skip to main content
10.1145/3611315.3633265acmotherconferencesArticle/Chapter ViewAbstractPublication PagesnanoarchConference Proceedingsconference-collections
research-article

Accurate and Energy-Efficient Stochastic Computing with Van Der Corput Sequences

Published: 25 January 2024 Publication History

Abstract

In stochastic computing (SC), data is represented using random bit-streams. The efficiency and accuracy of SC systems rely heavily on the stochastic number generator (SNG), which converts data from binary to stochastic bit-streams. While previous research has shown the benefits of using low-discrepancy (LD) sequences like Sobol and Halton in the SNG, the potential of other well-known random sequences remains unexplored. This study investigates new random sequences for potential use in SC. We find that Van Der Corput (VDC) sequences hold promise as a random number generator for accurate and energy-efficient SC, exhibiting intriguing correlation properties. Our evaluation of VDC-based bit-streams includes basic SC operations (multiplication and addition) and image processing tasks like image scaling. Our experimental results demonstrate high accuracy, reduced hardware cost, and lower energy consumption compared to state-of-the-art methods.

References

[1]
Armin Alaghi and John P. Hayes. 2013. Exploiting correlation in stochastic circuit design. In ICCD. Asheville, NC, USA, 39–46.
[2]
Armin Alaghi and John P. Hayes. 2014. Fast and accurate computation using stochastic circuits. In 2014 DATE. 1–4. https://doi.org/10.7873/DATE.2014.089
[3]
Sina Asadi, M. Hassan Najafi, and Mohsen Imani. 2021. CORLD: In-Stream Correlation Manipulation for Low-Discrepancy Stochastic Computing. In 2021 ICCAD. 1–9. https://doi.org/10.1109/ICCAD51958.2021.9643450
[4]
Sercan Aygun, Mehran Shoushtari Moghadam, M. Hassan Najafi, and Mohsen Imani. 2023. Learning from Hypervectors: A Survey on Hypervector Encoding. arxiv:2308.00685 [cs.LG]
[5]
Sercan Aygun, M. Hassan Najafi, Mohsen Imani, and Ece Olcay Gunes. 2023. Agile Simulation of Stochastic Computing Image Processing with Contingency Tables. IEEE TCAD (2023). https://doi.org/10.1109/TCAD.2023.3243136
[6]
Sercan Aygün, Mustafa Altun, and Ece Olcay Güneş. 2017. Sobel filter operation in image processing via stochastic arithmetic-logic unit design. In 2017 IEEE SIU. https://doi.org/10.1109/SIU.2017.7960479
[7]
Timothy J. Baker and John P. Hayes. 2022. CeMux: Maximizing the Accuracy of Stochastic Mux Adders and an Application to Filter Design. ACM TDAES 27, 3, Article 27 (jan 2022), 26 pages. https://doi.org/10.1145/3491213
[8]
T. Blu, P. Thevenaz, and M. Unser. 2004. Linear interpolation revitalized. IEEE Transactions on Image Processing 13, 5 (2004), 710–719. https://doi.org/10.1109/TIP.2004.826093
[9]
K.T. Gribbon and D.G. Bailey. 2004. A novel approach to real-time bilinear interpolation. In DELTA 2004. 126–131. https://doi.org/10.1109/DELTA.2004.10055
[10]
Vincent T. Lee. 2019. Towards practical stochastic computing architectures for emerging applications. Ph. D. Dissertation. University of Washington, Seattle, USA. http://hdl.handle.net/1773/43658
[11]
Vincent T. Lee, Armin Alaghi, Rajesh Pamula, Visvesh S. Sathe, Luis Ceze, and Mark Oskin. 2018. Architecture Considerations for Stochastic Computing Accelerators. IEEE TCAD 37, 11 (2018), 2277–2289. https://doi.org/10.1109/TCAD.2018.2858338
[12]
Peng Li, David J. Lilja, Weikang Qian, Kia Bazargan, and Marc D. Riedel. 2014. Computation on Stochastic Bit Streams Digital Image Processing Case Studies. IEEE TVLSI 22, 3 (2014).
[13]
Zhe Li, Ji Li, Ao Ren, Ruizhe Cai, Caiwen Ding, Xuehai Qian, Jeffrey Draper, Bo Yuan, Jian Tang, Qinru Qiu, and Yanzhi Wang. 2019. HEIF: Highly efficient stochastic computing-based inference framework for deep neural networks. IEEE TCAD 38, 8 (2019), 1543–1556. https://doi.org/10.1109/TCAD.2018.2852752
[14]
C. Devon Lin and Boxin Tang. 2022. Latin Hypercubes and Space-filling Designs. arxiv:2203.06334 [stat.ME]
[15]
Zhendong Lin, Guangjun Xie, Wenbing Xu, Jie Han, and Yongqiang Zhang. 2021. Accelerating Stochastic Computing Using Deterministic Halton Sequences. IEEE TCAS II 68, 10 (2021), 3351–3355. https://doi.org/10.1109/TCSII.2021.3073680
[16]
Siting Liu and Jie Han. 2017. Energy efficient stochastic computing with Sobol sequences. In 2017 DATE. 650–653. https://doi.org/10.23919/DATE.2017.7927069
[17]
S. Liu and J. Han. 2018. Toward energy-efficient stochastic circuits using parallel sobol sequences. IEEE TVLSI 26, 7 (2018).
[18]
Luka Marohnic 2012. Plastic Number: Construction and Applications.
[19]
M. Hassan Najafi, Devon Jenson, David J. Lilja, and Marc D. Riedel. 2019. Performing Stochastic Computation Deterministically. IEEE TVLSI 27, 12 (2019), 2925–2938. https://doi.org/10.1109/TVLSI.2019.2929354
[20]
William H Press, Saul A Teukolsky, William T Vetterling, and Brian P Flannery. 1995. Numerical Recipes in C: The Art of Scientific Computing. Camb. Univ. Press, New York, NY, USA.
[21]
W. Qian, X. Li, M. D. Riedel, K. Bazargan, and D. J. Lilja. 2011. An Architecture for Fault-Tolerant Computation with Stochastic Logic. Computers, IEEE Trans. on 60, 1 (Jan 2011), 93–105. https://doi.org/10.1109/TC.2010.202
[22]
Mohsen Riahi Alam, M. Hassan Najafi, and Nima TaheriNejad. 2021. Exact Stochastic Computing Multiplication in Memristive Memory. IEEE Design & Test 38, 6 (2021), 36–43. https://doi.org/10.1109/MDAT.2021.3051296
[23]
Paishun Ting and John P. Hayes. 2017. Eliminating a hidden error source in stochastic circuits. In 2017 IEEE DFT. 1–6. https://doi.org/10.1109/DFT.2017.8244436
[24]
J. G. van der Corput. 1935. Verteilungsfunktionen. I. Proc. Akad. Wet. Amsterdam 38 (1935), 813–821.
[25]
Ran Wang, Jie Han, Bruce F. Cockburn, and Duncan G. Elliott. 2016. Stochastic Circuit Design and Performance Evaluation of Vector Quantization for Different Error Measures. IEEE TVLSI 24, 10 (2016), 3169–3183. https://doi.org/10.1109/TVLSI.2016.2535313

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences
NANOARCH '23: Proceedings of the 18th ACM International Symposium on Nanoscale Architectures
December 2023
222 pages
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 January 2024

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Correlation
  2. image scaling
  3. low-discrepancy sequences
  4. random number generator
  5. stochastic computing

Qualifiers

  • Research-article
  • Research
  • Refereed limited

Funding Sources

Conference

NANOARCH '23

Acceptance Rates

Overall Acceptance Rate 55 of 87 submissions, 63%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)56
  • Downloads (Last 6 weeks)1
Reflects downloads up to 23 Jan 2025

Other Metrics

Citations

Cited By

View all

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media