Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing

Eugene Agyei-Kodie; Longxiu Huang; Shuang Li; Xiao Liang

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arXiv · 2609.37865

Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing

Eugene Agyei-Kodie·Longxiu Huang·Shuang Li·Xiao Liang

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Abstract

We study the optimization landscape of low-tubal-rank tensor sensing through a balanced factorization. Under a tubal restricted isometry condition, we establish a quantitative strict-saddle landscape with no spurious local minima for arbitrary Fourier multi-rank profiles. We further show that the local geometry depends on the Fourier-slice ranks rather than the tubal rank alone. Uniform ranks yield quadratic growth transverse to the solution orbit, whereas nonuniform ranks produce quartically flat directions through hidden frequency-wise overparameterization, even when the factor width equals the exact tubal rank. Numerical experiments illustrate the global optimization behavior and the contrasting local geometries.

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BibTeX RIS

Eugene Agyei-Kodie, Longxiu Huang, Shuang Li, Xiao Liang. 2026-09-29. Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing. https://arxiv.org/abs/2609.37865

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