Continual Memorization of Factoids in Language Models

Continual learning promises a language model that keeps acquiring knowledge after training, with each new fact written into its weights. Whether weight writes can support accumulation remains undecided. We follow invented facts written into Qwen3 models from creation through sequences of twenty to one hundred later writes, using held-out questions of five types, with the original model given the fact in its prompt as the reference. Across these experiments, the breadth of the training data determines the kind of knowledge created. Bare-statement training produces recitation, while diverse restatements reduce the recitation-to-use gap from 27.4 to 5.4 points without showing the model a conclusion. This difference carries into later writes: after twenty sequential writes, bare-statement facts retain 1% accuracy while facts written from broad study data retain 46%. We also find that facts can be behaviourally forgotten without being erased. Forgotten facts keep most of the log-probability added by their write, and under bare-statement training 70% of wrong answers about them contain the most recently written fact. The same writes barely degrade the model's use of facts in context, and a forgotten study fact supplied in the prompt recovers to 77-80% on its questions. These results describe knowledge that is stored but question-keyed: later writes redirect the questions that reached it. Damage to unrelated abilities tracks KL divergence from the original model, and the later writes cause interference regardless of how the earlier fact was stored. Broad data can create usable knowledge, and a frozen reference can preserve capability, but no intervention we tested, including those built on accurate local measurements of each write, keeps earlier facts reachable. When facts must be composed or survive later writes, the reliable channel is context rather than the weights.

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.

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.