Recursive Sketched Interpolation: Efficient Hadamard Products of Tensor Trains
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Quantum Physics arXiv:2602.17974 (quant-ph) [Submitted on 20 Feb 2026] Title:Recursive Sketched Interpolation: Efficient Hadamard Products of Tensor Trains Authors:Zhaonan Meng, Yuehaw Khoo, Jiajia Li, E.
Miles Stoudenmire View a PDF of the paper titled Recursive Sketched Interpolation: Efficient Hadamard Products of Tensor Trains, by Zhaonan Meng and 3 other authors View PDF Abstract:The Hadamard product of two tensors in the tensor-train (TT) format is a fundamental operation across various applications, such as TT-based function multiplication for nonlinear differential equations or convolutions. However, conventional methods for computing this product typically scale as at least $\mathcal{O}(\chi^4)$ with respect to the TT bond dimension (TT-rank) $\chi$, creating a severe computational bottleneck in practice. By combining randomized tensor-train sketching with slice selection via interpolative decomposition, we introduce Recursive Sketched Interpolation (RSI), a ``scale product'' algorithm that computes the Hadamard product of TTs at a computational cost of $\mathcal{O}(\chi^3)$. Benchmarks across various TT scenarios demonstrate that RSI offers superior scalability compared to traditional methods while maintaining comparable accuracy. We generalize RSI to compute more complex operations, including Hadamard products of multiple TTs and other element-wise nonlinear mappings, without increasing the complexity beyond $\mathcal{O}(\chi^3)$. Comments: Subjects: Quantum Physics (quant-ph); Numerical Analysis (math.NA) Cite as: arXiv:2602.17974 [quant-ph] (or arXiv:2602.17974v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.17974 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhaonan Meng [view email] [v1] Fri, 20 Feb 2026 04:07:37 UTC (1,499 KB) Full-text links: Access Paper: View a PDF of the paper titled Recursive Sketched Interpolation: Efficient Hadamard Products of Tensor Trains, by Zhaonan Meng and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.NA math math.NA References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)