Data Mixture Optimization

Data-centric training has emerged as a promising direction for improving large language models (LLMs) by optimizing not only model parameters but also the selection, composition, and weighting of training data during optimization. However, existing approaches to data selection, data mixture optimization, and data reweighting are often developed in isolated codebases with inconsistent interfaces, hindering reproducibility, fair comparison, and practical integration. In this paper, we present DataFlex, a unified data-centric dynamic training framework built upon LLaMA-Factory. DataFlex supports three major paradigms of dynamic data optimization: sample selection, domain mixture adjustment, and sample reweighting, while remaining fully compatible with the original training workflow. It provides extensible trainer abstractions and modular components, enabling a drop-in replacement for standard LLM training, and unifies key model-dependent operations such as embedding extraction, inference, and gradient computation, with support for large-scale settings including DeepSpeed ZeRO-3. We conduct comprehensive experiments across multiple data-centric methods. Dynamic data selection consistently outperforms static full-data training on MMLU across both Mistral-7B and Llama-3.2-3B. For data mixture, DoReMi and ODM improve both MMLU accuracy and corpus-level perplexity over default proportions when pretraining Qwen2.5-1.5B on SlimPajama at 6B and 30B token scales. DataFlex also achieves consistent runtime improvements over original implementations. These results demonstrate that DataFlex provides an effective, efficient, and reproducible infrastructure for data-centric dynamic training of LLMs.

Large language models (LLMs) rely on pretraining on massive and heterogeneous corpora, where training data composition has a decisive impact on training efficiency and downstream generalization under realistic compute and data budget constraints. Unlike sample-level data selection, data mixing optimizes domain-level sampling weights to allocate limited budgets more effectively. In recent years, a growing body of work has proposed principled data mixing methods for LLM pretraining; however, the literature remains fragmented and lacks a dedicated, systematic survey. This paper provides a comprehensive review of data mixing for LLM pretraining. We first formalize data mixture optimization as a bilevel problem on the probability simplex and clarify the role of data mixing in the pretraining pipeline, and briefly explain how existing methods make this formulation tractable in practice. We then introduce a fine-grained taxonomy that organizes existing methods along two dimensions: static versus dynamic mixing. Static mixing is further categorized into rule-based and learning-based methods, while dynamic mixing is grouped into adaptive and externally guided families. For each class, we summarize representative approaches and analyze their strengths and limitations from a performance-cost trade-off perspective. Building on this analysis, we highlight challenges that cut across methods, including limited transferability across data domains, optimization objectives, models, and validation sets, as well as unstandardized evaluation protocols and benchmarks, and the inherent tension between performance gains and cost control in learning-based methods. Finally, we outline several exploratory directions, including finer-grained domain partitioning and inverse data mixing, as well as pipeline-aware designs, aiming to provide conceptual and methodological insights for future research.

Current language model training commonly applies multi-task Supervised Fine-Tuning (SFT) using a homogeneous compute budget across all sub-datasets. This approach is fundamentally sub-optimal: heterogeneous learning dynamics cause faster-learning tasks to overfit early while slower ones remain under-fitted. To address this, we introduce mSFT, an iterative, overfitting-aware search algorithm for multi-task data mixtures. mSFT trains the model on an active mixture, identifies and excludes the earliest overfitting sub-dataset, and reverts to that specific optimal checkpoint before continuing. Extensive evaluations demonstrate that mSFT consistently outperforms 4 baselines across 10 benchmarks and 6 base models. Further analysis confirms mSFT maintains robust gains across diverse dataset sizes, task granularities, and is insensitive to its single new hyperparameter (compute budget). Notably, at low compute budget, mSFT can improve performance while lowering training FLOPs. Ultimately, mSFT establishes a practical overfitting-aware algorithm for multi-task SFT that maximizes the potential of models across diverse data mixtures.

In multilingual pretraining, the test loss of a pretrained model is heavily influenced by the proportion of each language in the pretraining data, namely the language mixture ratios. Multilingual scaling laws can predict the test loss under different language mixture ratios and can therefore be used to estimate the optimal ratios. However, the current approaches to multilingual scaling laws do not measure the cross-lingual transfer effect, resulting in suboptimal mixture ratios. In this paper, we consider multilingual pretraining as a cooperative game in which each language acts as a player that jointly contributes to pretraining, gaining the resulting reduction in test loss as the payoff. Consequently, from the perspective of cooperative game theory, we quantify the cross-lingual transfer from each language by its contribution in the game, and propose a game-theoretic multilingual scaling law called ShapleyLaw. Our experiments show that ShapleyLaw outperforms baseline methods in model performance prediction and language mixture optimization.

Instead of directly distilling a language model, this study addresses the problem of aligning a base model with a target model in distribution by designing the domain mixture of training data for pretraining or continued pretraining as a fixed training recipe. We propose a method for determining domain weights by viewing models as points in log-likelihood space and aligning the training update direction with the direction toward the target model. Experiments with NanoGPT show that the proposed method consistently reduces the KL divergence between the trained base model and the target model relative to training with Pile-original weighting. Although knowledge distillation remains more effective when available, the proposed method achieves meaningful alignment, and downstream task performance also tends to become closer to that of the target model.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks and domains, with data playing a central role in enabling these advances. Despite this success, the preparation and effective utilization of the massive datasets required for LLM training remain major bottlenecks. In current practice, LLM training data is often constructed using ad hoc scripts, and there is still a lack of mature, agent-based data preparation systems that can automatically construct robust and reusable data workflows, thereby freeing data scientists from repetitive and error-prone engineering efforts. Moreover, once collected, datasets are often consumed largely in their entirety during training, without systematic mechanisms for data selection, mixture optimization, or reweighting. To address these limitations, we advocate two complementary research directions. First, we propose building a robust, agent-based automatic data preparation system that supports automated workflow construction and scalable data management. Second, we argue for a unified data-model interaction training system in which data is dynamically selected, mixed, and reweighted throughout the training process, enabling more efficient, adaptive, and performance-aware data utilization. Finally, we discuss the remaining challenges and outline promising directions for future research and system development.

A data mixture refers to how different data sources are combined to train large language models, and selecting an effective mixture is crucial for optimal downstream performance. Existing methods either conduct costly searches directly on the target model or rely on mixture scaling laws that fail to extrapolate well to large model sizes. We address these limitations by introducing a compute-efficient pipeline for data mixture scaling. First, we propose CAMEL, a capacity-aware mixture law that models validation loss with the nonlinear interplay between model size and mixture. We also introduce a loss-to-benchmark prediction law that estimates benchmark accuracy from validation loss, enabling end-to-end performance prediction for the target model. Next, we study how to allocate a fixed compute budget across model scales to fit the law and reduce prediction error. Finally, we apply our method to Mixture-of-Experts models with up to 7B-A150M parameters to fit the law, and verify the optimal mixture derived from the law by extrapolating to a 55B-A1.2B target model. Compared to prior methods, we reduce mixture optimization costs by 50% and improves downstream benchmark performance by up to 3%.

Data mixing--the strategic reweighting of training domains--is a critical component in training robust machine learning models. This problem is naturally formulated as a bilevel optimization task, where the outer loop optimizes domain weights to minimize validation loss, and the inner loop optimizes model parameters to minimize the weighted training loss. Classical bilevel optimization relies on hypergradients, which theoretically require the inner optimization to reach convergence. However, due to computational constraints, state-of-the-art methods use a finite, often small, number of inner update steps before updating the weights. The theoretical implications of this approximation are not well understood. In this work, we rigorously analyze the convergence behavior of data mixing with a finite number of inner steps $T$. We prove that the "greedy" practical approach of using $T=1$ can fail even in a simple quadratic example. Under a fixed parameter update budget $N$ and assuming the per-domain losses are strongly convex, we show that the optimal $T$ scales as $Θ(\log N)$ (resp., $Θ({(N \log N)}^{1/2})$) for the data mixing problem with access to full (resp., stochastic) gradients. We complement our theoretical results with proof-of-concept experiments.

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the mixture parameters. We study the problem of approximating a target measure, available only through finitely many of its moments, by a mixture of distributions from a parametric family (e.g., Gaussian, exponential, Poisson), with approximation quality measured by the 2-Wasserstein or the total variation distance. Unlike many existing approaches, the parameter set is not assumed to be finite; it is modeled as a compact basic semi-algebraic set. We introduce a hierarchy of semidefinite relaxations with asymptotic convergence to the desired optimal value. In addition, when a certain rank condition is satisfied, the convergence is even finite and recovery of an optimal mixing measure is obtained. We also present an application to clustering, where our framework serves either as a stand-alone method or as a preprocessing step that yields both the number of clusters and strong initial parameter estimates, thereby accelerating convergence of standard (local) clustering algorithms.

As numerous instruction-tuning datasets continue to emerge, dynamically balancing and optimizing their mixtures has become a critical challenge. To address this, we propose DynamixSFT, a dynamic and automated method for instruction-tuning dataset mixture optimization. We formulate the problem as a multi-armed bandit setup and introduce a Prior-scaled Boltzmann Exploration that softly anchors the updated sampling distribution to the original dataset proportions, thereby preserving the inherent diversity and coverage of the collection. Sampling probabilities are updated using a lightweight 1-Step Look-ahead Reward, reflecting how much the dataset contributes to improving the model's performance at its current state. We demonstrate that DynamixSFT effectively optimizes the Tulu-2-mixture and Tulu-3-mixture collections across 10 benchmarks, while introducing minimal computational overhead over naive sampling. Furthermore, we provide a comprehensive analysis and visualizations to offer deeper insights into the adaptive dynamics of our method.