Spike-timing dependent plasticity in balanced random networks

Spike-timing dependent plasticity in
balanced random networks
M. Diesmann 1,2
1 Computational Neurophysics, Institute of Biology III, Albert-Ludwigs-University
2 Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University
Computational Approaches to Cortical Functions
Banbury Center, 2-5 April 2006
freiburg

Thanks
◮ Abigail Morrison
◮ Ad Aertsen
◮ Guo-qiang Bi
(for providing original data)
◮ NEST Initiative
A. Morrison, A. Aertsen, & M. Diesmann (2005)
Spike-timing dependent plasticity in balanced random networks
Neural Computation, under review
freiburg

Consistency of cortical network model
model
data
ν ext
J
E
J
X
ν ext
J
J
I
−gJ
−gJ
(Brunel, 2000)
(Bi & Poo, 1998)
Is the network model compatible with the data?
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Outline
Choice of STDP model
Plastic Networks
Development of structure
Robustness
Synchronous stimulation
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Outline
Choice of STDP model
Plastic Networks
Development of structure
Robustness
Synchronous stimulation
freiburg

Outline
Choice of STDP model
Plastic Networks
Development of structure
Robustness
Synchronous stimulation
freiburg

Outline
Choice of STDP model
Plastic Networks
Development of structure
Robustness
Synchronous stimulation
freiburg

Outline
Choice of STDP model
Plastic Networks
Development of structure
Robustness
Synchronous stimulation
freiburg

Choice of STDP model
◮ Additive, multiplicative, . . . ?
◮ All to all, nearest neighbor, . . . ?
Can the existent experimental data help to reduce the plethora
of possible models?
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Back to the original data
(Bi & Poo, 1998)
What, if anything, does this tell us about the weight
dependency of the STDP update?
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Weight dependency of STDP
A
PSC change [pA]
300
100
30
10
3
0
−3
−10
−30
−100
−300
30 100 300 1000 3000
Initial PSC [pA]
B
PSC change [%]
100
◮ pale gray additive
◮ dark gray multiplicative
50
◮ power law with µ = 0.4
◮ depression multiplicative
0
−50
−100 −50 0 50 100
Spike timing [ms]
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Weight dependency of STDP
B
PSC change [%]
100
50
0
◮ darker for higher initial w
◮ variability may result from
different initial w
◮ depression multiplicative
→ no dependence on w
−50
000 −100 −50 0 50 100
Spike timing [ms]
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Weight dependency of STDP
change in PSC amplitude
1
0.8
0.6
0.4
0.2
0
0 20 40 60 80 100
initial PSC amplitude [pA]
additive (Song, Miller, & Abbott)
multiplicative (Rubin, Lee, & Sompolinsky)
in between (Gütig, Aharonov et al.)
∆w − (w, t) = −λαw µ K (t, θ post)
∆w + (w, t) = λ (1 − w) µ K (t, θ pre)
∑
−(T −tx)/τ
K (T, θ x) =
e
power law
t x∈θ x:t x

Spike pairing scheme
A
48
nearest neighbor
A
48
B
45.6
B
45.6
all to all
weight [pA]
47
46
45
44
weight [pA]
47
45.55 45.55
46
45.5 45.5
45
45.45 45.45
44
45.4 45.4
0 100 0 100 200 300 200 300 0 1000 200 100 300 200 300
time [s] time [s]
time [s] time [s]
◮ self-consistent rate necessary for stability
◮ nearest neighbor scheme amplifies rate disparity
◮ all to all spike scheme counteracts rate disparity
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Weight distribution in a fully plastic network
A
area diff. [%]
1
0.8
0.6
0.4
0.2
B
frac. synapses
0.1
0.05
C
C(τ)
0
0 500 1000 1500 2000
time [s]
4
2
0
−2
6 x 10−4
−75 −50 −25 0 25 50 75
D
0
4
2
0
−2
6 x 10−4
35 45 55
weight [pA]
Given a desired w ∗ of a static BRN, α p can be calculated.
◮ α = 1.057α p to compensates for correlation
◮ weight distribution settles to Gaussian within 200 s
−75 −50 −25 0 25 50 75
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a
0.2
fr
Activity in a fully plastic network
0
0 500 1000 1500 2000
time [s]
0
35 45 55
weight [pA]
C
6 x 10−4 τ [ms]
4
D
6 x 10−4 τ [ms]
4
C(τ)
2
2
0
0
−2
−2
−75 −50 −25 0 25 50 75
−75 −50 −25 0 25 50 75
◮ AI dynamics
◮ rate slightly higher (8.8 Hz) than in static network (7.7 Hz)
◮ similar Fano factor and coefficient of variation
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Individual weight trajectories
56
54
52
50
weight [pA]
48
46
44
42
40
38
0 100 200 300 400 500
time [s]
◮ weight distribution settles fairly quickly ...
◮ ... but individual weight trajectories remain dynamic
◮ neither spontaneous development of structure nor
withering
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Survival time of strong synapses
10 6 survival time [s]
10 5
10 4
synapses
10 3
10 2
10 1
10 0
0 200 400 600 800 1000
◮ exponential decay with τ ≈ 55s of top 10%
◮ time shift invariant statistics, steps of 200s shown
◮ no development of structure
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Sensitivity to scaling of depression
C(τ)
5
4
3
2
1
0
−1
x 10 −4
3
0
−3
−50 0 50
◮ at higher α (stronger
depression), here 2%, a
new stable state emerges
at a lower rate
◮ but, if α chosen 2% too
low, the network explodes
6 x 10−4 τ [ms]
−2
−75 −50 −25 0 25 50 75
◮ new regime displays
strongly patterned activity
interspersed with silence
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Sensitivity to scaling of depression
frac. synapses
0.12
0.1
0.08
0.06
0.04
0.02
rate [Hz]
200
150
100
50
0
5 15 25
time [s]
◮ at higher α (stronger
depression), here 2%, a
new stable state emerges
at a lower rate
◮ but, if α chosen 2% too
low, the network explodes
0
0 50 100 150 200 250 300
weight [pA]
◮ new regime displays
strongly patterned activity
interspersed with silence
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Sensitivity to scaling of depression
A
rate [Hz]
B
rate [Hz]
C
3500
3000
2500
2000
1500
1000
500
2000
1500
1000
500
0
29 29.2 29.4 29.6 29.8 30
time [s]
0
100
D
E
◮ at higher α (stronger
depression), here 2%, a
new stable state emerges
at a lower rate
◮ but, if α chosen 2% too
low, the network explodes
◮ new regime displays
strongly patterned activity
interspersed with silence
neuron id
75
50
25
29.1 29.1025 29.105
time [s]
29.7 29.7025 29.705
time [s]
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Synchronous stimulation
A
neuron id
B
neuron id
C
neuron id
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
3 3.2 3.4 3.6 3.8 4
time [s]
◮ current injected into 500
neurons irregularly at 3 Hz
◮ injection times for each
neuron drawn from
Gaussian
(σ = 0.5 ms)
◮ moderate effect on
high-connectivity group
(K synch ≥ 69)
◮ weak effect on rest of
network
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Synchronous stimulation
A
neuron id
B
neuron id
C
neuron id
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
3 3.2 3.4 3.6 3.8 4
time [s]
◮ current injected into 500
neurons irregularly at 3 Hz
◮ injection times for each
neuron drawn from
Gaussian
(σ = 0.5 ms)
◮ moderate effect on
high-connectivity group
(K synch ≥ 69)
◮ weak effect on rest of
network
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Synchronous stimulation
A
neuron id
B
neuron id
C
neuron id
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
3 3.2 3.4 3.6 3.8 4
time [s]
◮ current injected into 500
neurons irregularly at 3 Hz
◮ injection times for each
neuron drawn from
Gaussian
(σ = 0.5 ms)
◮ moderate effect on
high-connectivity group
(K synch ≥ 69)
◮ weak effect on rest of
network
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Development of activity during stimulation
A
20
B
20
rate [Hz]
15
10
15
10
5
5
C
neuron id
D
0
0 100 200
time [s]
100
40
0
0 100 200 300 400
time [s]
◮80intra-group connections amplify stimulus
60
◮20removing intra-group connections permits stable network
100
80
◮60rate of stimulated group plummets
neuron id
40
20
→ explosion
activity for N synch = 500
222.95 223 223.05 223.1 223.15
time [s]
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Development of weights
A
frac. synapses
0.12
0.1
0.08
0.06
0.04
0.02
0
20 40 60 80
weight [pA]
B
weight [pA]
65
60
55
50
45
20 40 60 80
convergence
◮ incoming synapses to stimulated group decrease
→ rate drop
◮ outgoing synapses increase as K synch increases
◮ effect does not transfer to high connectivity group
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Development of correlation
B
C(τ)
x 10 −3
3
2
1
0
A
C(τ)
x 10 −3
3
2
1
0
−40 −20 0 20 40
τ [ms]
x 10 −3
C
3
2
1
0
◮ expect increase in correlation
due to weight increase (A→B)
◮ decrease in correlation
observed (A→C)
◮ reduction of input to stimulated
group lowers responsiveness
to stimulus
◮ development of structure
counteracted
−40 −20 0 20 40
τ [ms]
−40 −20 0 20 40
τ [ms]
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Summary
◮ power law description fits STDP data
◮ predicts small changes for small weights
◮ compatible with balanced random networks
◮ equilibrium weight distribution is unimodal
◮ weights fluctuate on time scale of minutes
◮ no spontaneous development of structure
◮ stimulation creates structure, but
(oversimplified?) network counteracts
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