{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37865",
  "author_total": 4,
  "authors": [
    {
      "name": "Eugene Agyei-Kodie"
    },
    {
      "name": "Longxiu Huang"
    },
    {
      "name": "Shuang Li"
    },
    {
      "name": "Xiao Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cdwd6ayx5d7k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37865",
  "fulltext_url": null,
  "id": "1cdwd6ayx5d7k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37865",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7214914749",
  "pdf_url": "https://arxiv.org/pdf/2609.37865",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cdwd6ayx5d7k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37865",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37865"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing",
  "title_text": "Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/1cdwd6ayx5d7k",
  "venue": "arXiv",
  "versions": []
}