Research map / Learning theory and algorithms
Matrix and tensor methods: research map
1,074 accepted papers on Matrix and tensor methods in Learning theory and algorithms, from ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026), grouped into 3 clusters and 13 approaches. The busiest year so far is 2017.
Within Learning theory and algorithms, its share held steady from 7.8% in 2023–24 to 7.7% in 2025–26 (173 → 186 papers at ICML, NeurIPS, CVPR and AAAI, the venues with data for all four years).
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Approaches and key papers
matrices · matrix completion · rank matrix · 514 papers
Approaches in this cluster:
- Low-rank approximation theory (142 papers)
Analyzes error and perturbation bounds for SVD and low-rank estimation of matrices. - Matrix completion and factorization (118 papers)
Recovers low-rank matrices from partial entries via alternating minimization and sparse regularization. - Randomized sketching for matrices (96 papers)
Uses random projections and frequent-directions sketches for fast approximate linear algebra. - Structured low-rank learning (87 papers)
Applies low-rank structure to ranking, fairness and probability matrix problems with guarantees. - Geometry of low-rank and SPD structure (71 papers)
Studies rank, random matrix geometry and positive-definite manifolds in network training and learning.
Most cited and most cited since 2024:
- Polynomial Codes: an Optimal Design for High-Dimensional Coded Matrix Multiplication (NeurIPS 2017 · 382 citations)
- Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula (NeurIPS 2016 · 125 citations)
- HyperAttention: Long-context Attention in Near-Linear Time (ICLR 2024 · 9 citations)
- Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry (CVPR 2025 · 6 citations)
sparse · recovery · pca · 427 papers
Approaches in this cluster:
- Sparse regression with guarantees (94 papers)
Recovers sparse signals through hard thresholding, group sparsity and robust estimation with statistical guarantees. - High-dimensional estimation theory (89 papers)
Analyzes spectral and message-passing estimators in high-dimensional regression and multi-index models. - Signal recovery and phase retrieval (66 papers)
Recovers signals from measurements through convex programming and generative or structured priors. - Sparse and robust PCA (66 papers)
Designs provable algorithms for sparse PCA and subspace recovery under noise, missing data and outliers. - Nonconvex low-rank and sparse optimization (112 papers)
Gives global convergence and landscape results for matrix factorization and primal-dual coordinate methods.
Most cited and most cited since 2024:
- Theoretical Linear Convergence of Unfolded ISTA and Its Practical Weights and Thresholds (NeurIPS 2018 · 151 citations)
- PD-Sparse : A Primal and Dual Sparse Approach to Extreme Multiclass and Multilabel Classification (ICML 2016 · 130 citations)
- Secure Distributed Sparse Gaussian Process Models Using Multi-Key Homomorphic Encryption (AAAI 2024 · 4 citations)
- Precise asymptotics of reweighted least-squares algorithms for linear diagonal networks (NeurIPS 2024 · 3 citations)
tensors · decomposition · rank tensor · 133 papers
Approaches in this cluster:
- Tensor network decompositions (45 papers)
Represents high-order tensors with tensor networks and tensor trains, with theory on their learning capacity. - Randomized tensor decomposition algorithms (43 papers)
Speeds up CP, Tucker and ring decompositions through sketching and sampling with guarantees. - Low-rank tensor completion (45 papers)
Recovers missing tensor entries with nuclear norm, nonconvex and approximate iterative methods.
Most cited and most cited since 2024:
- Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (CVPR 2016 · 556 citations)
- Supervised Learning with Tensor Networks (NeurIPS 2016 · 196 citations)
- Towards Multi-Mode Outlier Robust Tensor Ring Decomposition (AAAI 2024 · 9 citations)
- HDQMF: Holographic Feature Decomposition Using Quantum Algorithms (CVPR 2024 · 4 citations)
Related topics in Learning theory and algorithms
- Sample complexity (1,363)
- Combinatorial and search optimization (1,492)
- Fairness (516)
- Submodular and game algorithms (1,030)
- Prediction and decision losses (2,134)
- Kernels and regression theory (1,004)
- Clustering (725)
- Optimal transport (384)