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Part III: Models of synaptic plasticity

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  1. Swiss Federal Institute of Technology Lausanne, EPFL Laboratoryof Computational Neuroscience, LCN, CH 1015 Lausanne Part III: Models of synaptic plasticity BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapters 10-12

  2. Chapter 10: Hebbian Models • -Hebb rules • STDP BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 10

  3. Hebbian Learning pre j i k post When an axon of celljrepeatedly or persistently takes part in firing cell i, then j’s efficiency as one of the cells firing i is increased Hebb, 1949 - local rule - simultaneously active (correlations)

  4. pre j u i spikes of i Hebbian Learning in experiments (schematic) pre j u no spike of i EPSP i post post

  5. pre j Both neurons simultaneously active i post pre j no spike of i EPSP i Increased amplitude post Hebbian Learning in experiments (schematic) pre j u no spike of i EPSP i post

  6. Hebbian Learning

  7. Hebbian Learning item memorized

  8. Hebbian Learning Recall: Partial info item recalled

  9. Hebbian Learning pre j i k post When an axon of celljrepeatedly or persistently takes part in firing cell i, then j’s efficiency as one of the cells firing i is increased Hebb, 1949 - local rule - simultaneously active (correlations)

  10. activity (rate) Hebbian Learning: rate model pre j i k post - local rule - simultaneously active (correlations)

  11. + 0 0 0 - - - + 0 - + 0 Hebbian Learning: rate model pre j i k post on on off off pre post on off on off + - - +

  12. Rate-based Hebbian Learning pre j i k post - local rule - simultaneously active (correlations) Taylor expansion

  13. Rate-based Hebbian Learning pre j i post a = a(wij) a(wij) wij

  14. Oja’s rule Rate-based Hebbian Learning pre j i k post

  15. Spike based model

  16. 0 Pre before post Spike-based Hebbian Learning pre j i k post - local rule - simultaneously active (correlations)

  17. Spike-based Hebbian Learning pre j EPSP i k post 0 Pre before post causal rule ‘neuron j takes part in firing neuron’ Hebb, 1949

  18. Spike-time dependent learning window pre j i post 0 0 0 Pre before post Temporal contrast filter

  19. Spike-time dependent learning window pre j i post Zhang et al, 1998 review: Bi and Poo, 2001 Pre before post

  20. Spike-time dependent learning: phenomenol. model pre j i post 0 Pre before post

  21. spike-based Hebbian Learning pre j post i

  22. Translation invariance W(tif-tjk ) Learning window spike-based Hebbian Learning pre j BPAP post i

  23. Detailed models BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 10

  24. Detailed models of Hebbian learning pre j post i i at resting potential

  25. NMDA channel i at resting potential Detailed models of Hebbian learning pre j post i

  26. i at high potential Detailed models of Hebbian learning pre j BPAP post i NMDA channel : - glutamate binding after presynaptic spike - unblocked after postsynaptic spike elementary correlation detector

  27. a pre b post w Mechanistic models of Hebbian learning pre j BPAP post i

  28. 0 Pre before post sophisticated 2-factor Mechanistic models of Hebbian learning pre j BPAP post i pre 4-factor model Gerstner et al. 1998 Buonomano 2001 post Abarbanel et al. 2002

  29. a pre b post w Mechanistic models of Hebbian learning pre j BPAP post i 1 pre, 1 post

  30. 0 Pre before post Mechanistic models of Hebbian learning pre j Dynamics of NMDA receptor (Senn et al., 2001) BPAP post i

  31. Which kind of model? Descriptive Models Gerstner et al. 1996 Song et al. 2000 Gütig et al. 2003 Mechanistic Models Senn et al. 2000 Abarbanel et al. 2002 Shouval et al. 2000 Optimal Models Chechik, 2003 Hopfield/Brody, 2004 Dayan/London, 2004

  32. Chapter 11: Learning Equations • -rate based Hebbian learning • STDP BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 11

  33. Rate-based Hebbian Learning pre j i post a = a(wij) a(wij) wij

  34. Analysis of rate-based Hebbian Learning x1 x2 xk xk t Linear model Analysis - separation of time scales, expected evolution Correlations in the input

  35. supress index i eigenvectors Analysis of rate-based Hebbian Learning x1 x2 xk xk t Linear model Correlations in the input

  36. moves towards data cloud w Analysis of rate-based Hebbian Learning x1 x2 xk xk t x1

  37. becomes aligned with principal axis w Analysis of rate-based Hebbian Learning x1 x2 xk xk t x1

  38. spike-based Hebbian Learning pre j post i

  39. Translation invariance W(tif-tjk ) Learning window spike-based Hebbian Learning pre j BPAP post i

  40. Analysis - separation of time scales, expected evolution Average over doubly stochastic process Correlations pre/post Analysis of spike-based Hebbian Learning vjk vj1 Point process vk Linear model

  41. Stable if Rate stabilization (ii) input covariance (plus extra terms) Average over ensemble of rates Covariance of input Analysis of spike-based Hebbian Learning Rewrite equ. (i) fixed point equation for postsyn. rate

  42. Analysis of spike-based Hebbian Learning (iii) extra spike-spike correlations pre j spike-spike correlations

  43. Spike-based Hebbian Learning - picks up spatio-temporal correlations on the time scale of the learning window W(s) - non-trivial spike-spike correlations - rate stabilization yields competition of synapses Synapses grow at the expense of others Neuron stays in sensitive regime

  44. Chapter 12: Plasticity and Coding BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 12

  45. Learning to be fast: prediction BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 12

  46. Derivative filter and prediction pre j Mehta et al. 2000,2002 Song et al. 2000 + -

  47. + - Derivative filter and prediction pre j Mehta et al. 2000,2002 Song et al. 2000 Postsynaptic firing shifts, becomes earlier

  48. Derivative filter and prediction pre j Mehta et al. 2000,2002 Song et al. 2000 + - derivative of postsyn. rate Roberts et al. 1999 Rao/Sejnowski, 2001 Seung

  49. Learning spike patterns BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 12

  50. Spike-based Hebbian Learning pre j EPSP i k post 0 Pre before post causal rule ‘neuron j takes part in firing neuron’ Hebb, 1949