# Iterative Hard Thresholding for Low CP-rank Tensor Models

arXiv: https://arxiv.org/abs/1908.08479 · HTML: https://mlsanity.com/paper/1908.08479/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2019.

## Built on by (most cited first, 9 of 9)

- [Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery](https://mlsanity.com/paper/2401.02592/) (2024)
- [Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decomposition](https://mlsanity.com/paper/2406.06002/) (2024)
- [A Scalable Factorization Approach for High-Order Structured Tensor Recovery](https://mlsanity.com/paper/2506.16032/) (2025)
- [Robust Low-rank Tensor Train Recovery](https://mlsanity.com/paper/2410.15224/) (2024)
- [Federated Gradient Matching Pursuit](https://mlsanity.com/paper/2302.10755/) (2023)
- [Linear Convergence of Reshuffling Kaczmarz Methods With Sparse Constraints](https://mlsanity.com/paper/2304.10123/) (2023)
- [Information-Theoretic Guarantees for Recovering Low-Rank Tensors from Symmetric Rank-One Measurements](https://mlsanity.com/paper/2502.05134/) (2025)
- [Normalized Iterative Hard Thresholding for Tensor Recovery](https://mlsanity.com/paper/2507.04228/) (2025)
- [StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing](https://mlsanity.com/paper/2601.13522/) (2026)

## Abstract (arXiv)

Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical guarantees. However, extensions to tensor recovery have only recently began to be studied and developed, despite an abundance of practical tensor applications. Recently, a tensor variant of the Iterative Hard Thresholding method was proposed and theoretical results were obtained that guarantee exact recovery of tensors with low Tucker rank. In this paper, we utilize the same tensor version of the Restricted Isometry Property (RIP) to extend these results for tensors with low CANDECOMP/PARAFAC (CP) rank. In doing so, we leverage recent results on efficient approximations of CP decompositions that remove the need for challenging assumptions in prior works. We complement our theoretical findings with empirical results that showcase the potential of the approach.