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