Folie%201

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Spike-timing-dependent plasticity(STDP) and its
relation to differential Hebbian learning
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Overview over different methods
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Differential Hebb Learning Rule
Simpler Notation x Input u Traced Input
Xi
w
V
ui
Early Bell
S
X0
u0
Late Food
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Defining the Trace
In general there are many ways to do this, but
usually one chooses a trace that looks
biologically realistic and allows for some
analytical calculations, too.
EPSP-like functions
a-function
Shows an oscillation.
Dampened Sine wave
Double exp.
This one is most easy to handle analytically and,
thus, often used.
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Differential Hebbian Learning
Output
Produces asymmetric weight change curve (if the
filters h produce unimodal humps)
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Spike-timing-dependent plasticity(STDP) Some
vague shape similarity
Synaptic change
TtPost - tPre
ms
Weight-change curve (BiPoo, 2001)
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Hebbian learning
When an axon of cell A excites cell B and
repeatedly or persistently takes part in firing
it, some growth processes or metabolic change
takes place in one or both cells so that As
efficiency ... is increased. Donald Hebb
(1949)
A
B
A
t
B
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Conventional LTP
Synaptic change
Symmetrical Weight-change curve
The temporal order of input and output does not
play any role
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The biophysical equivalent of Hebbs postulate
Plastic Synapse
NMDA/AMPA
Pre-Post Correlation, but why is this needed?
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Plasticity is mainly mediated by so
called N-methyl-D-Aspartate (NMDA)
channels. These channels respond to Glutamate as
their transmitter and they are voltage depended
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Biophysical Model Structure
x
NMDA synapse
v
Hence NMDA-synapses (channels) do require a
(hebbian) correlation between pre and
post-synaptic activity!
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Local Events at the Synapse
x1
Current sources under the synapse
?Local
u1
v
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On Eligibility Traces

w
S
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Model structure

• Dendritic compartment
• Plastic synapse with NMDA channels
• Source of Ca2 influx and coincidence
  detector

Plastic Synapse
NMDA/AMPA
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Plasticity Rule (Differential Hebb)
Instantenous weight change
Presynaptic influence Glutamate effect on NMDA
channels
Postsynaptic influence
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Pre-synaptic influence
Normalized NMDA conductance
NMDA channels are instrumental for LTP and LTD
induction (Malenka and Nicoll, 1999 Dudek and
Bear ,1992)
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Depolarizing potentials in the dendritic tree
Dendritic spikes
(Larkum et al., 2001 Golding et al, 2002 Häusser
and Mel, 2003)
Back-propagating spikes
(Stuart et al., 1997)
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Postsyn. Influence
Filtered Membrane potential
source of depolarization
Low-pass filter
Filter h is adjusted to account for steep
rise and long tail of the observed Calcium
transients induced by back-propagating spikes and
dendritic spikes (Markram et al., 1995 Wessel et
al, 1999)
The time course of the Ca2 concentration is
important in defining the direction and
degree of synaptic modifications. (Yang et al.,
1999 Bi, 2002)
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Some Signals F
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Weight Change Curves Source of Depolarization
Back-Propagating Spikes
Back-propagating spike
Weight change curve
NMDAr activation
Back-propagating spike
T
TtPost tPre
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Weight Change Curves Source of Depolarization
Dendritic Spike
Dendritic spike
Weight change curve
NMDAr activation
Dendritic spike
T
TtPost tPre
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Local Learning Rules
The same learning rule
Hebbian learning for distal synapses
Differential Hebbian learning for proximal
synapses
Saudargiene et al Neural Comp. 2004
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Biologically inspired Artificial Neural Network
algorithm which implements local learning rules
Circuit Diagram Representation
vn
u
hnn
vn
X
un
hn
xn
v1
.
h11
X
.
v1
.
w1
wn
u1
x1
h1
v
w0
?
u0
h0
Site-specific learning using the same learning
rule
x0
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An example Application developing velocity
sensitivity
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LTP
STDP
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After learning the cell becomes sensitive to
stimulus velocity
1/vel.
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Figure 1. Dendritic Excitability Creates a
Switchable, Spatial Gradient of Plasticity in L5
Pyramids (Left) Short bursts of somatic spikes
elicit bAPs that fail to backpropagate fully to
distal dendrites. The result, as shown in
Sjöström and Häusser (2006), is LTP of
synchronously active proximal synapses, but LTD
or no plasticity at distal synapses. (Middle)
Cooperative activation of additional synapses
depolarizes the dendrite and boosts bAP
propagation into distal dendrites. This
cooperativity serves as a switch to enable distal
LTP (Sjöström and Häusser, 2006). (Right)
Plasticity also varies with firing mode of these
neurons when bAPs are coupled with strong distal
input, bAP-activated calcium spikes (BACs) are
evoked in the apical tuft, which enables robust
LTP (Kampa et al., 2006).
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Here we need a slide to explain why LTD at a
distal dendrite in NOT in conflict with the
models shown before. The argument would be to
claim that there was never enough activation AT
ALL to get the Ca above the LTP threshold.
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Here comes a slide on the phosphorilation of AMPA
and the different effects of gradient and
concentration of Ca
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Some more physiological complications !
Modeling Ca2 pathways
Back-propagating spike
We are modeling Ca2 rise and fall with just one
diff. hebb rule. More detailed models look at LTP
and LTD as two different processes.
Ca2 concentration
Calmodulin
Ca2/CaM Kinase II
Calcineurin
Phosporylation Synapse gets strongerLTP
Dephosporylation Synapse gets weaker-LTD
AMPA receptors
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Temporally local Learning
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Self-Influencing Plasticity
Hebbian Learning
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Equivalent Circuit Diagram
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BP before DS Acausal DS before BP Causal
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Local DS-Spike only
Cluster 1
Cluster 2
weak hebbian learning
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Why might this make sense ??
Single phase learning will lead to weight growth
regardless
Tamosiunaite et al. Comp. Nsci. in press