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Swiss Federal Institute of Technology Lausanne, EPFL Laboratory of 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

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slide1

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

slide2

Chapter 10: Hebbian Models

  • -Hebb rules
  • STDP

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 10

slide3

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)

slide4

pre j

u

i

spikes of i

Hebbian Learning in experiments (schematic)

pre j

u

no spike of i

EPSP

i

post

post

slide5

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

slide7

Hebbian Learning

item memorized

slide8

Hebbian Learning

Recall:

Partial info

item recalled

slide9

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)

slide10

activity (rate)

Hebbian Learning: rate model

pre j

i

k

post

- local rule

- simultaneously active (correlations)

slide11

+

0

0

0

-

-

-

+

0

-

+

0

Hebbian Learning: rate model

pre j

i

k

post

on

on

off

off

pre

post

on

off

on

off

+

-

-

+

slide12

Rate-based Hebbian Learning

pre j

i

k

post

- local rule

- simultaneously active (correlations)

Taylor expansion

slide13

Rate-based Hebbian Learning

pre j

i

post

a = a(wij)

a(wij)

wij

slide14

Oja’s rule

Rate-based Hebbian Learning

pre j

i

k

post

slide16

0

Pre

before post

Spike-based Hebbian Learning

pre j

i

k

post

- local rule

- simultaneously active (correlations)

slide17

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

slide18

Spike-time dependent learning window

pre j

i

post

0

0

0

Pre

before post

Temporal contrast filter

slide19

Spike-time dependent learning window

pre j

i

post

Zhang et al, 1998

review:

Bi and Poo, 2001

Pre

before post

slide22

Translation invariance

W(tif-tjk )

Learning window

spike-based Hebbian Learning

pre j

BPAP

post

i

slide23

Detailed models

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 10

slide24

Detailed models of Hebbian learning

pre j

post

i

i at resting

potential

slide25

NMDA

channel

i at resting

potential

Detailed models of Hebbian learning

pre j

post

i

slide26

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

slide27

a

pre

b

post

w

Mechanistic models of Hebbian learning

pre j

BPAP

post

i

slide28

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

slide29

a

pre

b

post

w

Mechanistic models of Hebbian learning

pre j

BPAP

post

i

1 pre, 1 post

slide30

0

Pre

before post

Mechanistic models of Hebbian learning

pre j

Dynamics of NMDA

receptor (Senn et al., 2001)

BPAP

post

i

which kind of model
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

slide32

Chapter 11: Learning Equations

  • -rate based Hebbian learning
  • STDP

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 11

slide33

Rate-based Hebbian Learning

pre j

i

post

a = a(wij)

a(wij)

wij

slide34

Analysis of rate-based Hebbian Learning

x1

x2

xk

xk

t

Linear model

Analysis - separation of time scales, expected evolution

Correlations

in the input

slide35

supress index i

eigenvectors

Analysis of rate-based Hebbian Learning

x1

x2

xk

xk

t

Linear model

Correlations

in the input

slide36

moves towards data cloud

w

Analysis of rate-based Hebbian Learning

x1

x2

xk

xk

t

x1

slide37

becomes aligned

with principal axis

w

Analysis of rate-based Hebbian Learning

x1

x2

xk

xk

t

x1

slide39

Translation invariance

W(tif-tjk )

Learning window

spike-based Hebbian Learning

pre j

BPAP

post

i

slide40

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

slide41

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

slide42

Analysis of spike-based Hebbian Learning

(iii) extra spike-spike correlations

pre j

spike-spike correlations

slide43

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

slide44

Chapter 12: Plasticity and Coding

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 12

slide45

Learning to be fast: prediction

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 12

slide46

Derivative filter and prediction

pre j

Mehta et al. 2000,2002

Song et al. 2000

+

-

slide47

+

-

Derivative filter and prediction

pre j

Mehta et al. 2000,2002

Song et al. 2000

Postsynaptic firing shifts, becomes earlier

slide48

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

slide49

Learning spike patterns

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 12

slide50

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

slide51

pre j

i

post

Spike-based Hebbian Learning: sequence learning

EPSP

0

Pre

before post

Strengthen the connection

with the desired timing

slide52

Subtraction of expectations:

electric fish

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 12

slide53

Spike-based Hebbian Learning

suppresses

temporal structure

experiment

model

C.C. Bell et al.,

Roberts and Bell

Novelty detector

(subtracts expectation)

slide54

Learning a temporal code:

barn owl auditory system

BOOK: Spiking Neuron Models,

W. Gerstner and W. Kistler

Cambridge University Press, 2002

Chapter 12

slide55

Delay tuning in barn owl auditory system

Accuracy 1 degree

Temporal precision <5us

slide56

Jeffress model

Accuracy 1 degree

Temporal precision <5us

slide58

Tuning of delay lines

Delay tuning in barn owl auditory system

Sound source

Jeffress, 1948

Carr and Konishi, 1990

Gerstner et al., 1996

slide61

Delay tuning in barn owl auditory system

Problem: 5kHz signal (period 0.2 ms)

but distribution of delays 2-3 ms

slide64

Conclusions (chapter 12)

-STDP is spiking version of Hebb’s rule

-shifts postsynaptic firing earlier in time

-allows to learn temporal codes