StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing

• URL: http://arxiv.org/abs/2601.13522v1
• Date: Tue, 20 Jan 2026 02:18:20 GMT
• Title: StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing
• Authors: Shuang Li,
• Abstract summary: Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning.<n>Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations.<n>In this work, we propose a alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization.
• Score: 7.549565266107219
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace structures in high-dimensional data. Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations, while most stochastic factorized approaches are restricted to tensor decomposition settings. In this work, we propose a stochastic alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization. The proposed method avoids repeated tensor projections and enables efficient mini-batch updates on low-dimensional tensor factors. Numerical experiments on synthetic tensor sensing demonstrate that the proposed algorithm exhibits favorable convergence behavior in wall-clock time compared with representative stochastic tensor recovery baselines.

Related papers

• Score-Based Model for Low-Rank Tensor Recovery [49.158601255093416]
  Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis.<n>Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions.<n>We propose a score-based model that eliminates the need for predefined structural or distributional assumptions.
  arXiv  Detail & Related papers  (2025-06-27T15:05:37Z)
• Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization [49.85875869048434]
  We propose a CP-based low-rank tensor function parameterized by neural networks for implicit neural representation.<n>To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components.<n>For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator.
  arXiv  Detail & Related papers  (2025-06-27T11:23:10Z)
• A Scalable Factorization Approach for High-Order Structured Tensor Recovery [30.876260188209105]
  decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters.<n>A computationally memory-efficient approach to these problems is to optimize directly over factors using local algorithms.<n>We present a unified framework for factorization approach to solving various tensor decomposition problems.
  arXiv  Detail & Related papers  (2025-06-19T05:07:07Z)
• Tensor cumulants for statistical inference on invariant distributions [49.80012009682584]
  We show that PCA becomes computationally hard at a critical value of the signal's magnitude. We define a new set of objects, which provide an explicit, near-orthogonal basis for invariants of a given degree. It also lets us analyze a new problem of distinguishing between different ensembles.
  arXiv  Detail & Related papers  (2024-04-29T14:33:24Z)
• Optimizing Orthogonalized Tensor Deflation via Random Tensor Theory [5.124256074746721]
  This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor. Non-orthogonal components may alter the tensor deflation mechanism, thereby preventing efficient recovery. An efficient tensor deflation algorithm is proposed by optimizing the parameter introduced in the deflation mechanism.
  arXiv  Detail & Related papers  (2023-02-11T22:23:27Z)
• Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery [52.21846313876592]
  Low-rank tensor function representation (LRTFR) can continuously represent data beyond meshgrid with infinite resolution. We develop two fundamental concepts for tensor functions, i.e., the tensor function rank and low-rank tensor function factorization. Our method substantiates the superiority and versatility of our method as compared with state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-12-01T04:00:38Z)
• MTC: Multiresolution Tensor Completion from Partial and Coarse Observations [49.931849672492305]
  Existing completion formulation mostly relies on partial observations from a single tensor. We propose an efficient Multi-resolution Completion model (MTC) to solve the problem.
  arXiv  Detail & Related papers  (2021-06-14T02:20:03Z)
• Understanding Deflation Process in Over-parametrized Tensor Decomposition [17.28303004783945]
  We study the training dynamics for gradient flow on over-parametrized tensor decomposition problems. Empirically, such training process often first fits larger components and then discovers smaller components.
  arXiv  Detail & Related papers  (2021-06-11T18:51:36Z)
• Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements [30.395874385570007]
  A fundamental task is to faithfully recover tensors from highly incomplete measurements. We develop an algorithm to directly recover the tensor factors in the Tucker decomposition. We show that it provably converges at a linear independent rate of the ground truth tensor for two canonical problems.
  arXiv  Detail & Related papers  (2021-04-29T17:44:49Z)
• Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion [3.498620439731324]
  We introduce a unified low-rank and sparse enhanced Tucker decomposition model for tensor completion. Our model possesses a sparse regularization term to promote a sparse core tensor, which is beneficial for tensor data compression. It is remarkable that our model is able to deal with different types of real-world data sets, since it exploits the potential periodicity and inherent correlation properties appeared in tensors.
  arXiv  Detail & Related papers  (2020-10-01T12:45:39Z)
• Multi-View Spectral Clustering Tailored Tensor Low-Rank Representation [105.33409035876691]
  This paper explores the problem of multi-view spectral clustering (MVSC) based on tensor low-rank modeling. We design a novel structured tensor low-rank norm tailored to MVSC. We show that the proposed method outperforms state-of-the-art methods to a significant extent.
  arXiv  Detail & Related papers  (2020-04-30T11:52:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.