Train Smarter, Not Longer: Memorization-Guided Data Reuse for Efficient LLM Training

High-quality data is scarce in large language model (LLM) training, yet how to schedule its use jointly with training dynamics lacks theoretical guidance. We extend functional scaling laws by incorporating a data-quality dimension, and solve the joint data-quality and batch-size scheduling problem in asymptotic closed form. The solution reveals two regimes and a dual role of high-quality data. In the noise-limited regime, high-quality data should be used as a signal amplifier: lowering the batch size converts cleaner data into more signal without amplifying noise. In the signal-limited regime, it should be used as a noise suppressor: late placement reduces terminal noise without sacrificing signal accumulation. Existing curriculum-style pipelines primarily exploit the second role by placing cleaner data late, but miss the first role because conventional decay schedules reduce update intensity exactly when high-quality data becomes available. Guided by this, we propose Drop-Stable-Rampup for LLM midtraining: upon the quality transition, drop the batch size, hold it stable to accumulate signal, then ramp up to suppress terminal noise. On a 15B Mixture-of-Experts model midtrained on 108B tokens, Drop-Stable-Rampup improves average accuracy over Warmup-Stable-Decay (WSD) by +1.70 and over Cosine-decay by +2.98, with particularly large gains on mathematical reasoning benchmarks such as GSM8K (+4.23) and MATH (+2.80).

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.

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.