Guaranteed Low-Rank Tensor Recovery from Modewise Measurements via Normalized Block-Weighted Riemannian Gradient Descent

Abstract:We consider the recovery of low-multilinear-rank tensors from linear measurements and propose an adaptive block-weighted modewise Riemannian gradient descent method. The method combines memory-efficient modewise measurements with a normalized adaptive weighting strategy for the core and factor components of the Riemannian gradient. The weighting improves convergence without increasing the multilinear-rank bound of the search direction or the size of the reduced core used for retraction. Under the tensor restricted isometry property and a suitable initialization, we establish local linear convergence and derive sampling guarantees for sub-Gaussian and subsampled orthogonal with random sign (SORS) measurements. Numerical experiments on synthetic low-Tucker-rank tensors show that the proposed method reduces iteration counts and computational time while maintaining reliable recovery performance, especially near the recovery threshold and for structured SORS measurements.

Machine Learning (cs.LG)

arXiv:2609.24679 [cs.LG]

(or arXiv:2609.24679v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.24679 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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