发表机构
Michigan State University; Iowa State University（密歇根州立大学; 爱荷华州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过平衡分解分析低管秩张量感知的优化景观，建立严格鞍点性质，揭示局部几何由傅里叶切片秩决定，并区分均匀与非均匀秩下的不同增长行为。
AI 中文摘要
我们通过平衡分解研究低管秩张量感知的优化景观。在管状受限等距条件下，我们为任意傅里叶多秩分布建立了无虚假局部极小值的定量严格鞍点景观。我们进一步证明，局部几何取决于傅里叶切片秩而非仅管秩。均匀秩在解轨道横向上产生二次增长，而非均匀秩则通过隐藏的频率-wise 过参数化产生四次平坦方向，即使因子宽度等于精确管秩。数值实验展示了全局优化行为及对比性的局部几何。
英文摘要
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.
