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Surv."],"published-print":{"date-parts":[[2026,10,31]]},"abstract":"<jats:p>\n                    Efficient numerical computation is foundational to many disciplines, whose computing demands continue to grow dramatically, yet their continued scaling is jeopardized by the slowdown in Moore\u2019s law.\n                    <jats:italic toggle=\"yes\">Multi-function multi-way analog<\/jats:italic>\n                    (MFMWA) architectures represent a promising computing framework that supports in-memory computation of matrix operations and offers the potential for tremendous improvements in computation time and energy consumption, but at the expense of inherent unpredictability and noise which prevents such architectures from supporting reliable numerical computation in general. In this article, we summarize and review a recent novel combination of MFMWA architectures and randomized algorithms tailored to these architectures that seek to mitigate the detrimental impact of imperfect analog computations with the goal of realizing the promising benefits of such advances in analog architectures for numerical speedups and energy reductions across various disciplines. Through a mixture of analysis, physical measurements and simulations, we organize and review recent research results that demonstrate the potential to achieve orders of magnitude reduction in both computation time and energy consumption for broadly applicable core numerical methods with algorithmic solution accuracy similar to digital computers. Together, these results provide understanding and insights into the computational and energy efficiencies of such a combination of MFMWA architectures and tailored randomized algorithms.\n                  <\/jats:p>","DOI":"10.1145\/3820882","type":"journal-article","created":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T20:57:18Z","timestamp":1781297838000},"page":"1-36","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Advances in Analog Architectures and Randomized Algorithms: Computational and Energy Efficiencies"],"prefix":"10.1145","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1474-8995","authenticated-orcid":false,"given":"Vasileios","family":"Kalantzis","sequence":"first","affiliation":[{"name":"Mathematical Sciences Department, IBM Research","place":["Yorktown Heights, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5195-8441","authenticated-orcid":false,"given":"Mark S.","family":"Squillante","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, IBM Research","place":["Yorktown Heights, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6942-7158","authenticated-orcid":false,"given":"Shashanka","family":"Ubaru","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, IBM Research","place":["Yorktown Heights, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5677-1723","authenticated-orcid":false,"given":"Tayfun","family":"Gokmen","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, IBM Research","place":["Yorktown Heights, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0657-0683","authenticated-orcid":false,"given":"Chai Wah","family":"Wu","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, IBM Research","place":["Yorktown Heights, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8013-3695","authenticated-orcid":false,"given":"Anshul","family":"Gupta","sequence":"additional","affiliation":[{"name":"New Yorkers for Clean Power","place":["Kingston, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1688-9030","authenticated-orcid":false,"given":"Haim","family":"Avron","sequence":"additional","affiliation":[{"name":"Tel Aviv University","place":["Tel Aviv-Yafo, Israel"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8260-0231","authenticated-orcid":false,"given":"Tomasz","family":"Nowicki","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, IBM Research","place":["Yorktown Heights, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7988-4624","authenticated-orcid":false,"given":"Malte","family":"Rasch","sequence":"additional","affiliation":[{"name":"SonyAI","place":["Zurich, Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7111-5546","authenticated-orcid":false,"given":"Murat","family":"Onen","sequence":"additional","affiliation":[{"name":"MIT","place":["Boston, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-3952-4663","authenticated-orcid":false,"given":"Vanessa","family":"Lopez-Marrero","sequence":"additional","affiliation":[{"name":"Brookhaven National Laboratory","place":["Upton, United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5231-1439","authenticated-orcid":false,"given":"Effendi","family":"Leobandung","sequence":"additional","affiliation":[{"name":"IBM Research - 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Squillante, Chai Wah Wu, Anshul Gupta, Shashanka Ubaru, Tayfun Gokmen, and Lior Horesh. 2023. Solving sparse linear systems via flexible GMRES with in-memory analog preconditioning. In Proceedings of the 2023 IEEE High Performance Extreme Computing Conference (HPEC). 1\u20137."},{"key":"e_1_3_3_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4655(00)00065-5"},{"key":"e_1_3_3_45_2","unstructured":"Will Knight. 2020. AI Can Do Great Things - if It Doesn\u2019t Burn the Planet. Retrieved June 9 2021 from https:\/\/www.wired.com\/story\/ai-great-things-burn-planet\/"},{"key":"e_1_3_3_46_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-020-0761-8"},{"key":"e_1_3_3_47_2","first-page":"36.2.1\u201336.2.4","volume-title":"Proceedings of the 2020 IEEE International Electron Devices Meeting (IEDM)","author":"Kohda Y.","year":"2020","unstructured":"Y. Kohda, Y. Li, K. Hosokawa, S. Kim, R. Khaddam-Aljameh, Z. Ren, P. Solomon, T. Gokmen, S. Rajalingam, C. Baks, et\u00a0al. 2020. Unassisted true analog neural network training chip. In Proceedings of the 2020 IEEE International Electron Devices Meeting (IEDM). 36.2.1\u201336.2.4."},{"issue":"1","key":"e_1_3_3_48_2","first-page":"1","article-title":"A machine-compiled database of genome-wide association studies","volume":"10","author":"Kuleshov Volodymyr","year":"2019","unstructured":"Volodymyr Kuleshov, Jialin Ding, Christopher Vo, Braden Hancock, Alexander Ratner, Yang Li, Christopher R\u00e9, Serafim Batzoglou, and Michael Snyder. 2019. A machine-compiled database of genome-wide association studies. 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EnCharge raises $100M+ to accelerate AI using analog chips | TechCrunch \u2014 techcrunch.com. Retrieved February 15 2025 from https:\/\/techcrunch.com\/2025\/02\/13\/encharge-raises-100m-to-accelerate-ai-using-analog-chips\/"},{"key":"e_1_3_3_55_2","doi-asserted-by":"publisher","DOI":"10.1109\/JETCAS.2018.2796379"},{"key":"e_1_3_3_56_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41588-021-00870-7"},{"issue":"11","key":"e_1_3_3_57_2","doi-asserted-by":"crossref","first-page":"2000085","DOI":"10.1002\/aisy.202000085","article-title":"Memristors - From in-memory computing, deep learning acceleration, and spiking neural networks to the future of neuromorphic and bio-inspired computing","volume":"2","author":"Mehonic Adnan","year":"2020","unstructured":"Adnan Mehonic, Abu Sebastian, Bipin Rajendran, Osvaldo Simeone, Eleni Vasilaki, and Anthony J. Kenyon. 2020. 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Retrieved November 2 2021 from https:\/\/www.nvidia.com\/en-us\/data-center\/a100\/"},{"key":"e_1_3_3_61_2","doi-asserted-by":"publisher","DOI":"10.1101\/gr.5741407"},{"key":"e_1_3_3_62_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.0030160"},{"key":"e_1_3_3_63_2","doi-asserted-by":"publisher","DOI":"10.1080\/14786440109462720"},{"key":"e_1_3_3_64_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2020.107281"},{"key":"e_1_3_3_65_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-51221-z"},{"key":"e_1_3_3_66_2","doi-asserted-by":"publisher","DOI":"10.1109\/MDAT.2019.2952341"},{"key":"e_1_3_3_67_2","first-page":"1","volume-title":"Proceedings of the 2021 IEEE 3rd International Conference on Artificial Intelligence Circuits and Systems (AICAS)","author":"Rasch Malte J.","year":"2021","unstructured":"Malte J. Rasch, Diego Moreda, Tayfun Gokmen, Manuel Le Gallo, Fabio Carta, Cindy Goldberg, Kaoutar El Maghraoui, Abu Sebastian, and Vijay Narayanan. 2021. 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