Stochastic Computing: A Design Sciences Approach to Moore’s 

Law

Naresh Shanbhag

Department of Electrical and Computer EngineeringCoordinated Science Laboratory

University of Illinois at Urbana‐Champaign

Computing and Moore’s Law

ideal switch

Boole

Boolean logic

Architecture

Applications

Programming models

Devices

TuringMachine

DETER

MINISTIC

STAT

ISTICA

LSTAT

ISTICA

L

Stochastic Computing and Moore’s Law

probabilistic switch

Boolean logic

Architecture

Applications

Programming models

Devices

STAT

ISTICA

L

statisticalinference

Von Neumann (1956)

....treatment of error is unsatisfactory and ad hoc 

....error should be treated .....as information has been, by the work of L. Szilard and C. E. Shannon. The present treatment falls short of achieving this……….

4

J. Von Neumann, Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components,  Princeton University Press (1956)

communications‐inspired (stochastic) computation

5

Alternative Computational 

Models

Sponsors:DOD & SRC

Research theme in the 

GigascaleSystemsResearch

Center (GSRC)

Stochastic Computing Panorama

6

Kernels:FIR, FFT, Viterbi, video, comm., ML

Stochastic Processors

SSNOC ECG FIR

Custom ICs

Theoretical Foundations

Application‐specific Kernels

Comp(LSB)

Comp(MSB)AD

D

Dec

isio

n PMe

AD

D

PM

BM

ADD Estimator

PMest

AN

TD

ecis

ion PM

BEE2‐ ERSA

S. Mitra (Stanford)

Design Methodologies

Stochastic  SOC

FPGA Prototypes 

R. Kumar (UIUC),Roychowdhury (UCB)Malik (Princeton)

Jones (UIUC)Singer (UIUC)

one‐to‐one (relabeling)

deterministic computing

2N 2Mmany‐to‐one (clustering)

many‐to‐many (don’t cares) many‐to‐many 

(probabilistic)

stochastic computing

p1 p

, ( , )P

y

logic minimization

many‐to‐one (clustering)

logic minimization

Statistical Estimation & Detection

Metrics: maximum a posteriori probability (MAP), maximum likelihood (ML), minimum mean‐squared error (MMSE), minmax, 

minimum absolute error 

8

)|,...,,(maxargˆ 21 iNH

HyyyPyi

N

kk

yyyPy

1~

)~|(maxarg~

9

Error StatisticsPath delay distribution (8b RCA)

16‐bit ripple‐carry adder

Error Probability Mass Function (PMF)

VOS induced timing violation

FIR filter in 180nmMeasured error PMF

at Vdd = 0.76V

effective error rate vs. energy trade‐offengineer circuit error statisticsprefer long‐tailed PDDs

Stochastic Computing Techniques10

Algorithmic noise‐tolerance (ANT) Stochastic sensor NOC (SSNOC)

Soft NMR Likelihood Processing

Stochastic ComputingFramework

IEEE Spectrum, Nov. 2010

PIs: Shanbhag, Jones

Algorithmic Noise‐Tolerance (ANT)

x

oa yy

eyy oe

y

[Hegde, Wang, Shim, Varatkar, Abdallah]

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Energy savings

Voltage

Pow

er

Pmain

PTOTALPEC

1.0

1.0

≪ ≪ ≅

high error‐rates (up to 60%)

overhead (gate‐count): 5%‐22%

energy savings: 40%‐70% (<1dB SNR loss)

ANT Techniques

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prediction‐based

adaptive error‐cancellation

input subsampled replica

maximum a posteriori (MAP)

reduced‐precision replica

ANT‐based Error‐resilient FIR Filter13

Prediction‐based ANT (Hegde)

Chip architecture microphotographmeasured results

Simulation results

3‐tap predictor0.5 BW

29‐tap FIR

5X energy savings

3X energy savingsFMAC: 88MHz;ECMAC: 11MHz;Vdd‐crit =3.55V;2.25VVdd‐min =2.32V

0.35 m 3.3V CMOS32‐tap FIR

Wiener‐Hopf 

ideal conventional proposed14

Error‐resilient Motion Estimationinput sub‐sampled replica (ISR‐ANT) (Varatkar)

2.5X energy‐savingsarea overhead = 26%

conventional

ISR‐ANT

130nm CMOS

Stochastic Sensor Network‐on‐a‐Chip

prototype IC in

180nm CMOS

-20 -10 0 10 200

500

1000

1500

2000

2500Error PMF at Vdd = 085

magnitude

occu

renc

e

Vdd =0.85V

PIs: Shanbhag, Jones

5.8X energy reduction86% error‐rate handling, Pdet > 90%

robust estimation

errorPMF

(sim) 130nm CMOSWID process variations

[Varatkar,Narayanan,Jones]

ECG Analysis IC @ MEOPPAM‐Tompkin Algorithm[Abdallah]

ECG waveform

BIH‐MIT ECG DB: 11bits, 200Hz

45nm, IBM processC

NTR

L 1

CN

TRL 2

CN

TRL 3

dt

d 2 321

x

oyy1

oyy2

][ˆ ny

CN

TRL 4

CN

TRL 4

pe=0.58

pe=0.38

pe=0.1pe=0

pe=0.38

pe=0.1pe=0

23% energy reduction

28% energy reduction

Critical Supply Voltage (Vdd-crit)[V]

(0.33V,600 kHz)

(0.28V, 65kHz)

pe=0.58

Soft NMR17

[Kim]

-1 -0.5 0 0.5 1x 105

0

0.5

1

1.5

2

2.5

3x 10-3 VOS Noise with Pe,c = 0.05

Error Magnitude

Pro

babi

lity

soft NMR architecture soft voter

error statistics

MAP rule

soft DCT

soft DMR vs. TMR35% energy savings2X more robust

statistical application‐level metrics

STOCHASTIC COMPUTING

statistics of nanoscale fabrics

Matching the statistical requirements of applications to the statistics of nanoscale fabrics

Implications on Device Design

• In return for energy‐efficiency, we can handle– non‐deterministic device behavior– improved average case behavior for worse corner‐case  long‐tailed distributions

– ‘low SNR switches’    smaller gap between 1‐variable and a 0‐variable

– ‘multi‐state switches’ (instead of two)

Summary• Device design combined with stochastic computing can drive Moore’s Law

• Device design for stochastic platforms– what are the device properties that result in favorable error statistics?

– ideal switch model unnecessary– relaxed device specifications 

• Design and programming methodologies• New applications in biomedical, energy and security

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