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
12
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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