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Bridging theory of neural populations and Bridging theory of neural populations and neuromorphicneuromorphic implementations: implementations: neuromorphicneuromorphic implementations: implementations:
concepts and experiencesconcepts and experiences
Paolo Del Giudice
Italian Institute of Health
http://neural.iss.infn.it/papers.htmp // /p p
pioneerspioneers
Caltech, mid ’80: ‘physics of computation’ courseCaltech, mid ’80: ‘physics of computation’ course
understanding the relationship between the physical structure of a understanding the relationship between the physical structure of a computational system, its dynamics and its computational capabilities
Mead
neuromorphic de ices:neuromorphic de ices:
Distinctive features of Distinctive features of neuromorphicneuromorphic devicesdevices
analog electronic implementation of neurons and synapses
neuromorphic devices:neuromorphic devices:
use silicon as an additional medium to understand the brain (understanding by building)mimic the computational strategies of the brain to pave the way to future computers
are based on:are based on:
analog local computationasynchronous digital events (spikes) for long-range communicationy g ( p ) g gcomputation as an emergent property of the substrate
"We are in no better position to 'copy' biological nervous systems than we are to create a flying
thoughts from the pioneerthoughts from the pioneer
p py g y f y gmachine with feathers and flapping wings. But we can use the organizing principles as a basis for our silicon systems in the same way that a glider is an excellent model of a soaring bird."
Neurophysiology on silicon?Neurophysiology on silicon?
First of all: Should we undertake to design ‘neural’ chips?
Strategy 1: let theory reach a mature state, relying on simulations along the way, and only later try hardware implementationStrategy 2: the new ‘neuromorphic’ technology evolve in parallel with the theory gy p gy p y
In favor of strategy 2:
a large body of interdisciplinary experience required: establishing a new scientific community.‘neural’ chips are not finite-state automata, they should interact in real time with natural
l h h d l d bl d d f ‘ ’stimuli, have a rich and partly unpredictable dynamics: new strategies required for ‘testing’.the knowledge of the circuitry does not predict the collective dynamics of a neural network on silicon: some theory is required, which will feed back on chip design strategies.
First First successes in successes in emulating sensory functions: the ‘silicon retina’emulating sensory functions: the ‘silicon retina’
The silicon retina detects contrast changes, and adapts to local luminosityThe silicon retina detects contrast changes, and adapts to local luminosity
First successesMore recent achievements…
Kramer, DelbruckINI-Zurich
Mead,Mahowald
Beyond sensory processing: brainBeyond sensory processing: brain--inspired computational primitives? inspired computational primitives?
Cortex has a fairly homogeneous structure across areas supporting a Cortex has a fairly homogeneous structure across areas, supporting a diversity of functions ï search for reusable dynamic components, possibly subserving several computational functions.
Cortex is known to be largely organized in modules with high local recurrent synaptic connectivity and sparser inter-modules connectivityrecurrent synaptic connectivity and sparser inter modules connectivity.
Each strongly self-coupled module can be modeled as a highly non-linear d l h ddynamical systems with attractor dynamics
The simplest cortex picture is a web of individually mono-stable or bi-p p ystable modules (interesting recent evidence from Mattia et al, Journal of Neuroscience 2013)
Noise is important
Construct neuromorphic systems of increasing complexityusing attractor networks as basic computational elements
The integrateThe integrate--andand--fire neuron: the workhorse of network modelingfire neuron: the workhorse of network modeling
V̇ (t) V (t) + I(t) if V (t̄) ≥ θ ik V (t ∈ (t̄ t̄+ )) HV (t) = −V (t)τ + I(t) if V (t) ≥ θ : spike; V (t ∈ (t, t+ τarp)) = H
Diffusion approximation: I(t) is a Gaussian memoryless process with moments μΙ and σ2Ι
Single integrate and fire neuron: stationar firing rateï first passage time of O U process
pp ) y p Ι Ι
neuron’s gain function2
Single integrate-and-fire neuron: stationary firing rateï first-passage time of O.U. process
Neuron
Φν0 = Φ(μI , σ
2I )I
ν0
increasing σ2Ι
0
increasing σ Ι
Signal‐Dominated,
Noise‐Dominated,high‐σ 2,sub‐threshold regime
low‐σ 2, supra‐threshold regime
μΙ
For the interacting population, the afferent current is a function of the emission rate ν(t)
From single From single neuron neuron to the recurrent population: meanto the recurrent population: mean--field theoryfield theoryg p p ,
μ = μ(ν) σ2 = σ2(ν)
Assume: currents driving different neurons share the
S lf i t ti f th t ti t t
Assume: currents driving different neurons share the same μ and σ 2 (“extended” mean field approx.)
l ti i f ti
Self-consistency equation for the stationary states
ν
population gain function
Φ(ν)stable
fixed points
firing rate ν
unstable fixed point
synaptic input due to pre-synaptic populations x:μ =
Px cxnxJxνx + Iext
σ2 =P
x cxnxJ2xνx + σ2ext
coexistent stable collective states of low and high activity
Synaptic coupling controls nonSynaptic coupling controls non--linearity: linearity: the onset of the onset of bistabilitybistability
an external stimulus can provoke transitions between the two states
stimulus
stimuli
Φ(ν)
ν
D.J. Amit and N.Brunel, Cerebral Cortex 1997stimulus
Models of working memory…
aVLSIaVLSI RECURRENT NETWORKS OF IF NEURONS AND PLASTIC SYNAPSESRECURRENT NETWORKS OF IF NEURONS AND PLASTIC SYNAPSES
Generations:
LANN21BLANN21B 9 mm2, AMS CMOS 0.6 μm 21 exc/inh neurons. Amit Fusi dynamical synapses ISS INFN
AERANNAERANN, 16.8 mm2, AMS CMOS 0.6 μm 21 exc/inh neurons AER on chip
Amit‐Fusi dynamical synapses ISS‐INFN
21 exc/inh neurons ‐ AER on chipneuron adaptation via moving thresholdtwo versions of synaptic dynamics ISS‐INFN
CC‐‐LANNLANN, 16.8 mm2, AMS CMOS 0.35 μmStop‐learning AER and recurrent synapsesConfigurability of recurrent and AER synaptic matrix32 neurons, 2048 plastic synapses ISS‐INFN32 neurons, 2048 plastic synapses ISS INFN
FF‐‐LANNLANN, 69 mm2, AMS CMOS 0.35 μmSt l i AER d tStop‐learning AER and recurrent synapsesExtended configurability of recurrent and AER synaptic matrix128 neurons, 16384 plastic synapses
ISS‐INFN, ETHZ and UNIMD
Thanks to
Attractor dynamics on Attractor dynamics on chip: recovering the bifurcation diagramchip: recovering the bifurcation diagramGiulioni et al, Frontiers in Neuromorphic Engineering 2012
Mean-field approx for multiple populations: ‘effective’ gain function
(Mascaro&Amit 1999)(Mascaro&Amit 1999)
Theory-inspired on-chip y p pprocedure to measure the ‘effective’ gain function
Attractors as Attractors as computational primitives: perceptual decisionprimitives: perceptual decisionExternal stimuli
Competition via inhibitionmodelexperiment
Decision space
‘hard’ ‘easy’
Accuracy / speed Accuracy / speed tradeoff
decision is expressed as the ti ti f tt t t t
Roitman and Shadlen, J. Neurosci., 2002. XJ Wang, Neuron, 2002.
activation of an attractor state
Attractor chips taking Attractor chips taking decisions with simulated stimulidecisions with simulated stimuli
L. Federici et al, in preparation
ν B
M. Giulioni and P. Del Giudice, Frontiers in Artificial Intelligence and Applications, proc. WIRN2011 νA
Attractor chips performing perceptual decision with real stimuliAttractor chips performing perceptual decision with real stimuli
AmbiguousAmbiguousstimulus
E. Annavini et al, in preparation
Autonomous associative learning of visual stimuli on chip Autonomous associative learning of visual stimuli on chip
corrupted stimulus(retina output)
The mature attractor network shows
network activity
time
The mature attractor network shows error correction property:
timeF. Corradi et al, in preparation
M. Giulioni and P. Del Giudice,, proc. WIRN2011
The cortex as a web of interacting, heterogeneous The cortex as a web of interacting, heterogeneous bistablebistable modules modules
A mesoscopic theoryA mesoscopic theoryA mesoscopic theoryA mesoscopic theory
Single mact m
odulestivity
Fractionof
activitymo fhigh odulesN Mattia et al ECVP 2013
τ ν̇(t) = −ν(t) + Φ(νN (t))νN (t) = ν(t) + σ(ν, N)Γ(t)
Mean-field dynamics of single module:
Stochastic process for the fraction of active
νN (t) ν(t) + σ(ν, N)Γ(t)
Finite-size effectsmodules
What this buys us: generate dynamics on the widely different time scales observed in behaviour
(e.g. binocular rivalry, see Gigante et al PLoS Comp. Biol. 2009)
Steps towards a Steps towards a mesoscopicmesoscopic neuromorphicneuromorphic chip chip
Synapticweight
Neuronal‘fatigue’ Synaptic
‘fatigue’
3 filters for differentsynaptic currents
‘NMDA’
‘AMPA’
‘GABA’
Activity‐dependent
Population gain function Φ
y pfinite‐size noise
Population gain function Φ
aa pilot pilot mesoscopicmesoscopic neuromorphicneuromorphic chip chip
synpop &noisefiltersdigital
Φsyn noisefiltersdigital
Rehabilitation of a discrete motor learning Rehabilitation of a discrete motor learning function function by by a prosthetic chipa prosthetic chip
Lesion / aging
Neuromorphic chip restores the function(!?!)(!?!)
FieldField--programmable mixedprogrammable mixed--signal array signal array for for neural signal processing and neural neural signal processing and neural modellingmodellingBamford et al, IEEE Trans. Neural Sys. Rehab Eng. 2012
g p gg p g gg
We designed it for the real-time closed-loop in-vivo replacement learning circuit
Lessons learntLessons learnt
Neuromorphic chips adequate for real life contexts need major Neuromorphic chips adequate for real life contexts need major technological advance
b
technological advance
bbut:but:
For real progress technological advance must be rooted in the theoryFor real progress technological advance must be rooted in the theory
Theory and technology must progress hand in handTheory and technology must progress hand in hand
People involvedPeople involved
M.Mattia S. Bamford M. GiulioniG. Gigante
Theory and simulations Chip design and analog electronics
E. PetettiV. Dante students
P. Camilleri
F. Corradi
FPGA and digital electronics
L. Federici
E. AnnavinicollaborationscollaborationsUniv. Sapienza – Rome, UPF Barcelona, Univ. Magdeburg, INI-Zurich, Univ. Genoa, IDIBAPS Barcelona, TECHNION Haifa, SISSA Trieste, Columbia NY, UnivTel Aviv
collaborationscollaborations