Transcript 9-Lecture1(updated)

Artificial Intelligence
Neural Networks
(Chapter 9)
Outline of this Chapter
•
•
•
•
•
•
Biological Neurons
Neural networks History
Artificial Neural Network
Perceptrons
Multilayer Neural Network
Applications of neural networks
Definition
Neural Network
A broad class of models that mimic functioning inside the human brain
There are various classes of NN models.
They are different from each other depending on
 Problem types
 Structure of the model
 Model building algorithm
For this discussion we are going to focus on
Feed-forward Back-propagation Neural Network
(used for Prediction and Classification problems)
Biological Neurons
• The brain is made up of neurons (nerve cells) which
have
– dendrites (inputs)
– a cell body (soma)
– an axon (outputs)
– synapse (connections between cells)
• Synapses can be excitatory (potential-increasing activity) or
inhibitory (potential-decreasing), and may change over time
• The synapse releases a chemical transmitter – the sum of which
can cause a threshold to be reached – causing the neuron to fire
(electrical impulse is sent down the axon )
Biology of a neuron
A bit of biology . . .
Most important functional unit in human brain – a class of cells called –
NEURON
Dendrites
Cell Body
Axon
Synapse
Hippocampal Neurons
Source: heart.cbl.utoronto.ca/ ~berj/projects.html
• Dendrites – Receive information
Schematic
• Cell Body – Process information
• Axon – Carries processed information to other neurons
• Synapse – Junction between Axon end and Dendrites of other Neurons
An Artificial Neuron
Dendrites
X1
X2
Xp
w1
w2
..
.
wp
Cell Body
Axon
Direction of flow of Information
I
f
V = f(I)
I = w1X1 + w2X2
+ w3X3 +… + wpXp
• Receives Inputs X1 X2 … Xp from other neurons or environment
• Inputs fed-in through connections with ‘weights’
• Total Input = Weighted sum of inputs from all sources
• Transfer function (Activation function) converts the input to output
• Output goes to other neurons or environment
Biological Neurons (cont.)
• When the inputs reach some threshold an action potential
(electrical pulse) is sent along the axon to the outputs.
• The pulse spreads out along the axon reaching synapse &
releasing transmitters into the bodies of other cells.
• Learning occurs as a result of the synapse’ plasticicity: They
exhibit long-term changes in connection strength.
• There are about 1011 neurons and about 1014 synapses in the
human brain(!)
• A neuron may connect to as many as 100,000 other neurons
Brain structure
• We still do not know exactly how the brain works.
e.g, born with about 100 billion neurons in our brain. Many die as we
progress through life, & are not replaced, but we continue to learn.
But we do know certain things about it.
• Different areas of the brain have different functions
– Some areas seem to have the same function in all humans (e.g., Broca’s
region- speech & language); the overall layout is generally consistent
– Some areas vary in their function; also, the lower-level structure and function
vary greatly
senses
emotions, reasoning,
planning, movement,
& parts of speech.
hearing, memory,
meaning, and language
vision & ability to
recognize objects
Brain structure (cont.)
• We don’t know how different functions are “assigned” or
acquired
– Partly the result of the physical layout / connection to inputs (sensors)
and outputs (effectors)
– Partly the result of experience (learning)
• We really don’t understand how this neural structure/ collection
of simple cells leads to action, consciousness and thought
• Artificial neural networks are not nearly as complex as the actual
brain structure
Comparing brains with computers
Computer
Computational units
Storage units
Cycle time
Bandwidth
Neuron updates/sec
•
•
•
•
•
•
Human Brain
1 CPU, 105 gates
109 Bits RAM, 1011 bits disk
1011 neurons
1011neurons, 1014 synapses
10-8 Sec
109 bits/sec
105
10-3 sec
1014 bits/sec
1014
They are more neurons in human brain than they are bits in computers
Human brain is evolving very slowly---computer memories are growing rapidly.
There are a lot more neurons than we can reasonably model in modern digital computers,
and they all fire in parallel
NN running on a serial computer requires 100 of cycles to decided if a single N will fire--in real brain, all Ns do this in a single step.
e.g. brain recognizes a face in less than a sec--- billion of cycles
Neural networks are designed to be massively parallel
The brain is effectively a billion times faster at what it does
Neural networks History
•
McCulloch & Pitts (1943) are generally recognised as the designers of the
first neural network
•
Many of their ideas still used today (e.g. a neuron has a threshold level
and once that level is reached the neuron fires is still the fundamental way
in which artificial neural networks operate)
•
Hebb (1949) developed the first learning rule (on the premise that if two
neurons were active at the same time the strength between them should
be increased).
•
During the 50’s and 60’s many researchers such as Minsky & Papert,
worked on the perceptron (NNModel)
•
1969 saw the death of neural network research for about 15 years
•
Only in the mid 80’s (Parker and LeCun) NN research revived.
Artificial Neural Network
•
(Artificial) Neural networks are made up of nodes/units connected by
links which have
– inputs edges, each link has a numeric weight
– outputs edges (with weights)
– an activation level (a function of the inputs)
The computation is split into 2 components:
1. Linear component, called input function (ini)-- computes the weighted
sum of the unit’s input values.
2. Non-linear component, called activation function (g)– transforms the
weighted sum into the final value that serves as the unit’s activation value:
ai = g(ini) = g( aj wj,i )
•
Some nodes are inputs (perception), some are outputs (action)
Modeling a Neuron
in i   j Wj , iaj
Each unit does a local computation based on inputs from its neighbours &
compute a new activation level – sends along each of its output links
aj: Activation value of unit j
wj,I: Weight on the link from unit j to unit i
inI: Weighted sum of inputs to unit i
aI: Activation value of unit i
g: Activation function.
Activation Functions
• Different models are obtained by using different mathematical functions for g.
• 3 common choices are:
threshold function
logistic function
Step(x)
=
1 if x >= 0, else 0
Sign(x)
=
+1 if x >= 0, else –1
Sigmoid(x) =
1/(1+e-x)
( in which we try to minimize the error by adjusting the weights of the network,
e : represents error degree)
1  represents the firing of a pulse down the axon, & 0 represents no firing.
t (threshold) represents the min total weighted input needed to cause the neuron to
ANN (Artificial Neural Network) – Feed-forward Network
A collection of neurons form a ‘Layer’
X1
X2
X3
X4
Input Layer
Direction of information flow
- Each neuron gets ONLY
one input, directly from outside
Hidden Layer
- Connects Input and Output
layers
Output Layer
- Output of each neuron
directly goes to outside
y1
y2
ANN (Artificial Neural Network) – Feed-forward Network
Number of hidden layers can be
None
One
More
Implementing logical functions
• McCulloch and Pitts: every Boolean function AND, OR, & NOT can be
represented by units with suitable weights & thresholds.
• We can use these units to build a network to compute any Boolean function
(t = threshold or the value of the Bias weight that determines the threshold to
cause the neuron to fire)
Network Structure
They are 2 main categories of NN structure:
• Feed-forward/acyclic networks:
 allow signals to travel one way only; from input to output. There is no
feedback (loops).
 Tend to be straight forward networks that associate inputs with outputs. (i.e.
pattern recognition.)
 Usually arranged in layers– each unit receives input only from units in
preceding layer, no links between units in the same layer.
– single-layer perceptrons
– multi-layer perceptrons
• Recurrent/cyclic networks:
– Feeds its outputs back into its own inputs.
– recurrent neural nets have directed cycles with delays
– The links can form arbitrary topologies.
• The brain is recurrent network – activation is fed back to the units that caused
it.
Feed-forward example
No direct connection to the
outside world
Simple NN with 2 inputs, 2 hidden units & 1 output unit.
a5 = g(W3,5.a3 +W4,5.a4)
= g(W3,5. g(W1,3.a1 +W2,3.a2) +W4,5 g(W1,4.a1 +W2,4.a2))
By adjusting weights, we change the function that the Network
represents: learning occurs in NN this way!
Perceptron
• Is a network with all inputs connected
directly to the output.
• This is called a single layer NN (Neural
Network) or a Perceptron Network.
• It is a simple form of NN that is used for
classification of linearly separable
patterns. (i.e. If we have 2 results we can
separate them with a line with each group
result on a different side of the line)
Perceptron or a Single-layer NN
 A Feed-Forward NN with no
hidden units.
 Output units all operate
separately--no shared
weights.
 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.
 A single weight only affects
one output so we can limit
our study to a model as
shown on the right
 Notation can be simpler, i.e.
O  Step0 j WjIj
Multilayer NN
• Network with 1/more layers of hidden units
• Layers are usually fully connected;
• numbers of hidden units typically chosen by hand
Summary
• Most brains have lots of neurons; each neuron  linear threshold unit (?)
• Perceptrons (one-layer networks) insufficiently expressive
• Multi-layer networks are sufficiently expressive; can be trained by gradient
descent, i.e., error back-propagation
• Many applications: speech, driving, handwriting, fraud detection, etc.
• Engineering, cognitive modelling, and neural system modelling
• sub fields have largely diverged
End of Chapter 9