{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T05:50:17Z","timestamp":1782798617487,"version":"3.54.5"},"reference-count":38,"publisher":"American Association for the Advancement of Science (AAAS)","content-domain":{"domain":["spj.science.org"],"crossmark-restriction":true},"short-container-title":["Intell Comput"],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p>\n            The Mach\u2013Zehnder interferometer (MZI) mesh, a mainstream structure for optical matrix-vector multiplication (MVM), has been widely employed in recently developed optical neural networks (ONNs) and combination optimization problem solvers. The conventional MZI mesh was designed specifically for complex-valued optical MVM. The network includes 2\n            <jats:italic>N<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            phase shifters, and coherent detection is indispensable for retrieving the output complex-valued vectors. Nonetheless, the majority of applications, including ONNs, merely require real-valued optical matrices with\n            <jats:italic>N<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            degrees of freedom (DOFs). The DOF gap between the 2 types of matrices results in a severe redundancy in the number of phase shifters when the conventional MZI mesh is applied to implement real-valued optical MVM. In this study, we propose a simplified MZI mesh for performing real-valued incoherent optical MVM. It has\n            <jats:italic>N<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            phase shifters and an optical depth of\n            <jats:italic>N<\/jats:italic>\n            + 1, and it outperforms the conventional MZI mesh. Furthermore, we constructed an ONN with the proposed MZI mesh and successfully performed the iris classification task via in\u00a0situ training of particle swarm optimization. More importantly, we introduced a matched on-chip nonlinear activation function, so the proposed MZI mesh can be cascaded onto a single chip. Overall, the proposed real-valued MZI mesh and in\u00a0situ training method are space efficient, energy efficient, scalable, and robust to fabrication errors. Therefore, they are suitable for large-scale ONNs.\n          <\/jats:p>","DOI":"10.34133\/icomputing.0047","type":"journal-article","created":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T18:55:11Z","timestamp":1689360911000},"update-policy":"https:\/\/doi.org\/10.34133\/aaas_crossmark_01","source":"Crossref","is-referenced-by-count":33,"title":["Real-Valued Optical Matrix Computing with Simplified MZI Mesh"],"prefix":"10.34133","volume":"2","author":[{"given":"Bo","family":"Wu","sequence":"first","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaojie","family":"Liu","sequence":"additional","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junwei","family":"Cheng","sequence":"additional","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenchan","family":"Dong","sequence":"additional","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hailong","family":"Zhou","sequence":"additional","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianji","family":"Dong","sequence":"additional","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."},{"name":"Optics Valley Laboratory, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, \rChinese Academy of Sciences, Beijing 100083, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinliang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Wuhan National Laboratory for Optoelectronics, \rHuazhong University of Science and Technology, Wuhan 430074, China."},{"name":"Optics Valley Laboratory, Wuhan 430074, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"221","published-online":{"date-parts":[[2023,9,19]]},"reference":[{"issue":"1","key":"e_1_3_4_2_2","doi-asserted-by":"crossref","DOI":"10.1186\/s43074-021-00042-0","article-title":"The challenges of modern computing and new opportunities for optics","volume":"2","author":"Li C","year":"2021","unstructured":"Li C, Zhang X, Li J, Fang T, Dong X. 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