mlsanityData to 13 Oct 2026

Riemannian preconditioning

arXiv 1405.6055 ↗First posted 23 May 2014math.OCcited by 19

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Abstract (arXiv)

This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian structure is sought on a quotient manifold. The proposed method is shown to be particularly insightful and efficient in quadratic optimization with orthogonality and/or rank constraints, which covers most current applications of Riemannian optimization in matrix manifolds.

Key facts. Cited by 19 papers in the map (data through 13 Oct 2026). First posted on arXiv 23 May 2014.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 5; 2022: 2; 2023: 0; 2024: 2; 2025: 4; 2026: 6.

19 papers.

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  1. 2024Riemannian Preconditioned LoRA for Fine-Tuning Foundation Modelscited by 52
  2. 2021Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometrycited by 10
  3. 2025A Stronger Mixture of Low-Rank Experts for Fine-Tuning Foundation Modelscited by 9
  4. 2025AltLoRA: Towards Better Gradient Approximation in Low-Rank Adaptation with Alternating Projectionscited by 8
  5. 2026Manifold constrained steepest descent for smooth and closed-set optimizationcited by 8
  6. 2022Riemannian block SPD coupling manifold and its application to optimal transportcited by 7
  7. 2024Optimization without Retraction on the Random Generalized Stiefel Manifoldcited by 7
  8. 2026Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifoldscited by 6
  9. 2021New Riemannian preconditioned algorithms for tensor completion via polyadic decompositioncited by 4
  10. 2025Efficient Over-parameterized Matrix Sensing from Noisy Measurements via Alternating Preconditioned Gradient Descentcited by 4
  11. 2021Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimizationcited by 3
  12. 2021On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimizationcited by 3
7 more
  1. 2021Faster Randomized Methods for Orthogonality Constrained Problemscited by 2
  2. 2025Scalable Second-order Riemannian Optimization for K-means Clusteringcited by 2
  3. 2026A Unified Study of LoRA Variants: Taxonomy, Review, Codebase, and Empirical Evaluationcited by 2
  4. 2022Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controlscited by 1
  5. 2026A Riemannian Approach to Low-Rank Optimal Transportcited by 1
  6. 2026Riemannian Optimization for Hadamard Products of Low-Rank Matricescited by 0
  7. 2026Guaranteed Low-Rank Tensor Recovery from Modewise Measurements via Normalized Block-Weighted Riemannian Gradient Descentcited by 0