Chaos

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Chaos

• Linking Chaos in the Modelto Chaos in the Brain

Kaolin Fire http//erif.org
2
A quick look at Neurons

• Real neurons have inputs (dendrites) and outputs
  (via the axon)
• When a neurons inputs are strong enough, it is
  likely to fire (fits a poisson distribution)

http//www.lebenswissen.de/pix/bt/sciences_street
/08_hirnforschung/neuron.jpg
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And artificial neurons

• a.k.a. a perceptron
• Have artificial inputs and outputs typically
  either real-valued or binary
• fire in a wholly artificial manner, usually
  with a step or sigmoid function

1/(1e-z)
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The typical artificial Neural Network

• Is feed-forward
• Displays no recursion
• Has no chaos
• Can still do some amazing things
• Training and learning is very artificial
• Hebbian learning vs. standard forgetful
  (palimpsest) learning

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The typical biological neural network

• Is hideously complex
• Displays elements of chaotic behavior
• Olfactory bulb, LGN, auditory areas

http//www.interchange.ubc.ca/neurosci/faculty/ima
ges/thm/ast_red.jpg
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The magic ofThree

• Elements of regularity
• Elements of oneness
• Elements of unpredictability
• Period 3 implies Chaos

But what does that mean, in the brain?
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Chaos in the brain

• The brain is constantly active, at least to some
  baseline
• Many iterative/recursive processes
• As noted, firing tends to fit a poisson
  distribution
• Intimations of low-dimensional chaotic behavior
  (power-law statistical voodoo)
• Strange attractors (memories/pattern recognition)
• May even be a factor in the primeval evolution of
  language, along with synesthesia

http//www.colantonio.net/brain/brain12.jpg
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Chaos in an artificial neural network?

• RNN recurring neural network
• Chaos proven in a simple sigmoid-activated
  perceptron pair through the doubling map
• Chaotic palimpsest learning functions much better
  than nonchaotic (can learn 5x as much!)
• But

But what does that mean, to the brain?
http//citeseer.nj.nec.com/cache/papers/cs/1359/ht
tpzSzzSzwww.usc.eduzSzhsczSzlab_apkzSzarchiveszSz
chaos.pdf/wang91perioddoublings.pdf
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Modeling chaos in the brain
Two approaches take das blinkenlights (the
two-perceptron pair) and

• Threshold the sigmoid to only fire above a
  certain time, using an arbitrary clock
• Fast-forward and treat the value as the time
  between spikes, normalized against some
  reasonable (biologically valid) range

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So where does that leave us?

• With plenty to read
• http//erif.org/chaos/fire03chaosbrain.pdf
• http//tentacle.net/wiki/ChaosAndTheBrain/
• And plenty to do
• Current research in hearing aids and other
  prostheses
• Better models make better experiments
• Any Questions?