1 / 69

Information Geometry and Neural Netowrks

Information Geometry and Neural Netowrks. Shun-ichi Amari RIKEN Brain Science Institute Orthogonal decomposition of rates and (higher-order) correlations Synchronous firing and higher correlations Algebraic singularities caused by multiple stimuli

franz
Download Presentation

Information Geometry and Neural Netowrks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Information Geometryand Neural Netowrks Shun-ichi Amari RIKEN Brain Science Institute Orthogonal decomposition of rates and (higher-order) correlations Synchronous firing and higher correlations Algebraic singularities caused by multiple stimuli Dynamics of learning in multiplayer perceptrons

  2. Information Geometry Systems Theory Information Theory Statistics Neural Networks Combinatorics Physics Information Sciences Math. AI Riemannian Manifold Dual Affine Connections Manifold of Probability Distributions

  3. Information Geometry ? Riemannian metric Dual affine connections

  4. Manifold of Probability Distributions

  5. Two Structures Riemannian metric and affine connection Fisher information

  6. Riemannian Structure

  7. AffineConnection covariant derivative straight line

  8. Independent Distributions

  9. Neural Firing ----firing rate ----covariance higher-order correlations orthogonal decomposition

  10. Riemannian metric dual affine connections Pythagoras theorem Dual geodesics Information Geometry of Higher-Order Correlations ----orthogonal decomposition

  11. Correlations of Neural Firing firing rates correlations orthogonal coordinates

  12. ００１１０００１０１１０１０１００１００１１０１０００１０１１０１００１０１０firing rates:correlation—covariance?

  13. Independent Distributions

  14. Pythagoras Theorem p correlations D[p:r] = D[p:q]+D[q:r] q r p,q: same marginals r,q: same correlations independent estimation correlation testing invariant under firing rates

  15. 01100101……. 110001011001……. 101000111100……. 1001 No pairwise correlations, Triplewise correlation

  16. Pythagoras Decomposition of KL Divergence only pairwise independent

  17. Higher-Order Correlations

  18. Synfiring andHigher-Order Correlations Amari, Nakahara, Wu, Sakai

  19. Population and Synfire Neurons

  20. Population and Synfire s

  21. Synfiring

  22. Bifurcation : independent---single delta peak pairwise correlated higher-order correlation！ r

  23. Shun-ichi Amari RIKEN Brain Science Institute amari@brain.riken.go.jp Collaborators: Si Wu Hiro Nakahara Field Theory of Population Coding

  24. Population Coding and Neural Field

  25. f (z-x) x Population Encoding r(z) z

  26. b Noise

  27. Probability Model

  28. Fisher information Cramer-Rao

  29. Fourier Analysis

  30. Fisher Information

  31. Dynamics of Neural Fields Shaping Detecting Decoding

  32. How the Brain Solves Singularity in Population Coding S. Amari and H. Nakahara RIKEN Brain Science Institute

  33. Neural Activity

  34. Parameter Space

  35. synfiring resolves singularity

  36. synfiring mechanism common multiplicative noise

  37. S.Amari and H.Nagaoka,Methods of Information GeometryAMS &Oxford Univ Press, 2000

  38. Mathematical Neurons

  39. ｙ Multilayer Perceptrons

  40. Multilayer Perceptron neuromanifold space of functions

More Related