mlsanityData to 14 Oct 2026

Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach

arXiv 1609.03240 ↗First posted 12 Sep 2016stat.ML cs.IT cs.LGcited by 38

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Abstract (arXiv)

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-r matrix X ∈ ℝm × n is represented as UV^top, where U ∈ ℝm × r and V ∈ ℝn × r. In this paper, we complement recent findings on the non-convex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious local minima, under RIP.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Sep 2016.

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Citing papers per year: 2021: 9; 2022: 5; 2023: 7; 2024: 5; 2025: 6; 2026: 6.

38 papers.

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  1. 2023Saddle-to-Saddle Dynamics in Diagonal Linear Networkscited by 57
  2. 2021Global Convergence of Gradient Descent for Asymmetric Low-Rank Matrix Factorizationcited by 45
  3. 2021Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscited by 28
  4. 2022Preconditioned Gradient Descent for Overparameterized Nonconvex Burer--Monteiro Factorization with Global Optimality Certificationcited by 21
  5. 2025LoRA Training Provably Converges to a Low-Rank Global Minimum or It Fails Loudly (But it Probably Won't Fail)cited by 20
  6. 2022Improved Global Guarantees for the Nonconvex Burer--Monteiro Factorization via Rank Overparameterizationcited by 13
  7. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  8. 2021Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurementscited by 7
  9. 2023Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterizationcited by 6
  10. 2021Fast quantum state reconstruction via accelerated non-convex programmingcited by 5
  11. 2021Sharp Global Guarantees for Nonconvex Low-rank Recovery in the Noisy Overparameterized Regimecited by 5
  12. 2021Rank-one matrix estimation: analytic time evolution of gradient descent dynamicscited by 5
26 more
  1. 2022Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensingcited by 5
  2. 2023Fast and Accurate Estimation of Low-Rank Matrices from Noisy Measurements via Preconditioned Non-Convex Gradient Descentcited by 5
  3. 2021Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimizationcited by 4
  4. 2022Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspectivecited by 4
  5. 2024Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recoverycited by 4
  6. 2021Riemannian Perspective on Matrix Factorizationcited by 3
  7. 2024Asymptotic Dynamics of Alternating Minimization for Bilinear Regressioncited by 3
  8. 2024Non-convex matrix sensing: Breaking the quadratic rank barrier in the sample complexitycited by 3
  9. 2024Provable Acceleration of Nesterov's Accelerated Gradient for Rectangular Matrix Factorization and Linear Neural Networkscited by 3
  10. 2025One Rank at a Time: Cascading Error Dynamics in Sequential Learningcited by 3
  11. 2023A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimizationcited by 2
  12. 2023Exponentially Convergent Algorithms for Supervised Matrix Factorizationcited by 2
  13. 2025Smooth Quasar-Convex Optimization with Constraintscited by 2
  14. 2021Wave-Informed Matrix Factorization with Global Optimality Guaranteescited by 1
  15. 2022Supervised Dictionary Learning with Auxiliary Covariatescited by 1
  16. 2023Greedy Pruning with Group Lasso Provably Generalizes for Matrix Sensingcited by 1
  17. 2025Implicit Bias in Matrix Factorization and its Explicit Realization in a New Architecturecited by 1
  18. 2025Nonnegative Low-rank Matrix Recovery Can Have Spurious Local Minimacited by 1
  19. 2023Wave Physics-informed Matrix Factorizationscited by 0
  20. 2025Phase retrieval with rank d measurements -- descending algorithms phase transitionscited by 0
  21. 2026ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equationscited by 0
  22. 2026Exploiting Low-Rank Objective Structure in Discrete Quadratic Optimizationcited by 0
  23. 2026Scaled Gradient Descent for Ill-Conditioned Low-Rank Matrix Recovery with Optimal Sampling Complexitycited by 0
  24. 2026Sparse Network Inference under Imperfect Detection and its Application to Ecological Networkscited by 0
  25. 2026AdaPaD: Adaptive Parallel Deflation for PEFT with Self-Correcting Rank Discoverycited by 0
  26. 2026Finding the Signal in the Spam: Jointly Learning Rewards and Worker Reliability from Pairwise Comparisonscited by 0