Machine learning progress is often attributed to scaling model size and dataset volume, yet the composition of data can be just as consequential. Empirical findings repeatedly show that combining datasets from different domains yields nontrivial interactions. For instance, adding code improves mathematical reasoning, while certain mixtures introduce interference that reduces model performance. We refer to these effects collectively as data synergy, where the contribution of multiple domains exceeds or falls short of the sum of their isolated contributions. In this work, we formalize and quantify data synergy in language model pretraining. Leveraging observational variation across open-weight LLMs with diverse pretraining mixtures, we estimate both direct domain-to-benchmark synergy (how one domain contributes to performance on another) and a second-order domain-domain synergy (capabilities that require co-occurrence of multiple domains). Our framework improves predictive accuracy over domain-agnostic scaling laws and recovers stable synergy estimates. We validate these estimates by training models on predicted optimal and predicted anti-optimal mixtures and confirm that our synergy estimates correctly predict performance rankings.
Recent research has established empirical scaling laws to predict model performance on multi-domain data mixtures. However, a theoretical understanding of these model loss behaviors remains absent. In this work, we propose a unified framework to explain the underlying mechanics of data mixing. Our approach extends theoretical perspectives originally developed for standard neural scaling laws (e.g., Kaplan and Chinchilla) to the multi-domain setting. Based on the distributional assumption that domains overlap on fundamental skills while diverging on specialized skills, we identify two key factors that govern the domain losses of models trained on different data mixtures: \textit{Capacity Competition}, where the allocation of finite model capacity couples domain losses globally, and \textit{Noise Reduction}, where optimal weights shift toward harder-to-learn domains to minimize overall noise. Empirical evaluations show that our framework outperforms existing baselines by fitting the loss landscape with a lower Mean Relative Error and identifying higher-performing training mixtures. Most importantly, our model successfully extrapolates across scales, predicting highly effective mixtures for large, unseen scales using parameters fitted on smaller ones. In addition, our model achieves these results using significantly fewer parameters compared to previous empirical laws. Our code is available at https://github.com/meiqwq/Explaining-Data-Mixing-Scaling-Laws.
As language models scale, the amount of data they require grows -- yet many target data sources, such as low-resource languages or specialized domains, are inherently limited in size. A common strategy is to mix this scarce but valuable target data with abundant generic data, which presents a fundamental trade-off: too little target data in the mixture underexposes the model to the target domain, while too much target data repeats the same examples excessively, yielding diminishing returns and eventual overfitting. We study this trade-off across more than 2,000 language-model training runs spanning multiple model and target dataset sizes, as well as several data types, including multilingual, domain-specific, and quality-filtered mixtures. Across all settings, we find that repetition is a central driver of target-domain performance, and that mixture training tolerates much higher repetition than single-source training: scarce target corpora can be reused 15-20 times, with the optimal number of repetitions depending on the target data size, compute budget, and model scale. Next, we introduce a repetition-aware mixture scaling law that accounts for the decreasing value of repeated target tokens and the regularizing role of generic data. Optimizing the scaling law provides a principled way to compute effective mixture configurations, yielding practical mixture recommendations for pretraining under data constraints.
The training efficacy of large language models (LLMs) is fundamentally constrained by the quality and composition of training data. Existing dynamic data scheduling methods face critical limitations in industrial-scale pretraining and supervised fine-tuning (SFT): data selection incurs prohibitive O(N) costs on terabyte-scale corpora, mixture optimization schemes introduce severe I/O bottlenecks or require training auxiliary reference models, and sample-level reweighting strategies rely on loss signals that conflate noise, difficulty, and novelty. We present DomainPilot, a domain-level loss-guided two-stage data mixture optimization framework. DomainPilot introduces token-level domain loss monitoring to capture per-domain learning dynamics during training without halting the data pipeline. Building on these signals, we propose a Scaling Law guided coarse optimization stage that fits domain-specific convergence curves and derives a principled prior for mixture adjustment. A subsequent Mixing Law guided fine optimization stage refines the mixture by modeling cross-domain interaction effects through controlled sweep experiments. The entire mechanism is realized via a patch-based architecture that injects domain-aware loss computation into existing training frameworks (e.g., MindSpeed/Megatron-LM) with only ~30 lines of framework-specific adapter code. We validate DomainPilot on the Qwen3-1.7B model during SFT. Compared to the original data mixture, our optimized mixture achieves improvements of +2% on MMLU-Redux, +1.8% on AIME24, +3.8% on LiveCodeBench v5, and +3.6% on BFCL v3, without increasing total data volume or training cost. These results demonstrate that domain-level training signals provide an effective, lightweight alternative to expensive data selection or auxiliary model training for mixture optimization.