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

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

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

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

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

6. Hebbian Learning

7. item memorized

8. Hebbian Learning item recalled Recall: Partial info

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

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

11. Hebbian Learning: rate model pre j post i k pre post on off on off onoff onoff ++ + 000 -- + 0 0 - + - --

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

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

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

15. Spike based model

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

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

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

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

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

21. spike-based Hebbian Learning pre j post i

22. spike-based Hebbian Learning pre j post i BPAP Translation invariance W(t i f -t j k ) Learning window

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

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

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

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

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

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

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

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

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

34. Analysis of rate-based Hebbian Learning t xkxk x1x1 xkxk x2x2 Linear model Analysis - separation of time scales, expected evolution Correlations in the input

35. Analysis of rate-based Hebbian Learning t xkxk x1x1 xkxk x2x2 Linear model Correlations in the input supress index i eigenvectors

36. Analysis of rate-based Hebbian Learning t xkxk x1x1 xkxk x2x2 x1x1 moves towards data cloud w

37. Analysis of rate-based Hebbian Learning t xkxk x1x1 xkxk x2x2 x1x1 becomes aligned with principal axis w

38. spike-based Hebbian Learning pre j post i

39. spike-based Hebbian Learning pre j post i BPAP Translation invariance W(t i f -t j k ) Learning window

40. Analysis of spike-based Hebbian Learning vkvk Linear model vj1vj1 vjkvjk Analysis - separation of time scales, expected evolution Correlations pre/post Point process Average over doubly stochastic process

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

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 derivative of postsyn. rate pre j Mehta et al. 2000,2002 Song et al. 2000 + - 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 post i k causal rule ‘neuron j takes part in firing neuron’ Hebb, 1949 0 Pre before post EPSP

51. Spike-based Hebbian Learning: sequence learning pre j post i 0 Pre before post EPSP Strengthen the connection with the desired timing

52. Subtraction of expectations: electric fish BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 12

53. Spike-based Hebbian Learning suppresses temporal structure experiment model C.C. Bell et al., Roberts and Bell Novelty detector (subtracts expectation)

54. Learning a temporal code: barn owl auditory system BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 12

55. Delay tuning in barn owl auditory system Accuracy 1 degree Temporal precision <5us

56. Jeffress model Accuracy 1 degree Temporal precision <5us

57. Jeffress model

58. Delay tuning in barn owl auditory system Sound source Tuning of delay lines Jeffress, 1948 Carr and Konishi, 1990 Gerstner et al., 1996

59. Delay tuning in barn owl auditory system

60. ca. 150

61. Delay tuning in barn owl auditory system Problem: 5kHz signal (period 0.2 ms) but distribution of delays 2-3 ms

62. Spike-timing dependent plasticity: phenomenol. model pre j post i Pre before post 0 1ms

63. Delay tuning in barn owl auditory system

64. Conclusions (chapter 12) -STDP is spiking version of Hebb’s rule -shifts postsynaptic firing earlier in time -allows to learn temporal codes