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Chaos

Chaos. Linking Chaos in the Model to Chaos in the Brain. Kaolin Fire – http://erif.org. A quick look at Neurons. Real neurons have inputs (dendrites) and outputs (via the axon) When a neuron’s inputs are strong enough, it is :likely: to “fire” (fits a poisson distribution).

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Chaos

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  1. 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 neuron’s inputs are strong enough, it is :likely: to “fire” (fits a poisson distribution) http://www.lebenswissen.de/pix/b+t/sciences_street/08_hirnforschung/neuron.jpg

  3. 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/(1+e^-z)

  4. 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

  5. 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/images/thm/ast_red.jpg

  6. The magic ofThree • Elements of regularity • Elements of oneness • Elements of unpredictability … Period 3 implies Chaos But what does that mean, in the brain?

  7. 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

  8. 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/http:zSzzSzwww.usc.eduzSzhsczSzlab_apkzSzarchiveszSzchaos.pdf/wang91perioddoublings.pdf

  9. Modeling chaos in the brain • 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 Two approaches; take das blinkenlights (the two-perceptron pair) and:

  10. 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?

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