Data representation techniques for adaptation

Alexandra I. CristeaUSI intensive course “Adaptive Systems” April-May 2003

Overview: Data representation

1. Data or knowledge?2. Subsymbolic vs. symbolic techniques3. Symbolic representation4. Example5. Subsymbolic reprensentation6. Example

Data or knowledge?

• Data for AS becomes often knowledge– data < information < knowledge

• We divide into:– Symbolic– Sub-symbolic knowledge representation

Data representation techniques for adaptation

• Symbolic AI and knowledge representation, such as:– Concept Maps – Probabilistic AI (belief networks)

• see UM course

• Sub-symbolic: Machine learning, such as:– Neural Networks

Symbolic Knowledge Representation

Symbolic AI and knowledge representation

• Static knowledge– Concept mapping– terminological knowledge– concept subsumption (inclusion) inference

• Dynamic Knowledge– ontological engineering, e.g., temporal representation

and reasoning– planning

Concept Maps

Example

Proposition: Without the industrial chemical reduction

of atmospheric nitrogen, starvation would be rampant

in third world countries.

FOOD

Human Healthand Survival

Contains

Required for

and

Requiring more

Essential Amino Acids

Animals

Used for

Such as

Madeby

Plants

Grains Legumes

Required forgrowth of

Symbiotic Bacteria

“Fixed” Nitrogen

Possess

That produce

Agricultural Practices

Population Growth

Politics

Economics

Distribution

Climate

Starvation and Famine

Malthus 1819

Eastern Europe

India

Africa

Deprivation leads to

Can be limited by

and

Such as in

Pesticides HerbicidesGenetics & Breeding

Irrigation

Fertilizer Which significantly supplements naturally

Such as

Predicted by

Can be increased by

NH3Haber

ProcessAtmospheric N2

Protein

Includes

Eatenby

Use

d by

hu m

a ns

a s

Constructing a CM

• Brainstorming Phase: • Organizing Phase: create groups and sub-

groups of related items. • Layout Phase: • Linking Phase: lines with arrows

Reviewing the CM• Accuracy and Thoroughness.

– Are the concepts and relationships correct? Are important concepts missing? Are any misconceptions apparent?

• Organization. – Was the concept map laid out in a way that

higher order relationships are apparent and easy to follow? Does it have a representative title?

• Appearance. – spelling, etc.?

• Creativity.

Sub-symbolic knowledge representation

Subsymbolic systems

• human-like information processing:• learning from examples, • context sensitivity, • generalization, • robustness of behaviour, and • intuitive reasoning

Some notes on NNExample

Why NN?

• To learn how our brain works (!!)• High computation rate technology• Intelligence• User-friendly-ness

Applications

vsvs

Why NNs?Why NNs?

ApplicationsWhy NNs?Why NNs?

Man-machine hardware comparison

Man-machine information processing

What are humans good at and machines not?

• Humans: – pattern recognition– Reasoning with incomplete knowledge

• Computers:– Precise computing– Number crunching

The Biological Neuron

(very small) Biological NN

Purkinje cellPurkinje cell

Spike (width 0.2 – 5ms)

Firing

• Resulting signal– Excitatory:

• encourages firing of the next neuron– Inhibitory:

• Discourages firing of the next neuron

What does a neuron do?

• Sums its inputs• Decides if to fire or not with respect to

a threshold• But: limited capacity:

– Neuron cannot fire all the time– Refractory period: 10ms – min time to

fire again– So: max. firing frequency: 100 spikes/

sec

Hebbian learning rule (1949)

• If neuron A repeatedly and persistently contributes to the firing of neuron B, than the connection between A and B will get stronger.

• If neuron A does not contribute to the firing of neuron B for a long period of time, than the connection between A and B becomes weaker.

Different size synapses

Summarizing

• A neuron doesn’t fire if cumulated activity below threshold

• If the activity is above threshold, neuron fires (produces a spike)

• Firing frequency increases with accumulated activity until max. firing frequency reached

The ANN

The Artificial Neuron

InputInput

OutputOutput

Functions:Functions: InsideInside ：： SynapseSynapseOutsideOutside ：：ｆ ｆ

==thresholdthreshold

An ANNAn ANNInput

Output

Layer ：１

Layer ：２

Layer ：３

Black BoxBlack Box

• Let’s look in the Black Box!

ＮＥＵＲＯＮ ＬＩＮＫ

Ｗ： weight

neuron １ neuron ２

Ｖ１value

Ｖ２＝ｗ＊ｖ１value

ANN

• Pulse train – average firing frequency 0• Model of synapse (connecting element)

– Real number w0 : excitatory– Real number w0 : inhibitory

• N(i) – set of neurons that have a connection to neuron i– jN(i)– wij – weight of connection of j to i

ｎｅｕｒｏｎ ｃｏｍｐｕｔａｔｉｏｎ ｎｅｕｒｏｎ ｃｏｍｐｕｔａｔｉｏｎ

Ｖ１

Ｗ１

Ｖ２

Ｗ２ 。。。 Ｖｎ

Ｗｎ

O

Ｓ＝Ｓ＝ ΣViΣVi ＊＊ＷＷ i - i - ｂｂ i=1..n

internal activation fct

Ｏ = ｆ (S)external activation fct

Typical input output relation f

1. Standard sigmoid fct.: f(z)= 1/(1+e-z)2. Discrete neuron: fires at max. speed, or does not fire

xi={0,1}; f(z) = 1, z>0; 0 z0

Other I-O functions f

3. Linear neuron f(z)=z

output xi=zi – = …

4. Stochastic neuron: xi {0,1}; output 0 or 1

input zi = j wij vi – ii

probability that neuron fires f(zi)

probability that it doesn’t fire 1- f(zi)

Feedforward NNs

Recurrent NNs

Summarizing ANNs

• Feedforward network, layered– No connection from the output to the input, at

each layer but also at neuron level• Recurrent network

– Anything is allowed – cycles, etc.