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

Effect of feedback strength in coupled spiking neural networks Javier Iglesias 1 , 2 in collaboration with ıa-Ojalvo 1 and Alessandro E.P . Villa 2 Jordi Garc´ 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 12 4 neurons / mm x10 10 3 8 6 4 20 2 8 synapses / mm x10 15 NB 0.5 1 2 5 10 adult aged 3 (74-90) years 10 5 NB 0.5 1 5 10 15 20 40 60 80 100 years modified from Huttenlocher (1979), Synaptic density in human frontal cortex – developmental changes and effects of aging , Brain Research, 163:195–205

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

synaptic฀pruning synaptogenesis cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death cell฀differentiation stem฀division synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division model: network ontogeny 4

synaptic฀pruning synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division model: network ontogeny 4 actuators sensors

synaptic฀pruning synaptogenesis cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death cell฀differentiation stem฀division stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning model: network ontogeny 4 actuators actuators sensors sensors

synaptic฀pruning synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning cell฀death synaptogenesis cell฀differentiation stem฀division cell฀death cell฀death stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis synaptic฀pruning stem฀division cell฀differentiation synaptogenesis model: network ontogeny 4 actuators actuators actuators sensors sensors sensors

synaptic฀pruning stem฀division synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptic฀pruning cell฀differentiation cell฀differentiation synaptogenesis cell฀death synaptic฀pruning stem฀division cell฀differentiation synaptogenesis cell฀death synaptogenesis cell฀death stem฀division cell฀differentiation stem฀division cell฀differentiation synaptic฀pruning synaptogenesis cell฀death cell฀death synaptogenesis cell฀differentiation stem฀division synaptic฀pruning synaptic฀pruning stem฀division cell฀death synaptogenesis model: network ontogeny 4 actuators actuators actuators actuators sensors sensors sensors sensors

model: neuromimetic model leaky integrate and fire 5 Type I = 80% excitatory ~190 excitations Type II = 20% inhibitory B(t) = -76 [mV] V rest = -40 [mV] θ i S(t) w(t) V(t) = 8 [ms] τ mem = 2 [ms] t refract = 5 [spikes/s] λ i n = 50 ~115 inhibitions � V i ( t +1) = V rest[ q ] +(1 − S i ( t )) · (( V i ( t ) − V rest[ q ] ) · k mem[ q ] )+ w ji ( t )+ B i ( t ) j S i ( t ) = H ( V i ( t ) − θ q i ) w ji ( t + 1) = S j ( t ) · A ji ( t ) · P [ q j ,q i ] B i ( t + 1) = P reject ( λ q i ) · n · P [ q 1 ,q i ]

model: spike timing-dependent synaptic plasticity (STDP) 6 a b synaptic change synaptic change -40 0 40 -100 -50 0 50 100 ti m e [m s ] ti m e [m s ] c d e synaptic change synaptic change synaptic change -60 0 60 -25 0 25 -40 0 40 ti m e [m s ] ti m e [m s ] ti m e [m s ] 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 time S (t) i post L ji ( t + 1) = L ji ( t ) · k act[ q j ,q i ] +( S i ( t ) · M j ( t )) − ( S j ( t ) · M i ( t )) pre S (t) time j

model: STDP and synaptic pruning 7 time time S (t) S (t) i i post post -M (t) i L ji ( t + 1) = L ji ( t ) · k act[ q j ,q i ] +( S i ( t ) · M j ( t )) M (t) − ( S j ( t ) · M i ( t )) j pre pre S (t) S (t) time time j j

model: STDP and synaptic pruning 7 time time time S (t) S (t) S (t) i i i post post post -M (t) -M (t) i i L ji ( t + 1) = L ji ( t ) · k act[ q j ,q i ] +( S i ( t ) · M j ( t )) M (t) M (t) − ( S j ( t ) · M i ( t )) j j pre pre pre S (t) S (t) S (t) time time time j j j L (t) ji

model: STDP and synaptic pruning 7 time time time S (t) S (t) S (t) i i i post post post -M (t) -M (t) i i L ji ( t + 1) = L ji ( t ) · k act[ q j ,q i ] +( S i ( t ) · M j ( t )) M (t) M (t) − ( S j ( t ) · M i ( t )) j j pre pre pre S (t) S (t) S (t) time time time j j j L (t) ji L ji (t) 4 A ji (t) 2 1 0 0 50 100 150 time [s] w ji ( t + 1) = S j ( t ) · A ji ( t ) · P [ q j ,q i ]

model: experimental layout 8 stimulus S in I out I in injection N 1 N 2

model: experimental layout 8 stimulus S in I out I in injection N 1 N 2 feedback F in F out

model: experimental layout 8 stimulus S in I out I in injection N 1 N 2 feedback F in F out • size of I : 500, 1000, 2000, 4000.

model: experimental layout 8 stimulus S in I out I in injection N 1 N 2 feedback F in F out • size of I : 500, 1000, 2000, 4000. • relative size of F : 0, 0.25, 0.5, . . . , 2.75, 3 × I .

model: experimental layout 8 stimulus S in I out I in injection N 1 N 2 feedback F in F out • 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 9 t = 3 t = 4 t = 5 t = 6 t = 1 t = 2 t=duration stimulation (50, 100 onset or 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 10 stimulus S in I out I in injection experiment N 1 N 2 feedback – F in F out stimulus control S in I out I in injection N 1 N 2 = effective spike train time A B C

results: fixed 100’000 projections 11 N1 N2 60 60 cells with modified activity ρ [%] cells with modified activity ρ [%] 50 50 N1 N2 Ψt Ψt 40 40 30 30 20 20 10 10 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 F / I F / I × I = 500 ; ∗ I = 1000 ; � I = 2000 ; � I = 4000 .

results: 100 projections per neuron 12 N1 N2 60 60 cells with modified activity ρ [%] cells with modified activity ρ [%] 50 50 N1 N2 Ψu Ψu 40 40 30 30 20 20 10 10 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 F / I F / I + I = 250 ; × I = 500 ; ∗ I = 1000 ; � I = 2000 ; � I = 4000 .

results: network effect 13 fixed 100000 proj. 100 proj / neuron 3 3 2.5 2.5 2 2 N1 N1 u Ψt Ψ 1.5 1.5 ρ / ρ ρ / ρ N2 N2 Ψt u Ψ 1 1 0.5 0.5 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 F / I F / I + I = 250 ; × I = 500 ; ∗ I = 1000 ; � I = 2000 ; � I = 4000 .

results: spike insertion/deletion per cell 14 F = I = 1000 1.0 N1 0.8 0.6 cells [%] 0.4 0.2 0 1.0 N2 0.8 0.6 cells [%] 0.4 0.2 0 0 250 500 750 1000 spikes

results: timing of the spike insertion/deletion 15 F = I = 1000 10 N1 8 spikes [10 3 ] 6 4 2 0 10 N2 8 spikes [10 3 ] 6 4 2 0 0 125 250 375 500 time [s]

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