Data Mixing Made Efficient: A Bivariate Scaling Law for Language Model
  Pretraining
Authors: name: Ce Ge, name: Zhijian Ma, name: Daoyuan Chen, name: Yaliang Li, name: Bolin Ding

Large language models exhibit exceptional generalization capabilities,
primarily attributed to the utilization of diversely sourced data. However,
conventional practices in integrating this diverse data heavily rely on
heuristic schemes, lacking theoretical guidance. This research tackles these
limitations by investigating strategies based on low-cost proxies for data
mixtures, with the aim of streamlining data curation to enhance training
efficiency. Specifically, we propose a unified scaling law, termed BiMix, which
accurately models the bivariate scaling behaviors of both data quantity and
mixing proportions. We conduct systematic experiments and provide empirical
evidence for the predictive power and fundamental principles of BiMix. Notably,
our findings reveal that entropy-driven training-free data mixtures can achieve
comparable or even better performance than more resource-intensive methods. We
hope that our quantitative insights can shed light on further judicious
research and development in cost-effective language modeling.