Math gifts

- Art Gallery -

Approximate computing is a computation technique which returns a possibly inaccurate result rather than a guaranteed accurate result, and can be used for applications where an approximate result is sufficient for its purpose.[1][2] One example of such situation is for a search engine where no exact answer may exist for a certain search query and hence, many answers may be acceptable. Similarly, occasional dropping of some frames in a video application can go undetected due to perceptual limitations of humans. Approximate computing is based on the observation that in many scenarios, although performing exact computation requires large amount of resources, allowing bounded approximation can provide disproportionate gains in performance and energy, while still achieving acceptable result accuracy. For example, in k-means clustering algorithm, allowing only 5% loss in classification accuracy can provide 50 times energy saving compared to the fully accurate classification.[1]

The key requirement in approximate computing is that approximation can be introduced only in non-critical data, since approximating critical data (e.g., control operations) can lead to disastrous consequences, such as program crash or erroneous output.

Strategies

Several strategies can be used for performing approximate computing.

Approximate circuits
Approximate adders,[3][4] multipliers[5] and other logical circuits can reduce hardware overhead.[6][7][8] For example, an approximate multi-bit adder can ignore the carry chain and thus, allow all its sub-adders to perform addition operation in parallel.
Approximate storage
Instead of storing data values exactly, they can be stored approximately, e.g., by truncating the lower-bits in floating point data. Another method is accept less reliable memory. For this, in DRAM[9] and eDRAM, refresh rate can be lowered or controlled.[10] In SRAM, supply voltage can be lowered[11] or controlled.[12] Approximate storage can be applied to reduce MRAM's high write energy consumption.[13] In general, any error detection and correction mechanisms should be disabled.
Software-level approximation
There are several ways to approximate at software level. Memoization can be applied. Some iterations of loops can be skipped (termed as loop perforation) to achieve a result faster. Some tasks can also be skipped, for example when a run-time condition suggests that those tasks are not going to be useful (task skipping). Monte Carlo algorithms and Randomized algorithms trade correctness for execution time guarantees.[14] The computation can be reformulated according to paradigms that allow easily the acceleration on specialized hardware, e.g. a neural processing unit.[15]
Approximate system
In an approximate system,[16] different subsystems of the system such as the processor, memory, sensor, and communication modules are synergistically approximated to obtain a much better system-level Q-E trade-off curve compared to individual approximations to each of the subsystems.

Application areas

Approximate computing has been used in a variety of domains where the applications are error-tolerant, such as multimedia processing, machine learning, signal processing, scientific computing, etc. Google is using this approach in their Tensor processing units (TPU, a custom ASIC).
Derived paradigms

The main issue in approximate computing is the identification of the section of the application that can be approximated. In the case of large scale applications, it is very common to find people holding the expertise on approximate computing techniques not having enough expertise on the application domain (and vice versa). In order to solve this problem, programming paradigms[17][18] have been proposed. They all have in common the clear role separation between application programmer and application domain expert. These approaches allow the spread of the most common optimizations and approximate computing techniques.
See also

Artificial neural network
PCMOS

References

Mittal, Sparsh (May 2016). "A Survey of Techniques for Approximate Computing". ACM Comput. Surv. ACM. 48 (4): 62:1–62:33. doi:10.1145/2893356.
A. Sampson, et al. "EnerJ: Approximate data types for safe and general low-power computation", In ACM SIGPLAN Notices, vol. 46, no. 6, 2011.
J. Echavarria, et al. "FAU: Fast and Error-Optimized Approximate Adder Units on LUT-Based FPGAs", FPT, 2016.
J. Miao, et al. "Modeling and synthesis of quality-energy optimal approximate adders", ICCAD, 2012
Rehman, Semeen; El-Harouni, Walaa; Shafique, Muhammad; Kumar, Akash; Henkel, Jörg (2016-11-07). Architectural-space exploration of approximate multipliers. ACM. p. 80. doi:10.1145/2966986.2967005. ISBN 9781450344661.
S. Venkataramani, et al. "SALSA: systematic logic synthesis of approximate circuits", DAC, 2012.
J. Miao, et al. "Approximate logic synthesis under general error magnitude and frequency constraints", ICCAD, 2013
R. Hegde et al. "Energy-efficient signal processing via algorithmic noise-tolerance", ISLPED, 1999.
Raha, A.; Sutar, S.; Jayakumar, H.; Raghunathan, V. (July 2017). "Quality Configurable Approximate DRAM". IEEE Transactions on Computers. 66 (7): 1172–1187. doi:10.1109/TC.2016.2640296. ISSN 0018-9340.
Kim, Yongjune; Choi, Won Ho; Guyot, Cyril; Cassuto, Yuval (December 2019). "On the Optimal Refresh Power Allocation for Energy-Efficient Memories". 2019 IEEE Global Communications Conference (GLOBECOM). Waikoloa, HI, USA: IEEE: 1–6. arXiv:1907.01112. doi:10.1109/GLOBECOM38437.2019.9013465. ISBN 978-1-7281-0962-6.
Frustaci, Fabio; Blaauw, David; Sylvester, Dennis; Alioto, Massimo (June 2016). "Approximate SRAMs With Dynamic Energy-Quality Management". IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 24 (6): 2128–2141. doi:10.1109/TVLSI.2015.2503733. ISSN 1063-8210.
Kim, Yongjune; Kang, Mingu; Varshney, Lav R.; Shanbhag, Naresh R. (2018). "Generalized Water-filling for Source-aware Energy-efficient SRAMs". IEEE Transactions on Communications: 1–1. arXiv:1710.07153. doi:10.1109/TCOMM.2018.2841406. ISSN 0090-6778.
Kim, Yongjune; Jeon, Yoocharn; Guyot, Cyril; Cassuto, Yuval (June 2020). "Optimizing the Write Fidelity of MRAMs". 2020 IEEE International Symposium on Information Theory (ISIT). Los Angeles, CA, USA: IEEE: 792–797. doi:10.1109/ISIT44484.2020.9173990. ISBN 978-1-7281-6432-8.
C.Alippi, Intelligence for Embedded Systems: a Methodological approach, Springer, 2014, pp. 283
H. Esmaeilzadeh, et al. "Neural acceleration for general-purpose approximate programs", MICRO, 2012
Raha, Arnab; Raghunathan, Vijay (2017). "Towards Full-System Energy-Accuracy Tradeoffs: A Case Study of An Approximate Smart Camera System". Proceedings of the 54th Annual Design Automation Conference 2017. DAC '17. New York, NY, USA: ACM: 74:1–74:6. doi:10.1145/3061639.3062333. ISBN 9781450349277.
Nguyen, Donald; Lenharth, Andrew; Pingali, Keshav (2013). "A lightweight infrastructure for graph analytics". Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles. ACM: 456–471. doi:10.1145/2517349.2522739. ISBN 9781450323888.
Silvano, Cristina; Agosta, Giovanni; Cherubin, Stefano; Gadioli, Davide; Palermo, Gianluca; Bartolini, Andrea; Benini, Luca; Martinovič, Jan; Palkovič, Martin; Slaninová, Kateřina; Bispo, João; Cardoso, João M. P.; Rui, Abreu; Pinto, Pedro; Cavazzoni, Carlo; Sanna, Nico; Beccari, Andrea R.; Cmar, Radim; Rohou, Erven (2016). "The ANTAREX approach to autotuning and adaptivity for energy efficient HPC systems" (PDF). Proceedings of the ACM International Conference on Computing Frontiers. ACM: 288–293. doi:10.1145/2903150.2903470. hdl:11585/588256. ISBN 9781450341288.

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

World

Index

Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License