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.
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 Riemann...
Through high-probability concentration bounds on the random measurement operator, a novel landscape guarantee with statistically near-optimal sample complexity and recovery error is proved: new guarantees of a benign landscape under a weaker isometry condition.
Tensor-ring (TR) decompositions provide a natural representation of periodic systems but are difficult to optimize because the closed geometry prevents a global canonical form and leads to costly, ill conditioned environments. Existing periodic DMRG methods alleviate this difficulty by compressing long environments to...
Matthieu Jeannin, A. Chessari, J. von Delft· 0 citations
This work is concerned with the numerical computation of Gross-Pitaevskii ground states using the tensor train (TT) format. We regard the problem as the minimization of the Gross-Pitaevskii energy functional under a unit mass constraint, and propose a first-order Riemannian optimization scheme that preserves both the m...
Ivan Bioli, Carlo Marcati, M. Rakhuba· 0 citations
The homogeneous form associated with a symmetric tensor, restricted to the sphere, is the objective of the best rank-one approximation problem and, with random coefficients, the energy of a mean-field spin glass. Its critical points have been studied extensively, but the global organization of the landscape they form i...
Low-rank adaptation (LoRA) has become the standard method for parameter-efficient fine-tuning of large pretrained models, yet theoretical explanations for why low-rank updates suffice remain incomplete. Most existing analyses rely on the Neural Tangent Kernel (NTK) regime, which linearizes the network around the pretra...
Long Nguyen-Chi, Quynh Nguyen, Thanh Nguyen-Cung et al.· 0 citations
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