On the Convergence of Stochastic Low-Rank Adaptation

arXiv:2607.21975 · cs.LG, math.OC · Submitted 2026-07-24 · Read on arXiv

cs.LG, math.OC

Submitted: 2026-07-24

Updated: 2026-09-26

Code: https://github.com/tatsu-lab/stanford_alpaca

Terminology

• Adaptation — 15× in this paper · explained in 1 episode
• Fine-Tuning — 11× in this paper · explained in 5 episodes
• Calibration — 4× in this paper · explained in 7 episodes
• AUC — 3× in this paper · explained in 2 episodes
• Convergence Guarantees — 3× in this paper · explained in 3 episodes
• Low-Rank Adaptation (LoRA) — 3× in this paper · explained in 9 episodes
• Non-asymptotic Analysis — 3× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Data Augmentation — 1× in this paper · explained in 7 episodes
• Federated Learning — 1× in this paper · explained in 14 episodes
• Frozen model — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Instruction Tuning — 1× in this paper · explained in 2 episodes

Sources

• Randomized Asymmetric Chain of LoRA: The First Meaningful Theoretical Framework for Low-Rank Adaptation
• On the Convergence Rate of LoRA Gradient Descent
• Bernoulli-LoRA: A Theoretical Framework for Randomized Low-Rank Adaptation
• TinyLlama: An Open-Source Small Language Model

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