Emergence of Oriented Circuits driven ... - jiglesia.alawa.ch · introduction: synaptogenesis and...

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

NB 0.5 1 5 10 15 20 40 60 80 100

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

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

0.6probability

+500-50

+500-50x

-50+500-50

0 200 400

connection count

0 200 400

connection count

a b c d

i e i i

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)

~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])+∑

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))

S (t)i

S (t)j time

S (t)i

S (t)j time

timepost

S (t)i

-M (t)i

S (t)j

M (t)j

S (t)i

S (t)j time

timepost

S (t)i

-M (t)i

S (t)j

M (t)j

timepost

S (t)i

-M (t)i

S (t)j

M (t)j

L (t)ji

S (t)i

S (t)j time

timepost

S (t)i

-M (t)i

S (t)j

M (t)j

timepost

S (t)i

-M (t)i

S (t)j

M (t)j

L (t)ji

time [s]50 100 1500

wji(t + 1) = Sj(t) ·Aji(t) · P[qj,qi]

model: synaptic adaptation examples 7

timeL0

a b cA4

results: simulation evolution 8

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

ution [%

A (t)=0ji

A (t)=4ji

A (t)=2ji

A (t)=1ji

results: simulation evolution (cont.) 9

2001000

t=100s

2001000

t=100s

2001000

t=200s

2001000

t=100s

2001000

t=200s

2001000

t=500s

results: scaling factor 10

φ∗[exc] = f · φ[exc]

√104

(10·N)2

P ∗[exc,exc] =

(1 + f−1

)· P[exc,exc]

network sizeis defined as(10×N)2

100010010

active s

ynapses [A

time [s]

123456789

model: simple stimulus 11

stimulation

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.

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

10 7 5 3

ratio of input units [%]

90 x 90

100 x 100

110 x 110

10 7 5 3

ratio of input units [%]

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_in k_in k_in

0 100 200 0 100 200 0 100 200

k_in k_in k_in

0 100 200 0 100 200 0 100 200

k_in k_in k_in

0 100 200 0 100 200 0 100 200

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

k_in k_in k_in

0 100 200 0 100 200 0 100 200

40e f g

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

931931

81208120

80222267

5724 5724

490 490490

45478863

826782678267

1842 4622

24272427

492492

147214721472

time = 500 s

results: circuit 18

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

931931

81208120

80222267

5724 5724

490 490490

45478863

826782678267

1842 4622

24272427

492492

147214721472

time = 500 s

931931

81208120

80222267

5724 5724

490 490490

45478863

826782678267

1842 4622

24272427

492492

147214721472

time = 0 s

model: complex stimulus 19

stimulation

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 20 40 60 80 100 120

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

results: spatio-temporal pattern of activity 21

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

10008006005004002000time [seconds]

dctime [ms]

0-100 500400100 200 300time [ms]

0-100 500400100 200 3000

continuous pruning pruning stopped at t=500s

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

S (t)i

-M (t)i

S (t)j

M (t)j

a bpost

S (t)i

-M (t)i

S (t)j

M (t)j

L (t)ji L (t)ji

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

S (t)i

-M (t)i

S (t)j

M (t)j

a bpost

S (t)i

-M (t)i

S (t)j

M (t)j

L (t)ji L (t)ji

S (t)i

-M (t)i

S (t)j

M (t)j

c dpost

S (t)i

-M (t)i

S (t)j

M (t)j

L (t)ji L (t)ji

Emergence of Oriented Circuits driven ... - jiglesia.alawa.ch · introduction: synaptogenesis and...

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