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King Saud Univ. Comput. Inf. Sci."],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The heterogeneity of data between different clients limits the performance of federated learning training, and hyper-knowledge distillation has emerged as a potential solution to address heterogeneous data. However, existing hyper-knowledge distillation methods often sacrifice efficiency to improve model performance. To address these challenges, this paper proposes FedHDE, a novel federated learning framework based on hyper-knowledge distillation and efficient tensor optimization. FedHDE integrates a Dynamic Client Selection strategy within a teacher\u2013assistant\u2013student hierarchical structure to enhance global aggregation accuracy and reliability without relying on public datasets or server-side models. Furthermore, an efficient tensor optimization algorithm is introduced to improve numerical stability and reduce computation time. Theoretical analysis demonstrates that FedHDE achieves a convergence rate of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$O(1\/\\sqrt{T})$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>\/<\/mml:mo>\n                            <mml:msqrt>\n                              <mml:mi>T<\/mml:mi>\n                            <\/mml:msqrt>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , ensuring efficient and stable learning. Experimental results on the CIFAR10 dataset show that FedHDE improves both local and global accuracy by 0.14%\u20134.32%, while reducing training time by 65.28% compared to state-of-the-art baselines.Code is public at\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/anonymous.4open.science\/r\/FedHDE\" ext-link-type=\"uri\">https:\/\/anonymous.4open.science\/r\/FedHDE<\/jats:ext-link>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/s44443-026-00503-1","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T16:06:14Z","timestamp":1770998774000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["FedHDE: an efficient federated learning model based on hyper-knowledge distillation"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3398-5841","authenticated-orcid":false,"given":"Xingang","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-3141-1105","authenticated-orcid":false,"given":"Chuang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6809-044X","authenticated-orcid":false,"given":"Xiaofan","family":"Shao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5757-504X","authenticated-orcid":false,"given":"Tingzhi","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7454-0796","authenticated-orcid":false,"given":"He","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3991-6625","authenticated-orcid":false,"given":"Dongyan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"503_CR1","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s44443-025-00134-y","volume":"37","author":"SR Bandarapu","year":"2025","unstructured":"Bandarapu SR, Bilal M, Chatterjee P, Cheema AM, Rashid J, Kim J (2025) Blockchain-based federated learning framework for malicious node detection in internet of vehicles (iov) networks using fog and cloud computing. 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