000

other neurons Many neurons die as we progress through life We continue to learn


From a computational point of view, the fundamental processing unit of a brain is a neuron


A neuron consists of a cell body (soma with a nucleus)

Each neuron has a number of dendrites which receive signals from other neurons


Each neuron also has an axon, which goes out and splits into a number of strands to make a connection to other neurons

The point at which neurons join other neurons is called a synapse


Signals move between neurons via electrochemical reactions

The synapses release a chemical transmitter which enters the dendrite. This raises or lowers the electrical potential of the cell body


The soma sums the inputs it receives and once a threshold level is reached an electrical impulse is sent down the axon (often known as firing)

This increases or decreases the electrical potential of another cell (excitatory or inhibitory)


Long-term firing patterns formed – basic learning

Plasticity of the network Long term changes as patterns are repeated

Videos


http://www.youtube.com/watch?v=sQKma9uMCFk

http://www.youtube.com/watch?v=vvxXnQuvTD8&NR=1Various visualisations

http://www.youtube.com/watch?v=-SHBnExxub8Short neuron animation

History



Neural Networks

McCulloch & Pitts (1943) are generally recognised as the designers of the first neural network One Neuron The idea of a threshold Many of their ideas still used today


Neural Networks

Hebb (1949) developed the first learning rule McCulloch & Pitts network has fixed weights If two neurons were active at the same time the

strength between them should be increased

Rosenblatt (1958) The ‘perceptron’ Same architecture as McCulloch & Pitts, but

with variable weights


Neural Networks

During the 50’s and 60’s Many researchers worked on the perceptron

amidst great excitement This model can be proved to converge to

the correct weights More powerful learning algorithm than Hebb


Neural Networks

1969 saw the death of neural network research Minsky & Papert Perceptron can’t learn certain type of

important functions Research of ANN went to decline for about

15 years


Neural Networks

Only in the mid 80’s was interest revived Parker (1985) and LeCun (1986) independently

discovered multi-layer networks to solve problem of non-linear separable

Bryson & Ho publish an effective learning algorithm in 1969: ‘Backpropagation’

In fact Werbos and others make the link to neural networks in the late 70s and early 80s

Perceptrons(single layer, feed forward networks)



The First Neural Networks

It consisted of:A set of inputs - (dendrites)

A set of weights – (synapses)A processing element - (neuron)A single output - (axon)


McCulloch and Pitts Networks

-1

2

2X1

X2

X3

Y

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

Output function:If (input sum < Threshold) output 0Else output 1

θ = threshold



-1

2

2X1

X2

X3

Y

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

Neurons in a McCulloch-Pitts network are connected by directed, weighted paths



-1

2

2X1

X2

X3

Y

If the weight on a path is positive the path is excitatory, otherwise it is inhibitory

x1 and x2 encourage the neuron to firex3 prevents the neuron from firing



-1

2

2X1

X2

X3

Y

The threshold is set such that any non-zero inhibitory input will prevent the neuron from firing(This is only a rule for McCulloch-Pitts Networks!!)



-1

2

2X1

X2

X3

Y

It takes one time step for a signal to pass over one connection.


Worked Examples on Handout 1

1.5

0.5

21

0

1

?

Inputs

Threshold(θ) = 4

Does this neuron fire?Does it output a 0 or a 1?

1)Multiply the inputs to the neuron by the weights on their paths

2)Add the inputs

3)Apply the threshold function

2

0

1.5

3.5

3.5 < 4So neuron outputs 0

Threshold Function:If input sum < Threshold return 0Else return 1


Answers

• Using McCulloch-Pitts model we can model some logic functions

• In the exercise, you have been working on logic functions

•AND

•OR

•NOT AND


Answers

X

Y

Z

Threshold(θ) = 21

1

X Y Z

1 1 1

1 0 0

0 1 0

0 0 0

AND Function



Answers

X

Y

Z

Threshold(θ) = 22

2

X Y Z

1 1 1

1 0 1

0 1 1

0 0 0

OR Function



Answers (This one is not a McCulloch-Pitts Network)

X

Y

Z

Threshold(θ) = -1-1

X Y Z

1 1 0

1 0 1

0 1 1

0 0 1

NOT AND (NAND) Function

-1



One additional example

X

Y

Z

Threshold(θ) = 22

X Y Z

1 1 0

1 0 1

0 1 0

0 0 0

AND NOT Function

-1


Multi-Layer Neural Networks



Modelling Logic Functions

X1 XOR X2 = (X1 AND NOT X2) OR (X2 AND NOT X1)

XOR Function

2

2

2

2

-1

-1

Y1

Y2

Z

X1

X2

X1 X2 Z

1 1 0

1 0 1

0 1 1

0 0 0

XOR




22

-1

Y2

Z

X1

X2 X1 X2 Y2

1 1 0

1 0 0

0 1 1

0 0 0

ANDNOT




22

-1

Y1

Z

X1

X2 ANDNOT

X1 X2 Y1

1 1 0

1 0 1

0 1 0

0 0 0




2

2

Y1

Y2

Z

XOR

Y1 Y2 Z

1 1 1

1 0 1

0 1 1

0 0 0

OR

X1 X2 Z

1 1 0

1 0 1

0 1 1

0 0 0

X1 X2 Y1 Y2 Z

1 1 0 0 0

1 0 1 0 1

0 1 0 1 1

0 0 0 0 0





Key Idea!

Perceptrons cannot learn (cannot even represent) the XOR function

We will see why next lecture Multi-Layer Networks can,

as we have just shown


Worked Examples

1.5

0.5

21

0

1

?

Inputs

Threshold (θ) = 4

Does this neuron fire?Does it output a 0 or a 1?

1)Multiply the inputs to the neuron by the weights on their paths

2)Add the inputs

3)Apply the threshold function

2

0

1.5

3.5

3.5 < 4So neuron outputs 0


Example of Learning with a multi-layer neural network


http://www.youtube.com/watch?v=0Str0Rdkxxohttp://matthewrobbins.net/Projects/NeuralNetwork.html

Provided courtesy of:

Matthew RobbinsGames ProgrammerMelbourne Australia

Example of Learning with a multi-layer neural network


“Fully connected”...

...

All neurons are connected to all the neurons in the next level

Left wheel speed

Right wheel speed


Lecture Summary

Biology History (remember the names and what

they did) Perceptrons Multi-Layer Networks

introduction to artificial intelligence (g51iai)

Documents

aig51iai introduction

hebbg51iai introduction

inhibitoryg51iai introduction

braing51iai introduction

learng51iai introduction

neuronsg51iai introduction

neurong51iai introduction

synapseg51iai introduction