Continual Pre-Training (CPT) is essential for enabling Language Models (LMs) to integrate new knowledge without erasing old. While classical CPT techniques like data replay have become the standard paradigm, the mechanisms underlying how LMs acquire and retain facts over time, termed as continual Factual Knowledge Acquisition (cFKA), remain unclear. In this work, we present a theoretical framework that characterizes the training dynamics of cFKA using a single-layer Transformer, offering a unified explanation for the behavior of representative CPT methods. Our analysis reveals that regularization-based methods merely adjust the convergence rate of parameters without altering the inherent forgetting tendency, whereas data replay methods succeed in shifting convergence dynamics and stabilizing pretrained knowledge. Building on these insights, we propose a novel generative data replay approach, called \textbf{S}electing \textbf{T}okens via attenti\textbf{O}n \textbf{C}ontribution~(STOC), which identifies influential factual snippets to guide replay data generation. Extensive experiments on both synthetic and real-world datasets validate our findings and demonstrate that STOC effectively enhances cFKA by mitigating catastrophic forgetting.
As new knowledge rapidly accumulates, language models (LMs) with pretrained knowledge quickly become obsolete. A common approach to updating LMs is fine-tuning them directly on new knowledge. However, recent studies have shown that fine-tuning for memorization may be ineffective in storing knowledge or may exacerbate hallucinations. In this work, we introduce a setting we call continual memorization, where a model must memorize and retain a set of factoids through multiple stages of fine-tuning on subsequent datasets. We characterized the forgetting patterns through extensive experiments and show that LMs widely suffer from forgetting, especially when needing to memorize factoids in the second stage. We posit that forgetting can be alleviated by modifying training dynamics: (1) protecting the memorization process when learning factoids or (2) reducing interference from subsequent training stages. Intriguingly, we find that mixing randomly generated word sequences or generic data sampled from pretraining corpora at different training stages effectively mitigates forgetting REMIX: Random and Generic Data Mixing). REMIX can recover performance from severe forgetting, outperforming replay methods and other continual learning baselines. We analyze how REMIX influences the learning process and find that robust memorization follows a distinct pattern: the model stores factoids in earlier layers than usual and diversifies the layers that retain them, which results in easier recall and manipulate of the learned factoids.
Large language models (LLMs) drift out of date the moment their pretraining ends, yet retraining from scratch is prohibitively expensive. Continued pretraining (CPT) is the natural remedy, but it is typically evaluated through a continual learning lens that assumes disjoint data streams. This is a poor fit for time-incremental updates on web-scale crawls, where successive snapshots share substantial URL overlap by design. We study time-incremental CPT in this realistic regime: continued pretraining on FineWeb-Edu dumps drawn strictly from after each model's knowledge cutoff, evaluated across six open-weight models spanning three families (OLMo2, Llama-3.1/3.2, Gemma-3-1B) and four parameter scales (1B-3B-7B-8B). We organize our findings around four practical questions. (i) Is knowledge acquired? Yes, but heterogeneously, and without catastrophic forgetting: five of six models also improve on pre-cutoff factual recall, and the gains track pretraining saturation (driven primarily by token budget per parameter). (ii) What does it cost? Almost nothing: the macro-average across a thirteen-task suite stays within 0.01 of the base for every model. (iii) What is the recipe? Data quality dominates quantity (a curated 6B-token slice matches a broader 40B one); the optima for knowledge acquisition and general capability are separated by roughly an order of magnitude in learning rate; and LoRA at sufficient rank matches full CPT. (iv) Does it survive deployment? CPT gains transfer through SFT, while DPO's effect is family-dependent. Together, these results paint a more optimistic picture of time-incremental CPT than the prior continual learning literature suggests.
Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.