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A Physicist’s Brain

A Physicist’s Brain. J. C. Sprott Department of Physics University of Wisconsin - Madison Presented at the Chaos and Complex Systems Seminar In Madison, Wisconsin On October 18, 2005. Collaborators. David Albers , Max Planck Institute (Leipzig, Germany)

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A Physicist’s Brain

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  1. A Physicist’s Brain J. C. Sprott Department of Physics University of Wisconsin - Madison Presented at the Chaos and Complex Systems Seminar In Madison, Wisconsin On October 18, 2005

  2. Collaborators • David Albers, Max Planck Institute (Leipzig, Germany) • Matt Sieth, Univ Wisc - Undergrad

  3. A Physicist’s Neuron N inputs tanh x x

  4. Architecture N neurons

  5. Artificial Neural Network (P-Brain) • Nonlinear, discrete-time, complex, dynamical system • “Universal” approximator (?) • aij chosen from a random Gaussian distribution with mean zero and standard deviation s • Two parameters: N and s • Arbitrary (large) N infinity • Initial conditions random in the range -1 to +1.

  6. Probability of Chaos

  7. A Physicist’s EEG

  8. Strange Attractor

  9. Artist’s Brain

  10. Airhead

  11. Dumbbell

  12. Featherbrain

  13. Egghead

  14. Scatterbrain

  15. Attractor Dimension DKY = 0.46 N N

  16. Route to Chaos at Large N (=64)

  17. Animated Route to Chaos

  18. Summary of High-N Dynamics • Chaos is the rule • Maximum attractor dimension is of order N/2 • Quasiperiodic route is usual • Attractor is sensitive to parameter perturbations, but dynamics are not

  19. P-Brain Artist • Train a neural network to produce art • Choose N= 6 • Find “good” regions of the 36-D parameter space • Randomly explore a neighborhood of that region

  20. Automatic Preselection • Must be chaotic (positive Lyapunov exponent) • Not too “thin” (fractal dimension > 1) • Not too small or too large • Not too off-centered

  21. Training on an Image

  22. Problem – Rugged Landscape Relative Error -5% 0 +5%

  23. Hurricane Rita

  24. Robin Chapman

  25. Information Content • Robin: 244 x 340 x 3 x 8 = 2 Mbits Compresses (gif) to 283 kbits Compresses (jpeg) to 118 kbits Compresses (png) to 1.8 Mbits • P-Brain: 36 x 5 = 180 bits •  Cannot expect a good replica

  26. Future Directions • More biological realism • More neurons • More realistic architecture • Training on real EEG data or task performance

  27. http://sprott.physics.wisc.edu/ lectures/brain.ppt (this talk) sprott@physics.wisc.edu (contact me) References

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