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LargeLarge--scale neural modelingscale neural modeling
KwabenaKwabena BoahenBoahenStanford BioengineeringStanford [email protected]@stanford.edu
Goal: Link structure to function by Goal: Link structure to function by developing multideveloping multi--level level computational models of neural computational models of neural systems.systems.
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WeWe’’re acquiring brain data re acquiring brain data at an unprecedented rate at an unprecedented rate
Reid et al 2005
CaCa++++ imagingimaging
Computational Computational primitivesprimitives
Functional Functional behaviorbehavior
MicrocircuitryMicrocircuitry
Hausser et al 1997
Dendritic recordingDendritic recording Serial Scanning EMSerial Scanning EM
Denk et al 2005
Now all we have to is connect the dotsNow all we have to is connect the dots……
+ =
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MultiMulti--level simulations can link level simulations can link structure to functionstructure to functionThe problem is one of scaleThe problem is one of scale
7 levels of investigation7 levels of investigation
10 orders of magnitude10 orders of magnitude
Option 1: Option 1: ExperimentExperiment
Difficult to controlDifficult to control
Option 2: Option 2: TheoryTheory
Ignores detailsIgnores details
Option 3: Option 3: SimulationSimulation
Include all detailsInclude all detailsComplements theoryComplements theory
Control all parametersControl all parametersComplements experimentComplements experiment
Churchland & Sejnowski 1992
Levels of InvestigationLevels of Investigation
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2
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© Kwabena Boahen Ray Kurzweil 2001
3GHz Dell Precision
Brunsviga Model 20
100Mz Compaq Presario
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The fastest supercomputers can simulate The fastest supercomputers can simulate only 10,000 neurons in realonly 10,000 neurons in real--timetime
CellCell
8M neurons connected by 4B synapses8M neurons connected by 4B synapses99°° visual field in V1visual field in V1
1sec of activity took 1hr 20mins to simulate1sec of activity took 1hr 20mins to simulate47504750×× slower then realslower then real--timetime
Had to perform 38 trillion evaluationsHad to perform 38 trillion evaluations8M neurons 8M neurons ×× 6 comp. 6 comp. ×× 8 8 eqeq. . ×× 101055 steps/sec steps/sec
CompartmentCompartment
( )
( )1
V
Vu u
α
β−
( )( )
u V ududt Vτ
∞ −=
( ) ( )( ) ( )V
u VV Vα
α β∞=
+
( ) ( ) ( )1V
V Vτ
α β=
+
IonIon--channelchannel Blue Gene supercomputerBlue Gene supercomputer
LansnerLansner et al. used one et al. used one 20482048--processor rack processor rack (3Tflops, $2M)(3Tflops, $2M)
Shenoy et al. 2006
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Physicists revolutionized astrophysics Physicists revolutionized astrophysics by building their own supercomputerby building their own supercomputer
Hubble Telescope 1999
Two spiral galaxiesTwo spiral galaxies
Hardwired to calculate gravitational forceHardwired to calculate gravitational force
A third as fast as Blue Gene rack (1Tflop)A third as fast as Blue Gene rack (1Tflop)
Sixteen times more costSixteen times more cost--effective ($42K)effective ($42K)First to show First to show gravothermalgravothermal oscillationsoscillations
Resulted in 40 papers in 2000 aloneResulted in 40 papers in 2000 alone
Univ. of Tokyo Univ. of Tokyo astrophysicist astrophysicist Jun MakinoJun Makino
2001
Point mass approx.Point mass approx. Law of gravityLaw of gravity
2i
j ji ij
mF Gmr
= ∑
GRAPE6 supercomputerGRAPE6 supercomputer
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NeurogridNeurogrid——an affordable supercomputer an affordable supercomputer for neuroscientistsfor neuroscientists
88××8844××44Neurogrid Neurogrid (chips)(chips)
18,20018,200280280Speed Speed (TF)(TF)64M64M1M1MTotal Total (neurons)(neurons)
1K1K××1K1K256256××256256Neurocore Neurocore (neurons)(neurons)
201120112008 (!)2008 (!)
NeurogridNeurogrid: Board with grid of chips: Board with grid of chipsProgrammable connectionsProgrammable connections
One chip per cortical cellOne chip per cortical cell--layer or typelayer or type
NeurocoreNeurocore:: Chip with array of neuronsChip with array of neuronsProgrammable ionProgrammable ion--channel propertieschannel properties
Multiple compartments per neuronMultiple compartments per neuron
Chip 1
Chip 2
0 1 2 3
0 1 2 3
0 1 2 31 3 2 0
prepostRAM
3
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DonDon’’t evaluate equationst evaluate equations——emulate physicsemulate physics
Emulate ionic currents with electronic currentsEmulate ionic currents with electronic currents
Exploit physical Exploit physical analogyanalogyIncluding stochastic behaviorIncluding stochastic behavior
Analog VLSIAnalog VLSIVery Large Scale Integration Very Large Scale Integration
Runs in realRuns in real--timetimeTakes 1sec instead of 1hr and 20minsTakes 1sec instead of 1hr and 20mins
( )
( )1
V
Vu u
α
β−
( )( )
u V ududt Vτ
∞ −=
( ) ( )( ) ( )V
u VV Vα
α β∞=
+
( ) ( ) ( )1V
V Vτ
α β=
+
DrainSource
Gate
Bulk
e-⇔ ⇔
Ion channelIon channelTransistorTransistor
Mead 1989
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MultiMulti--area cortical models area cortical models
Society for Neuroscience 2005Essen & Fellerman 1991
isual areasisual areas
Sillito ‘06
MTMT
V1V1
Bac
kwar
dB
ackw
ard
Forward
Forward
Feedforward view of motionFeedforward view of motion
V1: PartsV1: Parts
MT: ObjectMT: Object
Anatomy has feedbackAnatomy has feedback
MT projects to V1MT projects to V1
Hypotheses about feedback:Hypotheses about feedback:
Aggregates parts into Aggregates parts into coherent objectcoherent object
Composes cues into Composes cues into unambiguous perceptunambiguous percept
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BioE332BioE332’’s thousands thousand--neuron babyneuron baby
RAM
Computer
STDP Chip
USB
CPLD
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The chip: SpikeThe chip: Spike--timing dependent plasticitytiming dependent plasticity
INTER-NEURON
PRINCIPLE CELLS
PRINCIPLE CELLS
PLASTIC SYNAPSES
PLASTIC SYNAPSES
PLASTIC SYNAPSES
PLASTIC SYNAPSES
1024 excitatory principle cells1024 excitatory principle cells21 plastic synapses each21 plastic synapses each
256 inhibitory interneurons256 inhibitory interneurons
750,000 transistors750,000 transistors
10.2mm10.2mm22 in 0.25in 0.25μμm CMOSm CMOS
95µm
60µm
4
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The GUI: Memorizing patternsThe GUI: Memorizing patterns
Before learning After learning
Synaptic strengths
LTP
LTD
Synaptic strengths
Neuron array Spike trains Neuron array Spike trains
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Lab 1: Synapse ModelLab 1: Synapse Model
Sum
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Lab 2: Neuron ModelLab 2: Neuron Model
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Lab 3: Adaptation and BurstingLab 3: Adaptation and Bursting
5
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Lab 4: Phase ResponseLab 4: Phase Response
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Lab 5: SynchronyLab 5: SynchronyW
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Lab 6: BindingLab 6: Binding
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Lab 7: Synaptic PlasticityLab 7: Synaptic Plasticity
6
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Lab 8: Plasticity and SynchronyLab 8: Plasticity and Synchrony
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Lab 9: Associative memoryLab 9: Associative memory
Before learning After learning
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Lab 10: AttentionLab 10: Attention
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