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STOCHASTIC LOGICSTOCHASTIC LOGICSTOCHASTIC LOGICArchitectures for post-CMOS switchesSTOCHASTIC LOGICArchitectures for post-CMOS switches
David S. Ricketts Jehoshua (Shuki) BruckElectrical & Computer Engineering Electrical EngineeringCarnegie Mellon University California Institute of TechnologyCarnegie Mellon University California Institute of Technologywww.ece.cmu.edu/~ricketts [email protected]
“Random” at the Nanoscale
Statistical Variation Probabilistic
St h ti Stochastic …….
© D. S. Ricketts 2009
“Statistical” VariationRandom Dopant
FluctuationsSiO2
GateSiO2Gate
wl
M M
A. Brown et al., IEEE Trans. Nanotechnology, p. 195, 2002
Source DrainSource Drain
Mp1 Mp2
Mn1 Mn2
Ms1 Ms21 2
Line Edge Roughness
Column muxwe we
data dataMwr
Mmux
Gate Oxide Variation
1µmK. Shepard, U.
Columbia
At nanoscale, nothing is deterministic
Gate Oxide VariationYear Leff 3σ Tox 3σ VT 3σ W 3σ H 3σ ρ 3σ
90 nm 47% 16% 13% 33% 36% 33%
© D. S. Ricketts 2009
Momose et al, IEEE Trans. Electron Devices, 45(3), 1998
[Sani Nassif, Proc. IEEE CICC, May 2001]
BOX Devices Wires
“Probabilistic” Random events during operation, dice are rolled
continuouslyE l P b bili ti CMOS (PCMOS) K V Example: Probabilistic CMOS (PCMOS), K. V. Palem, Rice Univ, et. al.
© D. S. Ricketts 2009 VLSI-SoC: Research Trends in VLSI and Systems on Chip, Springer Boston,
“Probabilistic” (2) Markov Random Field (MRF) Logic, A. Zaslavsky,
Brown Univ. Nepal, et. al. “Designing Logic Circuits for Probabilistic Computation inthe Presence of Noise”
RAZOR, T. Austin, T. Mudge, Univ Michigan
© D. S. Ricketts 2009D. Ernst, et. al., “Razor: A Low-Power Pipeline Based on Circuit-Level Timing
Speculation”
“Stochastic” LogicGoal: Leverage random fluctuations of nanoscale switches to build a new paradigm in logic/computation
Random events during operation, dice are rolled continuously
logic/computation.
dice are rolled continuously We don’t look to fix randomness,
but rather exploit it. We are investigating
architectures/logic families that are based on stochastic logicare based on stochastic logic using stochastic switches.
We leverage the inherent
© D. S. Ricketts 2009
“random” state of certain nanoscale devices….
Switch: Bistable Elements Basic idea of a switch* is a
bistable elementT iti b t t t Transition between states can be external, i.e. input, or internal, e.g. thermal energy.
Energy Barrierg gy
In nature, many physical systems have two stable, or meta stable states with anmeta-stable states with an energy barrier between them.
Transitions occur “randomly” ydue to the thermal energy of the system “0” “1”
© D. S. Ricketts 2009
Switch: Bistable Elements (2) Transition between states can
be calculated from the barrier height and the thermal energyheight and the thermal energy of the system ~ kT. Energy Barrier
Tk
EPB
exp
01/ expflipER f
“0” “1”E
0/ e pflipB
fk T
© D. S. Ricketts 2009
Switch: Bistable Elements (3) Probability of state determined
by symmetry of potential well
Energy Barrier
E 2EE
Tk
EPB
exp 2E1E
“0” “1”
© D. S. Ricketts 2009
Example #1 Rotaxane Molecule
Used for dense memory cross bar arrays Switching/relaxation
CHEMPHYSCHEM 2002, 3, 519 ― 525CHEMPHYSCHEM 2002, 3, 519 525
Phil. Trans. R. Soc. A (2007) 365, 1607–1625
1 expBk T GRh RT
: s days
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Eyring equation
Example #2 Data storage (disk drive) bit
VLow
FePt Nanoparticle arrays E K V V1
V2
Moderate
FePt Nanoparticle arrays uE K V
V3 < V1V2 < V3
High
Stored Data Data Lost
2
Stored Data Data Lost
%)
Magnetization Decay
1050
nm3.03.6 d
20 nm
V3
Mag
netiz
atio
n (
V1V2
S. Sun, C. Murray, D. Weller, L. Folks, A. Moser, Science, 287, pp. 1989 2000
nm05.0d
© D. S. Ricketts 2009
1 minute
Log Time (s)
10 years0
1 year
Stochastic Logic (J. Bruck)“Shannon’s work focused on deterministic switching circuits, circuits where each switch is associated with a Boolean variable defining whether the switch is closed. We instead focus on stochastic switching circuits,the switch is closed. We instead focus on stochastic switching circuits, circuits where each pswitch is associated with a Bernoulli random variable defining the (independent) probability that the pswitch is closed.”
D. Wilhelm and J. Bruck, “Stochastic switching circuit synthesis,” IEEE Int.Sym. on Inf. Theory, Toronto, 2008.
Deterministic switch
Deterministic switch
Switches are ON or OFF with a known probability (not necessarily 50%)( ot ecessa y 50%)
We construct global probabilities based upon a logical connection of probabilistic switches (P it h) d d t i i ti it h
© D. S. Ricketts 2009
(Pswitch) and deterministic switches.
Stochastic Logic (2) Series/Parallel Pswitches
© D. S. Ricketts 2009
Stochastic Logic (3) Examples: Series/Parallel Pswitches
75%
1) Let circuit C1 be the single-pswitch circuit.
37.5% 43.8%
) g p2) For bit Fi, i = 2 to n, let circuit Ci be:
a) If Fi = 0, C1 in series with Ci−1, orb) If Fi = 1, C1 in parallel with Ci−1 1101.011
© D. S. Ricketts 2009
3 2 1 0 1 2 32 2 2 2 .2 2 2
Stochastic Logic: Universal Probability Generator Generating a deterministic input to
desired probabilistic statesC ld t 2n i di id l Could generate 2n individual probability generators and select one Inefficient – exponential increase in switch
count. Need an algorithm that creates the Need an algorithm that creates the
desired probabilities with the minimum hardware
Need universal Pswitch network “synthesizer”
© D. S. Ricketts 2009
Universal Probability Generator Recursive architecture generates a
minimal sized probability generator using 4n 2 switchesusing 4n-2 switches
© D. S. Ricketts 2009
Universal Probability Generator (2) Example
© D. S. Ricketts 2009
Stochastic Logic Summary Goal: Leverage random fluctuations of nanoscale
switches to build a new paradigm in logic/computationlogic/computation.
Utilize thermal energy of nano-scale switches to generate switches that open/close randomlyg p y
Probability of open/close is determined by energy states, i.e. double well geometry. B ild t h ti it h “P it h ” f th Build stochastic switches “Pswitches” from these random devices.
Are able to synthesize arbitrary probabilities given a Are able to synthesize arbitrary probabilities given a known, but not “designed”, probability.
Universal Probability Generator allows for minimal
© D. S. Ricketts 2009
designs of arbitrary deterministic to probability logic networks.
An Application Example“1 Million RF temperature sensors distributed
uniformly over Indiana, powered by solar energy scavenging circuits that operate sensors for 15scavenging circuits that operate sensors for 15 min per 24 hour period”
© D. S. Ricketts 2009
An Application Example (2) How to ensure temperature readings throughout
the state 24 hours a day?N d 1/100 f t ll ti Need 1/100 of sensors on at all times.
Need sensors that are on to be even distributed, so that no area is missed.
What is the overhead of organization? Of communication?
B ild h ith 1/100 b bilit f b i Build each sensor with a 1/100 probability of being turned ON. Sensor network will inherently provide even coverage and time/energy organization.
What if 15 min varied by weather, by adjusting random wake-up, energy adaptive networks could be implemented
© D. S. Ricketts 2009
be implemented.
Outlook Applications
General probability generators Energy/distribution management Stochastic computation in
e ol tionar s stems e g evolutionary systems, e.g. “Stochastic switching as a survival strategy in fluctuating environments”, Nature Genetics
Efficient implementation of Ps ithces at the Efficient implementation of Pswithces at the nanoscale
Development of more complex synthesis and
© D. S. Ricketts 2009
p p ycomputation theory/ algorithms.
QUESTIONSQUESTIONS
© D. S. Ricketts 2009