Research map / Learning theory and algorithms / Matrix and tensor methods
Tensor network decompositions
Represents high-order tensors with tensor networks and tensor trains, with theory on their learning capacity.
45 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.
4 papers in 2023–24 and 11 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 2.3% to 5.9%.
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 · Supervised Learning with Tensor Networks (NeurIPS 2016 · 196 citations)
- 2017 · Scalable Demand-Aware Recommendation (NeurIPS 2017 · 12 citations)
- 2018 · Canonical Tensor Decomposition for Knowledge Base Completion (ICML 2018 · 48 citations)
- 2019 · Crowdsourcing via Pairwise Co-occurrences: Identifiability and Algorithms (NeurIPS 2019 · 16 citations)
- 2020 · Tensor Decompositions for Temporal Knowledge Base Completion (ICLR 2020 · 131 citations)
- 2021 · Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion (AAAI 2021 · 162 citations)
- 2022 · Random Tensor Theory for Tensor Decomposition (AAAI 2022 · 12 citations)
- 2023 · Constructive TT-representation of the tensors given as index interaction functions with applications (ICLR 2023 · 3 citations)
- 2024 · HDQMF: Holographic Feature Decomposition Using Quantum Algorithms (CVPR 2024 · 4 citations)
- 2025 · Tensor Decomposition Meets Knowledge Compilation: A Study Comparing Tensor Trains with OBDDs (AAAI 2025 · 1 citation)
- 2026 · Grokking Finite-Dimensional Algebra (ICML 2026 · 0 citations)
Earliest papers here
- Supervised Learning with Tensor Networks (NeurIPS 2016 · 196 citations)
- Polynomial Networks and Factorization Machines: New Insights and Efficient Training Algorithms (ICML 2016 · 60 citations)
- Tensor Switching Networks (NeurIPS 2016 · 2 citations)
What has been tried
37 papers here report 276 measured changes (a component added, removed or swapped, compared with a baseline): helped 63%, no clear effect 14%, hurt 15%, mixed 8%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase hypervector dimension | Factorization · peak probability of finding a marked state | Helped | HDQMF: Holographic Feature Decomposition Using Quantum Algorithms (CVPR 2024 · 4 citations) | |
| Add more channels to GTP | 3D Tetris pieces · ability to distinguish chiral pieces | No clear effect | The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Products (ICML 2025 · 0 citations) | |
| Increase the number of source tasks from K=1 to K=8 | akiyo video completion · PSNR | 22.19 -> 40.32 | Helped | Low-Rank Tensor Transitions (LoRT) for Transferable Tensor Regression (ICML 2025) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 15 papers; from OpenAlex and the papers' affiliations).
- China University of Petroleum-Beijing at Karamay · 3 papers
- RIKEN AIP · 3 papers
- RIKEN · 3 papers
- Guangdong University of Technology · 3 papers
Use it
Download BibTeX of 32 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Randomized tensor decomposition algorithms (43 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).