{"paper":{"title":"Dynamic Tensor Product Regression","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Aravind Reddy, Lichen Zhang, Zhao Song","submitted_at":"2022-10-08T08:06:00Z","abstract_excerpt":"In this work, we initiate the study of \\emph{Dynamic Tensor Product Regression}. One has matrices $A_1\\in \\mathbb{R}^{n_1\\times d_1},\\ldots,A_q\\in \\mathbb{R}^{n_q\\times d_q}$ and a label vector $b\\in \\mathbb{R}^{n_1\\ldots n_q}$, and the goal is to solve the regression problem with the design matrix $A$ being the tensor product of the matrices $A_1, A_2, \\dots, A_q$ i.e. $\\min_{x\\in \\mathbb{R}^{d_1\\ldots d_q}}~\\|(A_1\\otimes \\ldots\\otimes A_q)x-b\\|_2$. At each time step, one matrix $A_i$ receives a sparse change, and the goal is to maintain a sketch of the tensor product $A_1\\otimes\\ldots \\otime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.03961","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.03961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}