Bottom-up and top-down approaches in Computational Neuroscience

Mitglied der Helmholtz-Gemeinschaft 

Bottom-up and top-down 

approaches in 

Computational Neuroscience 

September 13th 2011, GRS 

Markus Diesmann 

1 INM-6 Computational and Systems Neuroscience, Juelich 2 RIKEN BSI, Tokyo

Research tracks 

Computational Neuroscience (Neuroinformatics) 

hypothesis 

hypothesis 

simulation 

technology 

network 

modeling 

data 

analysis 

progress 

progress 

Neuroscience with computational methods? 

(think of Computational Physics) 

How does the brain compute? 

September 13th 2011, GRS Markus Diesmann Folie 2

Research tracks 

Computational Neuroscience (Neuroinformatics) 

hypothesis 

hypothesis 

simulation 

technology 

network 

modeling 

data 

analysis 

progress 

progress 

network modeling is the central activity 

drives analysis of experimental data 

drives the development of simulation technology 

directions of arrows are non-trivial 

projects of individuals should cover all tracks 


www.csn.fz-juelich.de 


Top-down and bottom-up 

the computer analogy: 

system computer brain 

top multiplication maze navigation system-level behavior 

⇓ 

⇓ 

logical algorithm TD-learning system-level theory 

⇕ ⇕ ? 

electrical circuit neuronal network 

⇑ 

⇑ 

transistor I&F neuron model 

⇑ 

⇑ 

bottom electrons spikes (bio)physics 

comparison between levels: compatibility and consistency 


Structure of INM-6 

INM 

INM-6 (IAS-6), Computational and Systems Neuroscience 

Statistical 

Neuroscience 

Theoretical 

Neuroanatomy 

Computational 

Neurophysics 

Functional 

Neural Circuits 

Grün n. n. Diesmann cand. ident. 

(RWTH Biology) 

(RWTH Medicine) 

IAS 

most students and postdocs from physics 


Building 15.22 

opposite JSC and GRS 


Fundamental interactions 

-50 

pre 

V (mV) 

-60 

-70 

-80 

-90 

0 50 100 150 200 250 

x 

post 

∆V 

0.2 

0.1 

0 

0 50 100 150 200 250 

t 

(ms) 

membrane time constant 10 ms 

synaptic delay 1 ms 

small PSPs 

80% excitatory, 20% inhibitory 


Fundamental interactions 

x 

pre 

post 

V (mV) 

∆V 

in vitro 

-50 

-60 

-70 

-80 

-90 

0 50 100 150 200 250 

0.2 

0.1 

0 

0 50 100 150 200 250 

t 

(ms) 

V (mV) 

-50 

-55 

-60 

-65 

-70 

in vivo 

0 100 200 300 400 500 

t 

(ms) 

membrane time constant 10 ms 

synaptic delay 1 ms 

small PSPs 

80% excitatory, 20% inhibitory 

spontaneous spiking 

1-10 Hz 

10 5 neurons/mm 3 

10 4 synapses/neuron 

10 9 synapses 


Outline 

Multi-layered network model 

Simulation techniques 

Temporal-difference learning 


Structure-dynamics relationship 

? 

(Szentagothai 1978) 

(Luczak et al. 2007) 



1 mm 2 

1 

background input 

E I 

2/3 

4 

E 

I 

5 

? 


E 

E 

I 

I 

6 




1 mm 2 

1 

background input 

E I 

2/3 

4 

E 

I 

5 

? 


E 

E 

I 

I 

6 



Minimal layered cortical network model 

1 mm 2 = 80,000 I&F-neurons 

majority of local synapses 

2 populations (E,I) per layer 

no lateral profile 

layer- and type-specific C xy 

ij 

C xy = 

⎛ 

2/3 → 2/3 4 → 2/3 · · · 6 → 2/3 

2/3 → 4 4 → 4 · · · 6 → 4 

⎜ 

⎝ 

. 

. 

. 

.. 

. .. 

2/3 → 6 4 → 6 · · · 6 → 6 

⎞ 

⎟ 

⎠ 


Methods for estimating connectivity 

in vivo anatomy 

(Binzegger et al. 2004) 


Methods for estimating connectivity 

in vivo anatomy 

in vitro physiology 

(Binzegger et al. 2004) 

(Thomson et al. 2002) 


Comparison of connection probabilities 

E 

E 

I 

I 

connection probability 

0.6 

0.4 

0.2 

anatomy 

physiology 

intra-layer / inter-layer 

4 

2 

0.0 

connection index 

0 

anat. 

phys. 

consistent architectural relations 

inconsistent averages 

⇒ inconsistency due to methodological differences? 


Lateral connectivity 

Anatomy: 

complete local axons 

sampling radius: 

r a > 1 mm 

Physiology: 

Lateral confinement 

sampling radius: 

r p ∼ 100 µm 


Model of distance dependent connectivity 

c(r) = c 0 exp 

(− r 2 ) 

2σ 2 

∫ 

1 

rp 

∫ 2π 

〈c p 〉 = 

c(r ′ )r ′ dr ′ dϕ 

πr 

2 p 

〈c a 〉 = 

1 

πr a 

2 

0 0 

∫ ra 

∫ 2π 

⇒ estimation of c 0 and σ 

c 0 = 0.14 

0 

σ = 300µm 

0 

c(r ′ )r ′ dr ′ dϕ 

consistent with: Hellwig 2000, Stepanyants et al. 2008 

⇒ model connectivity determined by c 0 , σ and model size 


Model connectivity 

0.2 

overall connection probability 

0.1 

number of synapses per neuron (norm.) 

1.0 

0.5 

0.0 

10 3 10 4 10 5 

network size (number of neurons) 

0.0 

10 3 10 4 10 5 


appropriate model size to: 

prevent underestimation of local connectivity 

represent most local synapses within the network 



0.2 


0.1 


1.0 

0.5 

0.0 

10 3 10 4 10 5 


0.0 

10 3 10 4 10 5 








0.2 

0.1 


1.0 

0.5 

↑ 

0.0 

10 3 10 4 10 5 


0.0 

10 3 10 4 10 5 






Comparison of scaled connection probabilities 

E 

E 

I 

I 

connection probability 

0.3 

0.2 

0.1 

anatomy 

physiology 

scaling factor S 

10 

5 

S = max(cp,ca) 

min(c p,c a) 

0.0 

1 



majority of connectivity estimates consistent 

inconsistencies especially in interlayer connections 


Target type selection 

T x 

ji 

= Cex ji −Cji 

ix 

Cji 

ex +Cji 

ix 

anatomy physiology 

1.0 0.5 0.0 0.5 1.0 

target specificity 

I E I E I E 



T x 

ji 


ix 

Cji 

ex +Cji 

ix 

anatomy physiology 

1.0 0.5 0.0 0.5 1.0 


I E I E I E 


More data on target specificity 

L2/3→L6 



T x 

ji 


ix 

Cji 

ex +Cji 

ix 

anatomy physiology functional 

1.0 0.5 0.0 0.5 1.0 


I E I E I E 


Network simulations 

Simulation setup 

integrated connectivity data set 

80,000 I&F neurons 

≈ 0.5 billion synapses 

short-term synaptic plasticity 

all simulations performed in NEST 

existence of asynchronous irregular activity? 

layer specific spike rates? 

impact of target specificity on activity dynamics? 


Realistic local cortical networks 

connectivity c = 0.1 

synapses per neuron = 10 4 

⇒ minimal network size = 10 5 

network N = 10 5 

considered elementary unit 

corresponding to 1 mm 3 

total number of synapses = (cN) · N 

⇒ possible 

Morrison, Mehring, Geisel, Aertsen, Diesmann (2005) Neural Computation 17:1776–1801 

Morrison, Straube, Plesser, Diesmann (2007) Neural Computation 19:47–79 


Building 15.22, server room 

864 core cluster up 

and running 

cooling by cold water 

supply 

development and 

quasi-interactive use 


Simulation times 

time [s] 

2400 

1600 

800 

400 

200 

100 

50 

25 

10 

1s, 10 5 network 

linear prediction 

wotan: Intel Xeon 2.8 GHz 

freya: AMD Opteron 2.4 GHz 

montpellier: Power5 1.9 GHz 

v40z: AMD Opteron 2.2 GHz DualCore 

jump: Power4+ 1.7GHz 

hathor: AMD Opteron 2.6 GHz Dual Core 

1 2 4 8 16 32 64 96 

machines 

supra-linear 

speed-up 

reduction by 2 orders 

of magnitude 

plastic network: 

15 minutes biological time: 60(24) hours computation 

2 types of research: 

large-scale plastic networks 

qualitatively different: quasi-interactive 


Supercomputer 

1 peta flop 

294,912 processors 

72 Blue Gene/P racks 

Linux OS 

Pilot study: jinb33 (2009) JUGENE, Research Center Juelich 

in the BNT our group provides: 

competence 

software 


Enabling brain-scale simulations with NEST 

Computing time 

400 

strong scaling 

linear expectation 

visual cortex, reduced 

full cortex, reduced 

200 

weak scaling 

computing time [s] 

200 

100 

computing time [s] 

100 

50 

50 

1024 2048 4096 8192 1638432768 

number of cores 

252048 4096 8192 16384 

number of cores 

optimal job size for primate visual cortex model: 

4 Blue Gene/P racks = 16,384 cores 


MEXT Next-generation supercomputer project 

10 peta flops 

SPARC64TM VIIIfx 

Fujitsu LTD 

Linux OS 

Next-generation Supercomputer Center (Kobe Port Island, 2012) 

NEST software: 

selected priority target 

already porting with High-performance Computing Team 


Diesmann Computational Neurophysics 

major goal: 

systematically publish 

simulation technology 

collaboration of several labs (since 2001) 

incl. Honda Research Institute (HRI) 

teaching in international courses 

www.nest-initiative.org Gewaltig, Diesmann (2007) NEST Scholarpedia 2(4):1430 


Asynchronous irregular activity 

layer 2/3 

layer 4 

layer 6 

layer 5 

1000 1250 1500 1750 

time [ms] 

0 2 4 6 

rate [Hz] 

0 1 2 

Fano Factor 


Firing rates and experimental Data 


Stability and target specificity 












Transient thalamic inputs 


Cortial flow of activity 


Motivation: 

How is system-level learning realized on a cellular 

level? 

the computer analogy: 

system computer brain 

top multiplication maze navigation system-level behavior 

⇓ 

⇓ 

logical algorithm TD-learning system-level theory 

⇕ ⇕ ? 

electrical circuit neuronal network 

⇑ 

⇑ 

transistor I&F neuron model 

⇑ 

⇑ 

bottom electrons spikes (bio)physics 


Actor-critic temporal-difference learning 

figure adapted from Sutton & Barto (1998) 

able to solve problems with sparse 

rewards 

policy (actor): selects actions 

value function V (s) (critic): 

prediction of future reward, 

evaluates actions 

TD error: 

δ t = r t+1 + γV (s t+1 ) − V (s t ) 

r t+1 : reward at time t + 1; 

γ: discount factor ∈ [0, 1] 


TD learning and the brain 

Dopaminergic activity 

encodes TD error 

Dopamine-dependent 

plasticity 

from Schultz, W, Dayan, P, & Montague, PR (1997) 

Science 275, 1593-1599 

from Reynolds, JNJ, Hyland, BI, Wickens JR (2001) 

Nature 413, 67-70 


Neuronal actor-critic architecture 


Critic: Generation of TD signal 

Ḋ(t) = − 1 

τ D 

D + A τ D 

∑ 

δ ( t − t n ) 

DA 

t 

DA n

Synaptic plasticity: Exploitation of TD signal 

dopamine modulates 

synaptic plasticity at 

corticostriatal synapses 

(Reynolds et al. (2001) Nature 

413, 67-70) 

we developed synaptic 

plasticity rules using a 

top-down approach to 

implement value function 

and policy update rules 


Synaptic plasticity: Timing 

Discrete time implementation: V (s t ) ← V (s t ) + αδ t 

Presynaptic activity trace: 

˙Λ j (t) = − 1 (Λ j − ∑ ( )) 

δ t − tj 

n 

τ Λ 

Presynaptic efficacy trace: 

˙ε j (t) = − ε j − 1 

− ∑ ( ) 

ε j δ t − tj 

n 

τ ε 

ẇ ij = Λ j (t)ε j (t)f (t) 

results in strong plasticity when the agent leaves the state 

associated with presynaptic neuron j 

negligible plastic otherwise 


Synaptic plasticity: Prediction and experiment 

Plasticity between state neuron j and critic neuron i: 

{ 

} 

ẇ ij = Λ j (t)ε j (t) (D(t) − b) + (γ − 1) Λ i (t)C α 

Λ j : presynaptic activity trace, ε j : presynaptic efficacy trace, b: dopamine baseline, γ: discount factor, 

Λ i : postsynaptic activity trace, C: constant factor, α: learning rate 

Predictions 

pre post DA weight change 

x 0 0 0 

0 x 0 0 

0 0 x 0 

x x 0 LTD 

x 0 x LTD/LTP 

0 x x 0 

x x x LTD/LTP 


Synaptic plasticity: Prediction and experiment 

Plasticity between state neuron j and critic neuron i: 

{ 

} 

ẇ ij = Λ j (t)ε j (t) (D(t) − b) + (γ − 1) Λ i (t)C α 

Λ j : presynaptic activity trace, ε j : presynaptic efficacy trace, b: dopamine baseline, γ: discount factor, 

Λ i : postsynaptic activity trace, C: constant factor, α: learning rate 

Predictions 


x 0 0 0 

0 x 0 0 

0 0 x 0 

x x 0 LTD 

x 0 x LTD/LTP 

0 x x 0 

x x x LTD/LTP 

Experimental results 


x 0 0 0 

0 x 0 0 

0 0 x 0 

x x 0 LTD (LTP) 

x 0 x 0 

0 x x 0 

x x x LTD/LTP 

data from Reynolds JNJ and Wickens JR, Neural 

Networks 15 (2002) 507-521 


Model solves grid-world task 

Potjans, Morrison & Diesmann (2009) Neural Computation 21:301–339 

Potjans, Diesmann & Morrison (2011) PLoS Computational Biology, in press 


Value function and policy 

72 

64 

56 

48 

40 

32 

24 


Brain-scale connectivity 

Brain and Neural Systems Team, RIKEN Computational Science Research Program 

Pilot study: jinb33 (2008) Jugene Brain-scale simulations FZ Juelich 


Summary 

cubic millimeter of brain with realistic connectivity 

theory demonstrates consistency of experimental data 

spiking network implementation of TD-learning 

mapping of system-level theory to neuronal level 

combination of bottom-up and top-down approaches 

corresponding simulation technology 

need for brain-scale models 


References 

Dayan, P. and Abbott, L. F. (2001) Theoretical Neuroscience. 

MIT Press, Cambridge 

Gerstner, W. and Kistler, W. (2002) Spiking Neuron Models: 

Single Neurons, Populations, Plasticity. Cambridge University 

Press 

Gewaltig, M.-O. and Diesmann, M. (2007) NEST. Scholarpedia 

www.scholarpedia.org/article/NEST

Bottom-up and top-down approaches in Computational Neuroscience

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