Effect of feedback strength in coupled spiking neural networks - - PowerPoint PPT Presentation

Effect of feedback strength in coupled spiking neural networks

Javier Iglesias1,2

in collaboration with

Jordi Garc´ ıa-Ojalvo1 and Alessandro E.P . Villa2

1 Departament de F´ ısica i Enginyeria Nuclear, Universitat Polit` ecnica de Catalunya, Terrassa, Spain 2 Grenoble Institut des Neurosciences-GIN, NeuroHeuristic Research Group, Universit´ e Joseph Fourier, Grenoble, France

<javier.iglesias@upc.edu>

introduction: laser experiment

1 C.M. Gonz´ alez, M.C. Torrent and J. Garc´ ıa-Ojalvo (2007), Controlling the leader- laggard dynamics in delay-synchronized lasers, Chaos 17:033122

introduction: laser experiment

2

experimental numerical

C.M. Gonz´ alez, M.C. Torrent and J. Garc´ ıa-Ojalvo (2007), Controlling the leader- laggard dynamics in delay-synchronized lasers, Chaos 17:033122

introduction: synaptogenesis and synaptic pruning

3 NB 0.5 1 2 5 10 adult aged (74-90) years 10 6 8 4 12 2 neurons / mm x10

3 4

NB 0.5 1 5 10 15 20 40 60 80 100 years 15 10 20 5 synapses / mm x10

3 8

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

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: network ontogeny

4

stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning sensors actuators stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning

model: neuromimetic model leaky integrate and fire

5

V(t) S(t) B(t) w(t) ~190 excitations ~115 inhibitions

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

• 76

[mV] θi =

• 40

[mV] τmem = 8 [ms] trefract = 2 [ms] λi = 5 [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: spike timing-dependent synaptic plasticity (STDP)

6

• 40

40

• 60

60

• 25

25

• 40

40

• 50

50

• 100

100 synaptic change synaptic change synaptic change synaptic change synaptic change

a b c d e

time [ms] time [ms] time [ms] time [ms] time [ms] modified from Roberts and Bell, Spike timing dependent synaptic plasticity in biological systems, Biol. Cybern., 87:392–403, 2002

model: STDP and synaptic pruning

7

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 synaptic pruning

7

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 post pre S (t)

i

• M (t)

i

S (t)

j

M (t)

j

time time

model: STDP and synaptic pruning

7

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 post pre S (t)

i

• M (t)

i

S (t)

j

M (t)

j

time time post pre S (t)

i

• M (t)

i

S (t)

j

M (t)

j

time time L (t)

ji

model: STDP and synaptic pruning

7

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 post pre S (t)

i

• M (t)

i

S (t)

j

M (t)

j

time time post pre S (t)

i

• M (t)

i

S (t)

j

M (t)

j

time time L (t)

ji

Lji(t) Aji(t) time [s] 50 100 150 4 2 1

wji(t + 1) = Sj(t) · Aji(t) · P[qj,qi]

model: experimental layout

8

injection Iout I in Sin stimulus

N1 N2

model: experimental layout

8

injection Iout I in Sin stimulus

N1 N2

feedback F

• ut

Fin

model: experimental layout

8

injection Iout I in Sin stimulus

N1 N2

feedback F

• ut

Fin

• size of I: 500, 1000, 2000, 4000.

model: experimental layout

8

injection Iout I in Sin stimulus

N1 N2

feedback F

• ut

Fin

• size of I: 500, 1000, 2000, 4000.
• relative size of F: 0, 0.25, 0.5, . . . , 2.75, 3 ×I.

model: experimental layout

8

injection Iout I in Sin stimulus

N1 N2

feedback F

• ut

Fin

• size of I: 500, 1000, 2000, 4000.
• relative size of F: 0, 0.25, 0.5, . . . , 2.75, 3 ×I.
• connectivity: fixed 100’000 projections, 100 projections/neuron.

model: complex stimulus

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t = 1 stimulation

• nset

t = 2 t = 3 t = 4 t = 5 t = 6 t=duration (50, 100

• r 200 ms)

[...]

A B

[...]

every 2 seconds 10 groups of 40 units activated in sequence (5% stimulated units) during 100 time steps (AA, BB, AB, BA, AB|BA)

animated sequences are available for stimuli A and B.

model: effective spike train

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A B C experiment control effective spike train time – =

injection feedback Iout I in F

• ut

Fin Sin stimulus

N1 N2

injection Iout I in Sin stimulus

N1 N2

results: fixed 100’000 projections

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10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 cells with modified activity ρ [%] F / I 10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 F / I

N1 N2

N1 Ψt

cells with modified activity ρ [%]

N2 Ψt

× I = 500; ∗ I = 1000; I = 2000; I = 4000.

results: 100 projections per neuron

12

10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 F / I 10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 F / I

N1 N2

cells with modified activity ρ [%]

N1 Ψu

cells with modified activity ρ [%]

N2 Ψu

+ I = 250; × I = 500; ∗ I = 1000; I = 2000; I = 4000.

results: network effect

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0.5 1 1.5 2 2.5 3 0.5 1 1.5 2 2.5 3 F / I 0.5 1 1.5 2 2.5 3 0.5 1 1.5 2 2.5 3 F / I

fixed 100000 proj. 100 proj / neuron

ρ / ρ

N2 Ψt N1 Ψt

ρ / ρ

N2 Ψ u N1 Ψ u

+ I = 250; × I = 500; ∗ I = 1000; I = 2000; I = 4000.

results: spike insertion/deletion per cell

14

F = I = 1000

250 500 750 1000

spikes

0.2 0.4 0.6 0.8 1.0

cells [%]

0.2 0.4 0.6 0.8 1.0

cells [%]

N1 N2

results: timing of the spike insertion/deletion

15

F = I = 1000 N1 N2

time [s]

2 4 6 8 10

spikes [103]

125 250 375 500 2 4 6 8 10

spikes [103]

conclusion

16

• changes to network activity are induced by injection/feedback

conclusion

16

• changes to network activity are induced by injection/feedback
• changes are more important in N2 than in N1

conclusion

16

• changes to network activity are induced by injection/feedback
• changes are more important in N2 than in N1
• both insertion and deletion of spikes are observed

conclusion

16

• changes to network activity are induced by injection/feedback
• changes are more important in N2 than in N1
• both insertion and deletion of spikes are observed
• timing and amplitude of changes are comparable

between networks

conclusion

16

• changes to network activity are induced by injection/feedback
• changes are more important in N2 than in N1
• both insertion and deletion of spikes are observed
• timing and amplitude of changes are comparable

between networks

• the precise quality of the changes to be assessed

(preferred firing sequences?)

conclusion

16

• changes to network activity are induced by injection/feedback
• changes are more important in N2 than in N1
• both insertion and deletion of spikes are observed
• timing and amplitude of changes are comparable

between networks

• the precise quality of the changes to be assessed

(preferred firing sequences?)

• changes to the network topology?