mlsanityData to 14 Oct 2026

Tensor train completion: local recovery guarantees via Riemannian optimization

arXiv 2110.03975 ↗First posted 8 Oct 2021math.NA cs.LG cs.NAcited by 6

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Abstract (arXiv)

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 10 of its 62 references that are in the map. First posted on arXiv 8 Oct 2021.

Builds on

10 of 62 references.

References · 10

  1. 2018Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrievalcited by 71
  2. 2017Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolutioncited by 63
  3. 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
  4. 2013Square Deal: Lower Bounds and Improved Relaxations for Tensor Recoverycited by 37
  5. 2013Provable Inductive Matrix Completioncited by 32
  6. 2014On Tensor Completion via Nuclear Norm Minimizationcited by 32
  7. 2016Guarantees of Riemannian Optimization for Low Rank Matrix Completioncited by 19
  8. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  9. 2014Convergence results for projected line-search methods on varieties of low-rank matrices via Lojasiewicz inequalitycited by 10
  10. 2016Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completioncited by 10

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 3; 2025: 2.

6 papers.

  1. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  2. 2024Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decompositioncited by 4
  3. 2025A Scalable Factorization Approach for High-Order Structured Tensor Recoverycited by 4
  4. 2024Robust Low-rank Tensor Train Recoverycited by 2
  5. 2022Variational Bayesian inference for CP tensor completion with side informationcited by 1
  6. 2025Efficient Tensor Completion Algorithms for Highly Oscillatory Operatorscited by 0