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-grained analysis reveals a deterministic phase transition, demonstrating that a prediction probability of p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Driven by these insights, we introduce MemFT, a threshold-guided optimization strategy that dynamically redistributes the training budget toward sub-threshold tokens. Empirical evaluations demonstrate that MemFT can enhance memory fidelity and efficiency. Code will be released at https://github.com/zjunlp/ParametricMemoryLaw.

翻译：大型语言模型（LLMs）需持续学习与更新知识，以在动态真实环境中保持有效性。尽管低秩自适应（LoRA）被广泛用于此类记忆更新，现有研究主要依赖定性下游评估，对精确参数化记忆的量化容量上限及底层动力学机制尚缺乏探索。为弥补这一空白，我们采用LoRA作为潜空间中的可控记忆容量探针，系统性地量化精确参数化记忆。我们提出参数化记忆定律（Parametric Memory Law），该稳健的幂律将损失降低量ΔL与有效参数及序列长度相关联。在词元级别，细粒度分析揭示了确定性相变：在贪心解码条件下，预测概率p>0.5构成逐字回忆的充分条件。基于这些发现，我们引入MemFT——一种阈值引导的优化策略，将训练预算动态重分配给低于阈值的词元。实验评估表明，MemFT可增强记忆保真度与效率。代码将发布于https://github.com/zjunlp/ParametricMemoryLaw。