Data representation techniques for adaptation Alexandra I. Cristea USI intensive course “Adaptive Systems” April-May 2003

Overview: Data representation 1.Data or knowledge? 2.Subsymbolic vs. symbolic techniques 3.Symbolic representation 4.Example 5.Subsymbolic reprensentation 6.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 Health and Survival Contains Required for and Requiring more Essential Amino Acids Animals Used for Such as Made by Plants GrainsLegumes Required for growth 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 PesticidesHerbicidesGenetics & Breeding Irrigation Fertilizer Which significantly supplements naturally Such as Predicted by Can be increased by NH 3 Haber Process Atmospheric N 2 Protein Includes Eaten by Used by humans as

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 NN Example

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

Applications vs Why NNs?

Applications 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 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 NeuronInput Output Functions: Inside ： Synapse Outside ：ｆ =threshold

An ANN Input Output Layer ：１ Layer ：２ Layer ：３ Black Box

Let’s look in the Black Box!

ＮＥＵＲＯＮ ＬＩＮＫ Ｗ： weight neuron １ neuron ２ Ｖ１ value Ｖ２＝ｗ＊ｖ１ value

ANN Pulse train – average firing frequency  0 Model of synapse (connecting element) –Real number w  0 : excitatory –Real number w  0 : inhibitory N(i) – set of neurons that have a connection to neuron i –j  N(i) –wij – weight of connection of j to i

ｎｅｕｒｏｎ ｃｏｍｐｕｔａｔｉｏｎ Ｖ１ Ｗ１ Ｖ２ Ｗ２ 。。。 Ｖｎ Ｗｎ O Ｓ＝ ΣVi ＊Ｗ i - ｂ 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 z  0

Other I-O functions f 3. Linear neuron f(z)=z output x i =z i –  = … 4. Stochastic neuron: xi  {0,1}; output 0 or 1 input z i =  j w ij v i –  i i probability that neuron fires f(z i ) probability that it doesn’t fire 1- f(z i )

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.