Emergence of Oriented Circuits driven bySynaptic Pruning associated with

Spike-Timing-Dependent Plasticity (STDP)

Javier Iglesias1,2

under the supervision of

Alessandro E.P. Villa2 and Marco Tomassini1

1 Information Systems Department, University of Lausanne, Switzerland

2 Laboratory of Neurobiophysics, University Joseph-Fourier, France

<javier.iglesias@unil.ch>

introduction: synaptogenesis and synaptic pruning 1

NB 0.5 1 2 5 10 adult aged(74-90)years

10

6

8

4

12

2

ne

uro

ns /

mm

x1

03

4

NB 0.5 1 5 10 15 20 40 60 80 100

years

15

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5

syn

ap

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s /

mm

x1

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8

modified from Huttenlocher, Synaptic density in human frontal cortex – developmentalchanges and effects of aging, Brain Research, 163:195–205, 1979

introduction: synaptic plasticity 2

-40 400

-60 600 -25 250 -40 400

-50 500-100 100

syn

ap

tic c

ha

ng

esyn

ap

tic c

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ng

e

syn

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tic c

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e

syn

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tic c

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e

syn

ap

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ng

e

a b

c d e

time [ms]

time [ms] time [ms] time [ms]

time [ms]

modified from Roberts and Bell, Spike timing dependent synaptic plasticityin biological systems, Biol. Cybern., 87:392–403, 2002

introduction: existing work 3

• The memory performance of a network is optimally maximized if,under limited metabolic energy resources restricting their numberand strength, synapses are first overgrown and then pruned.

Chechik et al., Synaptic pruning in development:A computational account, Neural Computation, 10(7):1759–77, 1998

• Neuronal regulation might maintain the memory performance ofnetworks undergoing synaptic degradation.

Horn et al., Memory maintenance via neuronal regulationNeural Computation, 10(1):1–18, 1998

• STDP has been shown to maintain the postsynaptic input field.

Abbott et al., Synaptic plasticity: taming the beastNature Neuroscience, 3:1178–83, 2000

model: network 4

500

-50

x -50

0.0

0.2

0.4

0.6probability

e

500

-50

x

50

0

-50y

0.0

0.2

0.4

0.6probability

+500-50

x

+50

0

-50

y

f

+500-50x

+50

0

-50

y

+50

0

-50+500-50

y

x

+50

0

-50+500-50

y

x

g

0

250

500

0 200 400

cell

coun

t

connection count

0

250

500

0 200 400

cell

coun

t

connection count

a b c d

h

50

0 y

i e i i

600

e e

e i

600

Iglesias et al., Dynamics of Pruning in Simulated Large-ScaleSpiking Neural Networks, Biosystems, 79(1-3):11-20, 2005

introduction: leaky integrate and fire neuromimetic model 5

V(t)S(t)

B(t)

w(t)

~190 excitations

~115 inhibitions

Type I = excitatory 80%Type II = inhibitory 20%

Vrest = -76 [mV]θi = -40 [mV]τmem = 8 [ms]trefract = 1 [ms]λi = 10 [spikes/s]n = 50

Vi(t+1) = Vrest[q]+(1−Si(t))·((Vi(t)−Vrest[q])·kmem[q])+∑

j

wji(t)+Bi(t)

Si(t) = H(Vi(t)− θqi)

wji(t + 1) = Sj(t) ·Aji(t) · P[qj,qi]

Bi(t + 1) = Preject(λqi) · n · P[q1,qi]

model: STDP and pruning 6

Lji(t + 1) = Lji(t) · kact[qj,qi]

+(Si(t) ·Mj(t))−(Sj(t) ·Mi(t))

post

pre

S (t)i

S (t)j time

time

model: STDP and pruning 6

Lji(t + 1) = Lji(t) · kact[qj,qi]

+(Si(t) ·Mj(t))−(Sj(t) ·Mi(t))

post

pre

S (t)i

S (t)j time

timepost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

time

model: STDP and pruning 6

Lji(t + 1) = Lji(t) · kact[qj,qi]

+(Si(t) ·Mj(t))−(Sj(t) ·Mi(t))

post

pre

S (t)i

S (t)j time

timepost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

timepost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

time

L (t)ji

model: STDP and pruning 6

Lji(t + 1) = Lji(t) · kact[qj,qi]

+(Si(t) ·Mj(t))−(Sj(t) ·Mi(t))

post

pre

S (t)i

S (t)j time

timepost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

timepost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

time

L (t)ji

Lji(

t)A

ji(t)

time [s]50 100 1500

4

2

1

0

wji(t + 1) = Sj(t) ·Aji(t) · P[qj,qi]

model: synaptic adaptation examples 7

timeL0

L1

L2

L3

L4

timeL0

L1

L2

L3

L4

timeL0

L1

L2

L3

L4

a b cA4

A3

A2

A1

results: simulation evolution 8

0

20

40

60

80

100

0 200 400 600 800 1,000time [s]

cum

ula

ted

dis

trib

ution [%

]

A (t)=0ji

A (t)=4ji

A (t)=2ji

A (t)=1ji

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

200

100

0

2001000

t=10s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

200

100

0

2001000

t=10s

k_in

k_out

200

100

0

2001000

t=20s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

200

100

0

2001000

t=10s

k_in

k_out

200

100

0

2001000

t=20s

k_in

k_out

200

100

0

2001000

t=50s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

200

100

0

2001000

t=10s

k_in

k_out

200

100

0

2001000

t=20s

k_in

k_out

200

100

0

2001000

t=50s

k_in

k_out

200

100

0

2001000

t=100s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

200

100

0

2001000

t=10s

k_in

k_out

200

100

0

2001000

t=20s

k_in

k_out

200

100

0

2001000

t=50s

k_in

k_out

200

100

0

2001000

t=100s

k_in

k_out

200

100

0

2001000

t=200s

k_in

k_out

results: simulation evolution (cont.) 9

200

100

0

2001000

t=0s

k_in

k_out

200

100

0

2001000

t=2s

k_in

k_out

200

100

0

2001000

t=5s

k_in

k_out

200

100

0

2001000

t=10s

k_in

k_out

200

100

0

2001000

t=20s

k_in

k_out

200

100

0

2001000

t=50s

k_in

k_out

200

100

0

2001000

t=100s

k_in

k_out

200

100

0

2001000

t=200s

k_in

k_out

200

100

0

2001000

t=500s

k_in

k_out

results: scaling factor 10

φ∗[exc] = f · φ[exc]

f = 3

√104

(10·N)2

P ∗[exc,exc] =

(1 + f−1

2

)· P[exc,exc]

network sizeis defined as(10×N)2

1

10

100

100010010

active s

ynapses [A

4] (%

)

time [s]

123456789

10

model: simple stimulus 11

t = 1

stimulation

onset

t = 2 t = 3 t = 4 t = 5 t = 6 t=duration

(50, 100

or 200 ms)

[...]

every 2 secondsN vertical bars moving to the rightduring 50, 100, or 200 time steps.

input units ratio: 3, 5, 7, or 10% excitatory units.randomly selected before stimulation or in the beginning

See an animated sequence.

model: graph considerations 12

Strongly Interconnected (SI) unitsat the end of the simulationset of cells (discarding input units)maintaining kout ≥ 3 and kin ≥ 3with strongest activation level (Aji(t) = 4)with units with the same properties.

model: graph considerations 12

Strongly Interconnected (SI) unitsat the end of the simulationset of cells (discarding input units)maintaining kout ≥ 3 and kin ≥ 3with strongest activation level (Aji(t) = 4)with units with the same properties.

Neighbourhoodall excitatory units (including input units)with at least one projection to or from SI-units.

model: graph considerations 12

Strongly Interconnected (SI) unitsat the end of the simulationset of cells (discarding input units)maintaining kout ≥ 3 and kin ≥ 3with strongest activation level (Aji(t) = 4)with units with the same properties.

Neighbourhoodall excitatory units (including input units)with at least one projection to or from SI-units.

index of connected units (ICU)#input units in neighbourhood

#SI−units

results: with and without scaling factor 13

0

5

10

15

10 7 5 3

ICU

ratio of input units [%]

90 x 90

100 x 100

110 x 110

0

5

10

15

10 7 5 3

ratio of input units [%]

a b

ICU

Iglesias et al., Stimulus-Driven Unsupervised Pruningin Large Neural Networks, LNCS (in press, October 2005)

results: emergence of circuits from t=0 to t=50s 14

stimulus amplitude = 0mV stimulus amplitude = 60mV

stimulus protocol = random

stimulus amplitude = 60mV

stimulus protocol = fixed

k_o

ut

k_o

ut

k_in k_in k_in

0 100 200 0 100 200 0 100 200

0

100

200

0

100

200

k_

out

k_o

ut

0

100

200

100

200

0

a

b c d

t =

0 s

eco

nd

st =

50

seco

nds

results: emergence of circuits from t=50 to t=200s 15

stimulus amplitude = 0mV stimulus amplitude = 60mV

stimulus protocol = random

stimulus amplitude = 60mV

stimulus protocol = fixed

k_o

ut

k_o

ut

k_in k_in k_in

0 100 200 0 100 200 0 100 200

0

100

200

0

100

200

k_

out

k_o

ut

0

100

200

100

200

0

b c d

e f g

t =

50 s

econ

ds

t =

20

0 s

eco

nds

results: emergence of circuits from t=200 to t=500s 16

stimulus amplitude = 0mV stimulus amplitude = 60mV

stimulus protocol = random

stimulus amplitude = 60mV

stimulus protocol = fixed

k_o

ut

k_o

ut

k_in k_in k_in

0 100 200 0 100 200 0 100 200

0

100

200

0

100

200

k_

out

k_o

ut

0

100

200

100

200

0

t =

200 s

eco

nd

st =

50

0 s

eco

nds

e f g

h i j

results: emergence of circuits from t=200 to t=500s (cont.) 17

stimulus amplitude = 0mV stimulus amplitude = 60mV

stimulus protocol = random

stimulus amplitude = 60mV

stimulus protocol = fixed

k_o

ut

k_o

ut

k_in k_in k_in

0 100 200 0 100 200 0 100 200

0

0

k_

out

k_o

ut

0

0

t =

200 s

eco

nd

st =

50

0 s

eco

nds

20

40

20

40

20

40

20

40e f g

h i j

results: circuit 18

Iglesias et al., Emergence of Oriented Cell AssembliesAssociated with Spike-Timing-Dependent Plasticity, LNCS 3696:127-132, 2005

layer 1 layer 2 layer 3 layer 4 layer 5

5326

5697

2800

5550

7199

7297

9661

992

4695

1539

1202

8402

1608

8889

931931

81208120

80222267

3027

2007

1152

2666

8467

1151

7928

5724 5724

490 490490

45478863

4761

2279

804

826782678267

1234

1048

1435

8300

7794

1049

2532

1842 4622

24272427

9983

1845

2848

492492

147214721472

7235

time = 500 s

results: circuit 18

Iglesias et al., Emergence of Oriented Cell AssembliesAssociated with Spike-Timing-Dependent Plasticity, LNCS 3696:127-132, 2005

layer 1 layer 2 layer 3 layer 4 layer 5

5326

5697

2800

5550

7199

7297

9661

992

4695

1539

1202

8402

1608

8889

931931

81208120

80222267

3027

2007

1152

2666

8467

1151

7928

5724 5724

490 490490

45478863

4761

2279

804

826782678267

1234

1048

1435

8300

7794

1049

2532

1842 4622

24272427

9983

1845

2848

492492

147214721472

7235

time = 500 s

layer 1 layer 2 layer 3 layer 4 layer 5

5326

5697

2800

5550

7199

7297

9661

992

4695

1539

1202

8402

1608

8889

931931

81208120

80222267

3027

2007

1152

2666

8467

1151

7928

5724 5724

490 490490

45478863

4761

2279

804

826782678267

1234

1048

1435

8300

7794

1049

2532

1842 4622

24272427

9983

2848

1845

492492

147214721472

7235

time = 0 s

model: complex stimulus 19

t = 1

stimulation

onset

t = 2 t = 3 t = 4 t = 5 t = 6 t=duration

(50, 100

or 200 ms)

[...]A

B [...]

every 2 seconds10 groups of 40 units activated in sequence (5% input units)during 200 time steps (AA, BB, AB, BA, AB|BA)

continuous and interrupted pruning

Animated sequences are available for both stimuli A and B.

results: firing rates vs. connection degrees 20

26 units with kin = kout = 0 in absence of stimulationand kin > 0 and kout > 0 with all other stimuli (AA, BB, ...)

0

50

100

150

200

250

0

10

20

30

40

50

0 20 40 60 80 100 120

a b

0 20 40 60 80 100 120

mean firing rate [spikes/s]mean firing rate [spikes/s]

k_

in

k_

ou

t

results: spatio-temporal pattern of activity 21

<5, 9, 4, 2; 13, 53, 109>

10008006005004002000time [seconds]

10008006005004002000time [seconds]

a b

dctime [ms]

0-100 500400100 200 300time [ms]

0-100 500400100 200 3000

40

0

40

continuous pruning pruning stopped at t=500s

#5

#9

#4

#2

#5

#9

#4

#2

for methods, see Villa et al., 1999; Tetko and Villa, 2001

conclusion 22

• network size effect

• emergence of oriented circuitsby synaptic pruning associated with STDP

• circuits are able to producespatiotemporal patterns of activity

• role of firing rate

discussion: firing rates vs. connection degrees (cont.) 23

post

pre

S (t)i

-M (t)i

S (t)j

M (t)j

a bpost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

time

time

time

L (t)ji L (t)ji

discussion: firing rates vs. connection degrees (cont.) 23

post

pre

S (t)i

-M (t)i

S (t)j

M (t)j

a bpost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

time

time

time

L (t)ji L (t)ji

post

pre

S (t)i

-M (t)i

S (t)j

M (t)j

c dpost

pre

S (t)i

-M (t)i

S (t)j

M (t)j

time

time

time

time

L (t)ji L (t)ji