How LoRA Remembers? A Parametric Memory Law for LLM Finetuning
Large Language Models (LLMs) must continuously learn and update knowledge to remain effective in dynamic real-world environments. While Low-Rank Adaptation (LoRA) is widely used for such memory updates, existing studies mainly rely on qualitative downstream evaluations, leaving the quantitative capacity limits and underlying dynamics of exact parametric memory largely unexplored. To bridge this gap, we employ LoRA as a controlled memory capacity probe within the latent space to systematically quantify exact parametric memory. We introduce the Parametric Memory Law, a robust power law linking loss reduction Delta L to effective parameters and sequence length. At the token level, fine-grain...
| Authors | Ziwen Xu, Haiwen Hong, Linsong Yu et al. |
|---|---|
| Primary category | cs.CL |
| Published | 28 May 2026 |
| Last updated at source | 28 May 2026 |
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