Title: LayerMix Law: Scaling Law for Large Language Models on Quality-Weighted Mixture Data with Repetition
Primary area: foundation or frontier models, including LLMs
Keywords: SCALING LAW, LARGE LANGUAGE MODELS

Abstract: Upweighting high-quality data in large language model (LLM) pretraining typically improves performance. However, the limited availability of high-quality data—particularly in overtrained regimes—means that stronger upweighting often increases repetition, which can degrade performance. This creates a fundamental trade-off between data quality and data repetition. In this paper, we systematically investigate how varying data quality and repetition affects models across different scales. Concretely, we partition the source corpus into buckets based on quality scores and sample from each bucket with different weights, thereby constructing training sets with diverse scales, quality distributions, and repetition levels. We then train a family of models on these datasets to measure performance across conditions. Building on these observations, we introduce a theoretical framework analogous to scaling laws, which we call \textbf{LayerMix Law}. LayerMix Law predicts model loss as a function of consumed tokens, model size, sampling weights, and repetition levels. The key intuition is to view training as the accumulation of information from data, where the amount of information is governed by data quality, while model scale and repetition determine the information gained per training step. We show that LayerMix Law accurately predicts the model performance on unseen data recipes at larger computation scale (up to 7B parameter run with 425B token, each x2 invest compute), with 0.15\% average absolute error and 0.96\% maximum absolute error, which enables efficient search for optimal data recipes without costly additional experiments. Moreover, LayerMix Law extrapolates reliably to different degrees of overtraining, providing a efficient tool for selecting data recipes under varying computational budgets.