通过分析数据源的缩放规律，实现领域预训练中数据选择的成本优化。

We introduce a framework for optimizing domain-specific dataset construction in foundation model training. Specifically, we seek a cost-efficient way to estimate the quality of data sources (e.g. synthetically generated or filtered web data, etc.) in order to make optimal decisions about resource allocation for data sourcing from these sources for the stage two pre-training phase, aka annealing, with the goal of specializing a generalist pre-trained model to specific domains. Our approach extends the usual point estimate approaches, aka micro-annealing, to estimating scaling laws by performing multiple annealing runs of varying compute spent on data curation and training. This addresses a key limitation in prior work, where reliance on point estimates for data scaling decisions can be misleading due to the lack of rank invariance across compute scales -- a phenomenon we confirm in our experiments. By systematically analyzing performance gains relative to acquisition costs, we find that scaling curves can be estimated for different data sources. Such scaling laws can inform cost effective resource allocation across different data acquisition methods (e.g. synthetic data), data sources (e.g. user or web data) and available compute resources. We validate our approach through experiments on a pre-trained model with 7 billion parameters. We adapt it to: a domain well-represented in the pre-training data -- the medical domain, and a domain underrepresented in the pretraining corpora -- the math domain. We show that one can efficiently estimate the scaling behaviors of a data source by running multiple annealing runs, which can lead to different conclusions, had one used point estimates using the usual micro-annealing technique instead. This enables data-driven decision-making for selecting and optimizing data sources.