Stochastic Computing: A Design Sciences Approach to Moore s Law

Transcription

1 Stochastic Computing: A Design Sciences Approach to Moore s Law Naresh Shanbhag Department of Electrical and Computer Engineering Coordinated Science Laboratory University of Illinois at Urbana Champaign

2 Computing and Moore s Law Boole Turing Machine Applications Programming models Architecture Boolean logic DETERMINISTIC STATISTICAL ideal switch Devices STATISTICAL

3 Stochastic Computing and Moore s Law Applications Programming models statistical inference Architecture Boolean logic probabilistic switch STATISTICAL Devices

4 4 Von Neumann (1956) J. Von Neumann, Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components, Princeton University Press (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. communications inspired (stochastic) computation

5 Alternative Computational Models 5 Research theme in the Gigascale Systems Research Center (GSRC) Sponsors: DOD & SRC

6 Stochastic Computing Panorama Theoretical Foundations Design Methodologies Application specific Kernels Jones (UIUC) Singer (UIUC) R. Kumar (UIUC), Roychowdhury (UCB) Malik (Princeton) BEE2 ERSA FPGA Prototypes S. Mitra (Stanford) PM BM ADD ADD Comp (LSB) Comp (MSB) Decision PMe PMest ANT Decision PM Stochastic Processors ADD Estimator Kernels:FIR, FFT, Viterbi, video, comm., ML Custom ICs SSNOC ECG FIR Stochastic SOC 6

7 deterministic computing one to one many to one 2 N 2 M (relabeling) (clustering) logic minimization stochastic computing many to many (don t cares) p 1 p many to many (probabilistic) logic minimization P (, ), many to one (clustering) ŷ

8 8 Statistical Estimation & Detection yˆ arg max P( y, y2,..., y H i H 1 N i ) ~ y arg max ~ y N k 1 P( y k ~ y ) Metrics: maximum a posteriori probability (MAP), maximum likelihood (ML), minimum mean squared error (MMSE), minmax, minimum absolute error

9 Error Statistics VOS induced timing violation Path delay distribution (8b RCA) effective error rate vs. energy trade off engineer circuit error statistics prefer long tailed PDDs Measured error PMF FIR filter in 180nm at Vdd = 0.76V Error Probability Mass Function (PMF) 16 bit ripple carry adder 9

10 10 Stochastic Computing Techniques Algorithmic noise tolerance (ANT) PIs: Shanbhag, Jones Stochastic sensor NOC (SSNOC) Stochastic Computing Framework Soft NMR Likelihood Processing IEEE Spectrum, Nov. 2010

11 Algorithmic Noise Tolerance (ANT) [Hegde, Wang, Shim, Varatkar, Abdallah] x y a y o ŷ 1.0 Power P EC P main P TOTAL Energy savings y e y o e Voltage high error rates (up to 60%) overhead (gate count): 5% 22% energy savings: 40% 70% (<1dB SNR loss)

12 ANT Techniques prediction based reduced precision replica input subsampled replica adaptive error cancellation maximum a posteriori (MAP) 12

13 ANT based Error resilient FIR Filter 13 Prediction based ANT (Hegde) Wiener Hopf 3 tap predictor 0.5 BW 29 tap FIR Simulation results 5X energy savings Chip architecture microphotograph 0.35 m 3.3V CMOS 32 tap FIR FMAC: 88MHz; ECMAC: 11MHz; V dd crit =3.55V;2.25V V dd min =2.32V measured results 3X energy savings

14 Error resilient Motion Estimation input sub sampled replica (ISR ANT) (Varatkar) area overhead = 26% 2.5X energy savings conventional 130nm CMOS ISR ANT ideal conventional proposed 14

15 Stochastic Sensor Network on a Chip robust estimation [Varatkar,Narayanan,Jones] (sim) 130nm CMOS WID process variations PIs: Shanbhag, Jones occurence X energy reduction 86% error rate handling, P det > 90% error PMF Error PMF at V dd = 085 V dd =0.85V prototype IC in 180nm CMOS magnitude

16 ECG Analysis MEOP ECG waveform [Abdallah] PAM Tompkin Algorithm CNTRL 1 CNTRL 2 d 2 dt CNTRL BIH MIT ECG DB: 11bits, 200Hz x CNTRL 4 CNTRL 4 y 1 y 2 y o y o yˆ [ n] pe=0.1 pe=0 45nm, IBM process pe= % energy reduction pe=0.58 (0.28V, 65kHz) pe=0.1 pe=0 28% energy reduction pe=0.38 pe=0.58 (0.33V,600 khz) Critical Supply Voltage (V dd-crit )[V]

17 Soft NMR 17 soft NMR architecture [Kim] MAP rule soft voter error statistics x 10-3 VOS Noise with P e,c = 0.05 Probability Error Magnitude x 10 5 soft DCT soft DMR vs. TMR 35% energy savings 2X more robust

18 Matching the statistical requirements of applications to the statistics of nanoscale fabrics statistical application level metrics STOCHASTIC COMPUTING statistics of nanoscale fabrics

19 Implications on Device Design In return for energy efficiency, we can handle non deterministic device behavior improved average case behavior for worse cornercase long tailed distributions low SNR switches smaller gap between 1 variable and a 0 variable multi state switches (instead of two)

20 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 20