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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Publication details
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Cite this article
APA 7
Agyei-Kodie, E., Huang, L., Li, S., & Liang, X. (2026). Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing. https://omanscience.com/en/articles/strict-saddle-landscapes-and-multi-rank-geometry-in-low-tubal-rank-tensor-sensing
MLA 9
Agyei-Kodie, Eugene, et al. "Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing." https://omanscience.com/en/articles/strict-saddle-landscapes-and-multi-rank-geometry-in-low-tubal-rank-tensor-sensing.
Chicago (author–date)
Agyei-Kodie, Eugene, Longxiu Huang, Shuang Li, and Xiao Liang. 2026. "Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing." https://omanscience.com/en/articles/strict-saddle-landscapes-and-multi-rank-geometry-in-low-tubal-rank-tensor-sensing.
Harvard
Agyei-Kodie, E., Huang, L., Li, S. and Liang, X. (2026) 'Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing', Available at: https://omanscience.com/en/articles/strict-saddle-landscapes-and-multi-rank-geometry-in-low-tubal-rank-tensor-sensing.
Vancouver
Agyei-Kodie E, Huang L, Li S, Liang X. Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing. https://omanscience.com/en/articles/strict-saddle-landscapes-and-multi-rank-geometry-in-low-tubal-rank-tensor-sensing
IEEE
E. Agyei-Kodie, L. Huang, S. Li, and X. Liang, "Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing," https://omanscience.com/en/articles/strict-saddle-landscapes-and-multi-rank-geometry-in-low-tubal-rank-tensor-sensing.