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 1012
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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 1012
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 10
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)
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
item memorized
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)
Hebbian Learning: rate model
pre j
i
k
post
 local rule
 simultaneously active (correlations)
pre j
i
k
post
 local rule
 simultaneously active (correlations)
Taylor expansion
Pre
before post
Spikebased Hebbian Learning
pre j
i
k
post
 local rule
 simultaneously active (correlations)
pre j
EPSP
i
k
post
0
Pre
before post
causal rule
‘neuron j takes part in firing neuron’
Hebb, 1949
Spiketime dependent learning window
pre j
i
post
Zhang et al, 1998
review:
Bi and Poo, 2001
Pre
before post
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 10
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
Pre
before post
sophisticated 2factor
Mechanistic models of Hebbian learning
pre j
BPAP
post
i
pre
4factor model
Gerstner et al. 1998
Buonomano 2001
post
Abarbanel et al. 2002
Pre
before post
Mechanistic models of Hebbian learning
pre j
Dynamics of NMDA
receptor (Senn et al., 2001)
BPAP
post
i
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
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 11
Analysis of ratebased Hebbian Learning
x1
x2
xk
xk
t
Linear model
Analysis  separation of time scales, expected evolution
Correlations
in the input
eigenvectors
Analysis of ratebased Hebbian Learning
x1
x2
xk
xk
t
Linear model
Correlations
in the input
Analysis  separation of time scales, expected evolution
Average over doubly
stochastic process
Correlations
pre/post
Analysis of spikebased Hebbian Learning
vjk
vj1
Point process
vk
Linear model
Rate stabilization
(ii) input covariance
(plus extra terms)
Average over
ensemble of rates
Covariance of input
Analysis of spikebased Hebbian Learning
Rewrite equ.
(i) fixed point equation for postsyn. rate
Analysis of spikebased Hebbian Learning
(iii) extra spikespike correlations
pre j
spikespike correlations
 picks up spatiotemporal correlations on the time scale
of the learning window W(s)
 nontrivial spikespike 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
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
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 12
pre j
EPSP
i
k
post
0
Pre
before post
causal rule
‘neuron j takes part in firing neuron’
Hebb, 1949
i
post
Spikebased Hebbian Learning: sequence learning
EPSP
0
Pre
before post
Strengthen the connection
with the desired timing
electric fish
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 12
suppresses
temporal structure
experiment
model
C.C. Bell et al.,
Roberts and Bell
Novelty detector
(subtracts expectation)
barn owl auditory system
BOOK: Spiking Neuron Models,
W. Gerstner and W. Kistler
Cambridge University Press, 2002
Chapter 12
Delay tuning in barn owl auditory system
Sound source
Jeffress, 1948
Carr and Konishi, 1990
Gerstner et al., 1996
Delay tuning in barn owl auditory system
Problem: 5kHz signal (period 0.2 ms)
but distribution of delays 23 ms
STDP is spiking version of Hebb’s rule
shifts postsynaptic firing earlier in time
allows to learn temporal codes