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

arXiv · AI, language, vision and robotics · article · Sep 21, 2026 · UTC

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 conve

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