A Fine-Grained Analysis of the LoRA Fine-Tuning Landscape with Implications for Data Selection

arXiv:2610.06542 · cs.LG · Submitted 2026-10-05 · Read on arXiv

cs.LG

Submitted: 2026-10-05

Updated: 2026-10-05

Terminology

• Fine-Tuning — 1× in this paper · explained in 5 episodes
• LoRA Fine-Tuning — 1× in this paper · explained in 3 episodes

Sources

• LoRA Training Provably Converges to a Low-Rank Global Minimum or It Fails Loudly (But it Probably Won't Fail)
• The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing
• Data Shapley in One Training Run
• OPUS: Towards Efficient and Principled Data Selection in Large Language Model Pre-training in Every Iteration
• Sharp Global Guarantees for Nonconvex Low-rank Recovery in the Noisy Overparameterized Regime
• GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection
• Global Optimality in Low-rank Matrix Optimization

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