{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T15:50:34Z","timestamp":1757778634506,"version":"3.41.0"},"reference-count":30,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T00:00:00Z","timestamp":1565913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100003399","name":"Shanghai Science and Technology Committee","doi-asserted-by":"crossref","award":["18ZR1421400"],"award-info":[{"award-number":["18ZR1421400"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Alibaba Group through Alibaba Innovative Research (AIR) Program"},{"name":"State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61332001, 61834006, 61772331, 61602300"],"award-info":[{"award-number":["61332001, 61834006, 61772331, 61602300"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Key Research and Development Program of China","award":["2018YFB1403400"],"award-info":[{"award-number":["2018YFB1403400"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Des. Autom. Electron. Syst."],"published-print":{"date-parts":[[2019,11,30]]},"abstract":"<jats:p>Approximate computing is a promising design paradigm that introduces a new dimension\u2014error\u2014into the original design space. By allowing the inexact computation in error-tolerance applications, approximate computing can gain both performance and energy efficiency. A neural network\u00a0(NN) is a universal approximator in theory and possesses a high level of parallelism. The emerging deep neural network accelerators deployed with NN-based approximator is thereby a promising candidate for approximate computing. Nevertheless, the approximation result must satisfy the users\u2019 requirement, and the approximation result varies across different applications. We normally deploy an NN-based classifier to ensure the approximation quality. Only the inputs predicted to meet the quality requirement can be executed by the approximator. The potential of these two NNs, however, is fully explored; the involving of two NNs in approximate computing imposes critical optimization questions, such as two NNs\u2019 distinct views of the input data space, how to train the two correlated NNs, and what are their topologies.<\/jats:p>\n          <jats:p>In this article, we propose a novel NN-based approximate computing framework with quality insurance. We advocate a co-training approach that trains the classifier and the approximator alternately to maximize the agreement of the two NNs on the input space. In each iteration, we coordinate the training of the two NNs with a judicious selection of training data. Next, we explore different selection policies and propose to select training data from multiple iterations, which can enhance the invocation of the approximate accelerator. In addition, we optimize the classifier by integrating a dynamic threshold tuning algorithm to improve the invocation of the approximate accelerator further. The increased invocation of accelerator leads to higher energy efficiency under the same quality requirement. We propose two efficient algorithms to explore the smallest topology of the NN-based approximator and the classifier to achieve the quality requirement. The first algorithm straightforward searches the minimum topology using a greedy strategy. However, the first algorithm incurs too much training overhead. To solve this issue, the second one gradually grows the topology of NNs to match the quality requirement by transferring the learned parameters. Experimental results show significant improvement on the quality and the energy efficiency compared to the existing NN-based approximate computing frameworks.<\/jats:p>","DOI":"10.1145\/3342239","type":"journal-article","created":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T19:35:19Z","timestamp":1565984119000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Energy-Efficient and Quality-Assured Approximate Computing Framework Using a Co-Training Method"],"prefix":"10.1145","volume":"24","author":[{"given":"Li","family":"Jiang","sequence":"first","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhuoran","family":"Song","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyue","family":"Song","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengwen","family":"Xu","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Xu","sequence":"additional","affiliation":[{"name":"Chinese University of Hong Kong, Shatin, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naifeng","family":"Jing","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weifeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Alibaba Group, Hangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyao","family":"Liang","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,8,16]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TETC.2016.2598726"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1809028.1806620"},{"key":"e_1_2_1_3_1","volume-title":"Proceedings of the 2014 19th Asia and South Pacific Design Automation Conference (ASP-DAC\u201914)","author":"Du Zidong","year":"2014","unstructured":"Zidong Du , Krishna Palem , Avinash Lingamneni , Olivier Temam , Yunji Chen , and Chengyong Wu . 2014 . 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Learning both weights and connections for efficient neural networks. In Proceedings of the 28th International Conference on Neural Information Processing Systems, Volume 1 (NIPS\u201915). 1135--1143."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1166\/jolpe.2018.1575"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(91)90009-T"},{"volume-title":"Proceedings of the 2019 Design, Automation, and Test in Europe Conference and Exhibition (DATE\u201919)","author":"Imani M.","key":"e_1_2_1_12_1","unstructured":"M. Imani , R. Garcia , A. Huang , and T. Rosing . 2019. CADE: Configurable approximate divider for energy efficiency . In Proceedings of the 2019 Design, Automation, and Test in Europe Conference and Exhibition (DATE\u201919) . 586--589. M. Imani, R. Garcia, A. Huang, and T. Rosing. 2019. CADE: Configurable approximate divider for energy efficiency. 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Chippa, A. Raghunathan, and K. Roy. 2011. Design of voltage-scalable meta-functions for approximate computing. In Proceedings of the 2011 Design, Automation, and Test in Europe Conference and Exhibition (DATE\u201911). 1--6."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1594233.1594282"},{"volume-title":"Proceedings of the 2016 Design, Automation, and Test in Europe Conference and Exhibition (DATE\u201916)","author":"Rahimi Abbas","key":"e_1_2_1_21_1","unstructured":"Abbas Rahimi , Luca Benini , and Rajesh K. Gupta . 2016. An approximation workflow for exploiting data-level parallelism in FPGA acceleration . In Proceedings of the 2016 Design, Automation, and Test in Europe Conference and Exhibition (DATE\u201916) . 1279--1284. Abbas Rahimi, Luca Benini, and Rajesh K. Gupta. 2016. An approximation workflow for exploiting data-level parallelism in FPGA acceleration. 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