Research map / Learning theory and algorithms / Matrix and tensor methods
Randomized tensor decomposition algorithms
Speeds up CP, Tucker and ring decompositions through sketching and sampling with guarantees.
43 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Matrix and tensor methods, keyword cluster “tensors · decomposition · rank tensor”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
9 papers in 2023–24 and 2 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 5.2% to 1.1%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Sublinear Time Orthogonal Tensor Decomposition (NeurIPS 2016 · 30 citations)
- 2017 · On Tensor Train Rank Minimization : Statistical Efficiency and Scalable Algorithm (NeurIPS 2017 · 32 citations)
- 2018 · Low-Rank Tucker Decomposition of Large Tensors Using TensorSketch (NeurIPS 2018 · 69 citations)
- 2019 · A Recursive Algorithm for Projected Model Counting (AAAI 2019 · 17 citations)
- 2020 · Provable Online CP/PARAFAC Decomposition of a Structured Tensor via Dictionary Learning (NeurIPS 2020 · 8 citations)
- 2021 · Fast and accurate randomized algorithms for low-rank tensor decompositions (NeurIPS 2021 · 9 citations)
- 2022 · Handling Slice Permutations Variability in Tensor Recovery (AAAI 2022 · 6 citations)
- 2023 · Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition (NeurIPS 2023 · 2 citations)
- 2024 · Efficient Leverage Score Sampling for Tensor Train Decomposition (NeurIPS 2024 · 3 citations)
- 2026 · Subspace Kernel Learning on Tensor Sequences (ICLR 2026 · 0 citations)
Earliest papers here
- Sublinear Time Orthogonal Tensor Decomposition (NeurIPS 2016 · 30 citations)
- SPALS: Fast Alternating Least Squares via Implicit Leverage Scores Sampling (NeurIPS 2016 · 26 citations)
- Tensor Decomposition via Joint Matrix Schur Decomposition (ICML 2016 · 9 citations)
What has been tried
40 papers here report 316 measured changes (a component added, removed or swapped, compared with a baseline): helped 59%, no clear effect 17%, hurt 20%, mixed 4%. Papers mostly publish changes that helped, so "helped" is over-represented.
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 11 papers; from OpenAlex and the papers' affiliations).
- University of California, Berkeley · 3 papers
- Lawrence Berkeley National Lab · 2 papers
Use it
Download BibTeX of 26 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Tensor network decompositions (45 papers)
- Low-rank tensor completion (45 papers)
Elsewhere in the topic
- Low-rank approximation theory (142 papers)
- Matrix completion and factorization (118 papers)
- Nonconvex low-rank and sparse optimization (112 papers)
- Randomized sketching for matrices (96 papers)
- Sparse regression with guarantees (94 papers)
- High-dimensional estimation theory (89 papers)
- Structured low-rank learning (87 papers)
- Geometry of low-rank and SPD structure (71 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).