At test time, large language models (LLMs) can encode historical information in activation memory (i.e., KV caches) and parametric memory (i.e., updated parameters). While activation memory is generally considered effective for factual recall and parametric memory for learning new tasks, their interplay remains unclear. In this work, we systematically investigate the role of memory in few-shot learning through controlled experiments. We find that activation memory is superior for recalling facts, whereas parametric memory does not consistently outperform activation memory in task learning. Moreover, our experiments show that the composite task, Conditional Arithmetic, requires the synergy of both memory types. Through neuron-level analysis, we find that the model activates distinct sets of neurons when accessing the same historical information through activation versus parametric memory. When both memory types are combined, the model recruits neurons from both sets, which is crucial for solving Conditional Arithmetic. These findings suggest that neither memory mechanism alone is sufficient for this composite task, highlighting the importance of their collaboration.
Reinforcement learning (RL) has achieved remarkable success in LLM reasoning, but whether it can also improve direct recall of parametric knowledge remains an open question. We study this question in a controlled zero-shot, one-hop, closed-book QA setting with no chain-of-thought, training only on binary correctness rewards and applying fact-level train-test deduplication to ensure gains reflect improved recall rather than reasoning or memorization. Across three model families and multiple factual QA benchmarks, RL yields ~27% average relative gains, surpassing both training- and inference-time baselines alike. Mechanistically, RL primarily redistributes probability mass over existing knowledge rather than acquiring new facts, moving correct answers from the low-probability tail into reliable greedy generations. Our data-attribution study reveals that the hardest examples are the most informative: those whose answers never appear in 128 pre-RL samples (only ~18% of training data) drive ~83% of the gain, since rare correct rollouts still emerge during training and get reinforced. Together, these findings broaden the role of RL beyond reasoning, repositioning it as a tool for unlocking rather than acquiring latent parametric knowledge.
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.
Large tabular models (LTMs), i.e., tabular foundation models leveraging in-context learning (ICL), achieve state-of-the-art performance on tabular tasks. While LLMs are known to unintentionally memorize training data, the memorization dynamics of LTMs remain largely unexplored. We investigate the potential for parametric memorization in tabular ICL. We introduce ICLMEM, a probing framework designed to separate context-based predictions from parametric memorization. Our zero-information multiple-choice context strips away valid contextual patterns to force the model to fall back on its parametric memory. Our controlled fine-tuning setup establishes membership ground truth and accounts for common pitfalls, e.g., distribution shift, feature contamination, base-rate fallacy, and the pre-trained base model acts as reference to calibrate for sample difficulty. Our controlled evaluation on a leading real-world-trained LTM detects moderate memorization signals in 8 out of 10 tasks (AUC up to 0.67 and TPR at 1% FPR >0.1). Notably, memorization signals are strongest for low-cardinality and binary tasks. However, they largely vanish under realistic training conditions. Our findings show LTM memorization signals under specific circumstances (single-task fine-tuning with fixed samples across many epochs and small query size). To protect sensitive data, appropriate measures must be taken, which we discuss.