Data mixing is a central design problem in large language model pretraining: given a fixed token budget, practitioners must decide how much data to allocate to each domain. Recent proxy-based methods address this problem by training small models on candidate mixtures, fitting a response model, and using the response to select mixtures for larger-scale training. We show that this workflow has the structure of a classical mixture experiment. Under this view, data domains are mixture components, token shares are component proportions, proxy-training runs are experimental design points, and validation loss defines a response surface over the probability simplex. We develop this formulation using sparse second-order Scheffé response-surface models and construct model-robust $\mathcal{I}$-optimal designs for proxy data-mixing experiments. Using RegMix as an empirical case study, we demonstrate how the framework can both interpret observed mixture responses and design more efficient proxy experiments. The Scheffé analysis shows that domain value is strongly relational: several domains that are weak under additive effects become favourable through pairwise interactions, especially through combinations with web-derived text. The sparse Scheffé model preserves mixture rankings across model scales and remains competitive with a flexible machine-learning predictor while providing an explicit decomposition of additive and interaction effects. In a simulation study calibrated to observed proxy-training responses, model-robust $\mathcal{I}$-optimal designs recover the relevant mixture ordering after removing about 25\% of the original proxy runs. These results suggest that LLM data mixing should be treated not only as a prediction problem, but also as an experimental-design problem in which the proxy mixtures themselves can be chosen to improve statistical efficiency.
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.