Pith. sign in

REVIEW 2 cited by

Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2410.16826 v2 pith:GFCH2RCB submitted 2024-10-22 math.OC cs.LG

Paris Giampouras , HanQin Cai , Rene Vidal This is my paper · ORCID
classification math.OCcs.LG
keywords asymmetricmatrixapproachalgorithmconvergencecorruptionsguaranteeslow-rank
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In this paper, we focus on a matrix factorization-based approach to recover low-rank {\it asymmetric} matrices from corrupted measurements. We propose an {\it Overparameterized Preconditioned Subgradient Algorithm (OPSA)} and provide, for the first time in the literature, linear convergence rates independent of the rank of the sought asymmetric matrix in the presence of gross corruptions. Our work goes beyond existing results in preconditioned-type approaches addressing their current limitation, i.e., the lack of convergence guarantees in the case of {\it asymmetric matrices of unknown rank}. By applying our approach to (robust) matrix sensing, we highlight its merits when the measurement operator satisfies a mixed-norm restricted isometry property. Lastly, we present extensive numerical experiments that validate our theoretical results and demonstrate the effectiveness of our approach for different levels of overparameterization and outlier corruptions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. LoRA-One: One-Step Full Gradient Could Suffice for Fine-Tuning Large Language Models, Provably and Efficiently

    stat.ML 2025-02 conditional novelty 6.0 of 10

    Initializing LoRA adapters from the SVD of the first full fine-tuning gradient yields subspace alignment and fast convergence in theory, and the resulting LoRA-One method beats standard LoRA on several LLM benchmarks.

  2. Efficient Over-parameterized Matrix Sensing from Noisy Measurements via Alternating Preconditioned Gradient Descent

    cs.LG 2025-02 conditional novelty 5.0 of 10

    An alternating preconditioned gradient algorithm removes the damping term and achieves linear convergence to near-optimal error for noisy over-parameterized matrix sensing and related low-rank problems.

Pith tools