Part III Models of synaptic plasticity BOOK Spiking

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

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

Hebbian Learning pre j k i post 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 - local rule - simultaneously active (correlations)

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

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

Hebbian Learning

Hebbian Learning item memorized

Hebbian Learning Recall: Partial info item recalled

Hebbian Learning pre j k i post 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 - local rule - simultaneously active (correlations)

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

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

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

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

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

Spike based model

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

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

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

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

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

spike-based Hebbian Learning pre j post i

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

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

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

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

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

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

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

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

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

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

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

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

Analysis of rate-based Hebbian Learning x 1 x 2 xk xk t Linear model Analysis - separation of time scales, expected evolution Correlations in the input

Analysis of rate-based Hebbian Learning x 1 x 2 xk xk t Linear model supress index i Correlations in the input eigenvectors

Analysis of rate-based Hebbian Learning x 1 x 2 xk xk t moves towards data cloud x 1 w

Analysis of rate-based Hebbian Learning x 1 xk x 2 xk t x 1 w becomes aligned with principal axis

spike-based Hebbian Learning pre j post i

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

Analysis of spike-based Hebbian Learning v j 1 v jk Point process vk Linear model Analysis - separation of time scales, expected evolution Average over doubly stochastic process Correlations pre/post

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

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

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

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

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

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

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

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

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

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

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

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

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

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