CausalMix: Data Mixture as Causal Inference for Language Model Training

Data mixing decides how to combine different sources or types of data and is a consequential problem throughout language model training. In pretraining, data composition is a key determinant of model quality; in continual learning and adaptation, it governs what is retained and acquired. Yet existing data mixing methods address only one phase of this lifecycle at a time: some require smaller proxy models tied to a single training phase, others assume a fixed domain set, and continual learning lacks principled guidance altogether. We argue that data mixing is fundamentally an online decision making problem -- one that recurs throughout training and demands a single, unified solution. We introduce OP-Mix (On-Policy Mix), a data mixing algorithm that operates across the entire language model training lifecycle. Our main insight is that candidate data mixtures can be cheaply simulated by interpolating between low-rank adapters trained directly on the current model, eliminating separate proxy models and ensuring the search is always grounded in the model's actual learning dynamics. Across pretraining, continual midtraining, and continual instruction tuning, OP-Mix consistently finds near-optimal mixtures while using a fraction of the compute of the baselines. In pretraining, OP-Mix improves upon training without mixing by 6.3% in average perplexity. For continual learning, OP-Mix matches the performance of both retraining and on-policy distillation while using 66% and 95% less overall compute, respectively. OP-Mix suggests a different view of language model training: not a sequence of distinct phases, but a single continuous process of learning from data.

Data mixture selection is critical for Large Language Model pretraining. Existing methods such as RegMix select a single static mixture by fitting a regression model on small-scale proxy runs. We propose RegMix-D, a simple extension of RegMix to dynamic mixing. Our key observation is that proxy runs produce not only endpoint losses, but also full loss trajectories, which can be used to further improve data mixture. By training regression model on these trajectories, we can predict optimal mixtures at multiple training stages. RegMix-D supports two deployment modes: an offline variant that generates a complete mixture schedule before target training, and an online variant that adapts the mixture during training using observed loss. Experiments on 25B tokens of the Pile dataset with a 1B parameter target model show that RegMix-D consistently improves over RegMix and DoReMi across 13 downstream tasks while remaining proxy-efficient: it surpasses RegMix even with only 128 proxy models (25% of RegMix's proxy compute budget).

The pretraining data mixture of Large Language Models (LLMs) constitutes their "digital DNA", shaping model behaviors, capabilities, and failure modes. Yet this composition is rarely disclosed, making post-hoc auditing of data combination or provenance difficult. In this work, we formalize $\textbf{Data Mixture Surgery (DMS)}$: given only generated text from a target LLM, estimate the domain-level distribution of its pretraining corpus under a predefined taxonomy. We propose $\textbf{LLMSurgeon}$, a strong framework that casts DMS as an inverse problem under the label-shift assumption. Rather than directly aggregating classifier outputs, LLMSurgeon estimates a calibrated $\textit{soft}$ confusion matrix and solves a constrained inverse problem to correct systematic domain confusion and recover the latent mixture prior. To evaluate, we introduce $\textbf{LLMScan}$, a recipe-verifiable evaluation suite built from open-source LLMs with transparent pretraining mixtures. Across LLMScan, LLMSurgeon recovers domain mixtures with high fidelity under fixed protocols. Our work presents a practical, post-hoc approach for auditing the digital DNA of foundation models without access to their training data.