Data Mixture Optimization

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1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 23

Oct 5, 2026cs.LG

Differentially Private Mixing of Public Datasets Improves Private Learning

Many machine learning applications involve sensitive data and therefore require training under differential privacy (DP). However, DP training often degrades model utility. In some cases, first pre-training the model on "public" data before finetuning with DP on the sensitive data can reduce the drop in utility. However, the success of this depends on how relevant the selected public dataset is to the sensitive data. We introduce the first pipeline that privately learns the mixture of several public datasets to pretrain on for a given sensitive downstream task. Our key insight is that we can privately find the best mixture of multiple public datasets by privately learning a low-dimensional linear model. We tested our method on the NIH dataset for X-ray classification and the ENRON email dataset for language modeling. Applying our method to find tailored mixtures of X-ray datasets to pretrain on for diseases in the NIH ChestX-ray14 dataset, we improved macro AUC by up to 0.037 across privacy budgets compared to the baselines, with gains as large as +22.8% relative AUC on Cardiomegaly at

ε=1

. For DP training on the ENRON dataset, pre-training on our mixture of The Common Pile (a collection of public-domain text datasets) decreased test perplexity by 16% relative to the baseline mixtures.

Yufei Chen, Tejumade Afonja, Anvith Thudi +1

University of Toronto and Vector Institute, Toronto, Canada · CISPA Helmholtz Center for Information Security, Saarbrucken, Germany

Privacy-Preserving ML Differential Privacy Data Mixture Optimization

Sep 8, 2026cs.AI

Everything in Moderation: Per-Domain Coverage Optima and Alignment-Resistant Domain Gaps in Multi-Domain Mid-Training

Mid-training, the stage between pre-training and alignment, is where a model's per-domain data composition is typically set by data availability rather than principled design. We ask what that decision buys, and whether a later alignment pass can undo it. In a controlled logical-reasoning setting (Qwen3-8B-Base, with a 4B replication; five semantically rule-disjoint KOR-Bench domains) we train 30 allocations spanning the five-domain simplex, 24 sweep configurations plus six withheld from the fit, at five seeds each. Three findings emerge. First, every domain has an interior coverage optimum: the moderate band (

10\%

-

40\%

) is best for all five domains, and a calibrated permutation test for quadratic interiority gives

P\approx0.010

; the fitted mid-training-only curves, with 8B peaks between

9.9\%

and

35.1\%

, reproduce for curve shape but not peak location. Second, the gaps survive a fixed-budget alignment pass: compensatory SFT raises 116/120 cells (mean

+4.32\%

) yet bridges

0/240

pairs at a

5\%

threshold and

30/240

at a

10\%

ratio, an equal-budget uniform control behaves almost identically, and a permutation null would bridge

13.8\pm3.3

and

77.9\pm8.5

pairs (

P<0.001

). Third, zero coverage collapses mid-training-only accuracy, though a FineWeb-Edu-only control shows the collapse is commingled with generic drift. An exploratory

θ^*

allocation attains the largest full-pipeline gain (

+4.36\%

vs.

+0.80\%

/

+0.64\%

,pp) but is marginal under Welch test.

Yunpeng Xu, Kun Zheng

LLM Alignment Domain-Adaptive Pretraining Data Mixture Optimization

Aug 31, 2026cs.SE

LLM Post-Training as Brownfield Maintenance: An Industrial Perspective on Dataware Engineering

Industrial post-training is a brownfield regime. Teams inherit a deployed checkpoint and must land targeted improvements under fixed compute and mixture budgets without regressing the rest. The maintained artifact is increasingly dataware: behavior governed by a curated post-training mixture, updated via bounded mixture patches rather than clean-slate retraining. From an industrial code-generation improvement effort, we offer a maintainer's perspective on why this work is hard in practice, distilling three recurring challenges, zero-sum mixture design, yield as the binding metric, and end-to-end integration under uncertainty, and arguing that progress depends less on one-off recipes than on an engineering discipline for programming dataware. In our case study, interventions that raised the conversion of teacher distillation into usable training data increased accepted supervision by 2.84 times while using the same solution teacher and four solution attempts per candidate problem. In our primary evaluation, the yield-engineered patch improved CodeForces pass@1 by +2.59 points (+3.11 pass@3) and held-out LiveCodeBench v6 pass@1 by +6.11 (+8.05 pass@3), all statistically significant across 16 stochastic evaluations of each benchmark from one fixed checkpoint per condition, with internal AIME and MATH regression suites within tolerance.

Gopi Krishnan Rajbahadur, Amir M. Ebrahimi, Boyuan Chen +1

Queen’s University, Canada · Centre for Software Excellence, Huawei Technologies, Canada

Training Data Curation LLM Post-Training Data Mixture Optimization LLM Code Generation

Aug 16, 2026cs.CL

Token Distribution versus Data Volume: Domain Balancing in Multi-Domain Meeting Summarisation

Jointly fine-tuning an LLM on meeting-summarisation corpora of widely varying size raises a question that prior work leaves confounded: when a domain-balanced training mixture helps, is the gain due to the distribution of tokens across domains, or merely to the volume of data seen? We disentangle these factors by constructing balanced and natural (native-proportional) token mixtures at matched token budgets (2-32M) over five English meeting corpora, fine-tuning Mistral-7B with QLoRA, and evaluating per domain. Balancing redistributes quality, improving the data-scarce minority domains at a low cost to the data-rich ones. The trade favours balancing whenever the minority domains matter: their share under proportional allocation is fixed at 1-2% regardless of budget, so matching balanced quality on those domains requires far more total data. We further find that pruning low-value transcript lines removes ~15% of tokens from the conversational corpora at no measurable cost, and that balancing by tokens is not the same as balancing by examples. Fine-tuning one model per domain is competitive only on the data-rich domains and falls below the zero-shot model on the data-scarce ones. A two-annotator study of 741 judge-labelled facts validates our fact-level evaluation. Together these results give practitioners a basis for deciding when to balance an imbalanced multi-domain mixture, and on what unit.

Ashima Sood, Bryan Gardiner, Joan Condell

School of Computing, Engineering and Intelligent Systems, Ulster University Londonderry, Northern Ireland, United Kingdom

LLM Fine-Tuning Text Summarization Training Data Selection Data Mixture Optimization

Jul 30, 2026cs.LG

Harnessing the Potential of Optimizing Data Mixtures via Bayesian Domain Reweighting

The performance of Large Language Models (LLMs) is fundamentally influenced by the distributional composition of multi-domain pre-training data. While manual heuristics were prevalent in early models, they increasingly fail to capture the intricate synergies between domains as data complexity grows. To overcome the issue, a dominant approach seeks to fit a proxy function mapping between domain weights and their corresponding validation losses, and then find the optimal domain weights to minimize validation losses. These methods rely on strong structural assumptions, such as rank invariance or scaling laws, which are often violated, resulting in non-negligible estimation bias. A promising approach is to directly optimize the weighting scheme from data. However, it suffers from unstable optimization trajectory and prohibitive computational overhead, limiting its potential to search better domain weights configurations. This paper presents a Bayesian domain weighting method to infer the weights from a Dirichlet distribution via introducing Gamma prior information learned from observations. Experimental results demonstrate that proposed method could achieve stable and efficient domain weights learning, and identifies optimal mixtures while consuming substantially less data than search-based function-fitting methods, revitalizing optimization-based domain weighting for large-scale applications.

Xiang Yuan, Kaiqing Lei, Zhenyu Jin +3

School of Mathematics and Statistics, Xi’an Jiaotong University · Northwest University, Shaanxi, China

Data Mixture Optimization LLM Training

Jul 27, 2026cs.CV

DecoupleMix: Decoupled Ratio Search and Convex Allocation for Scalable VLM Data Recipes

While data curation for Vision Language Models (VLMs) is increasingly active, public practice for constructing pretraining mixtures remains largely heuristic: practitioners stack datasets that pass quality filters, set cross-domain ratios by intuition, and lack a principled, attributable criterion for admitting new data, while frontier recipes remain undisclosed. We formulate data construction as a systematic mixture-optimization problem and turn it into a reproducible engineering discipline by decoupling the mixture into two orthogonal sub-problems: inter-class ratios across capabilities and intra-class ratios within a category. For inter-class allocation, we use a single-variable iterative search; for intra-class composition, we apply a multidimensional, dataset-level assessment scoring Quality and Difficulty, and formulate selection as a constrained convex optimization with a diversity objective. The DecoupleMix framework delivers two critical capabilities: guiding what data to collect next and rendering dataset validation a controlled, attributable experiment. Experiments show our approach consistently surpasses heuristic baselines. Moreover, optimal ratios discovered on small-scale proxies transfer seamlessly to larger scales without retuning. Using 80B additional multimodal continue-pretraining tokens, our VLM is competitive with strong open-source models trained with substantially larger multimodal budgets.

Jiahao Xie, Zhongbin Guo, Qianle Wang +4

ByteDance · ByteDance Commercial AI Team

Training Data Curation Data Mixture Optimization Vision-Language Pretraining

Jul 24, 2026cs.LG

DomainPilot: Domain-Level Loss-Guided Two-Stage Data Mixture Optimization for Efficient Language Model Fine-Tuning

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.

He Zhang

Tsinghua University

Supervised Fine-Tuning Large Language Model-Guided Optimization Efficient Language Model Training Data Mixture Optimization

Jul 13, 2026cs.LG

Domain-Aware Scaling Laws Uncover Data Synergy

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.

Kimia Hamidieh, Lester Mackey, David Alvarez-Melis

MIT CSAIL · Microsoft Research · Harvard University

Language Model Pretraining Language Model Scaling Laws Data Mixture Optimization

Jul 2, 2026cs.LG

HERMES: A Multi-Granularity Labeling Substrate for Pre-training Data Mixtures

Most data-mixing methods assume the corpus has already been partitioned into groups, and the choice of those groups determines what a mixer can express. Existing labels, including provenance, topic or format taxonomies, and flat embedding clusters, commit to one semantic axis at one granularity; changing the resolution rebuilds the labels. We argue the bottleneck is the label system, not the mixer, and provide a hierarchical one. HERMES is a data-derived labeling substrate: a Learned Semantic Transform followed by 3-stage residual vector quantization annotates each document once into a coarse-to-fine code whose prefix length controls granularity up to approximately 130k cells. At coarse granularity HERMES sits at a plateau with KMeans-family methods on standard clustering metrics, so the contribution is the substrate, not the clusterer. On 1B-parameter, 25B-token pre-training, the hierarchy exposes an interaction fixed-granularity pipelines cannot test: at one prefix length, a combined Stage-2 rule contrast, equal-subbucket coverage versus size-proportional within-bucket quality top-30%, lifts a 16-task capability macro-average by +0.0253; at the next finer level, the same rule loses its measurable edge as candidate pools contract approximately 5x. HERMES reframes data mixture design from choosing among fixed label sets to navigating a reusable, data-derived granularity hierarchy.

Ziyun Qiao, Yue Min, Ruining Chen +1

Wizard Quant, Beijing, China · University of Science and Technology of China, Hefei, China

Language Model Pretraining Training Data Curation Hierarchical Representation Learning Data Mixture Optimization

Jul 1, 2026cs.LG

CausalMix: Data Mixture as Causal Inference for Language Model Training

In Large Language Model (LLM) training, data mixing plays a pivotal role in determining model performance. Recent methods optimize mixture weights via proxy models, but they rely on the assumption of static data distributions. As a result, when the underlying data pool shifts, these methods require costly retraining from scratch. This limitation restricts their ability to scale seamlessly from small settings to larger data pools and model sizes. In this paper, we propose CausalMix to address this limitation by casting data mixture optimization as a causal inference problem. We formulate the statistical features of the data pool as covariates and the domain mixture as the treatment. After fitting a causal model on 512 runs of Qwen2.5-0.5B to estimate the Conditional Average Treatment Effect (CATE), we extrapolate the optimal mixture for an 800K data pool and apply it to train a 7B model. Furthermore, we successfully generalize the framework to long chain-of-thought data on Qwen3-4B-Base. By leveraging causal modeling to isolate confounding biases, CausalMix dynamically infers state-dependent optimal data mixtures. Extensive experiments show that the mixture guided by CausalMix consistently improves performance across multiple downstream tasks, outperforming RegMix and other baselines. In addition, we use the CATE Interpreter to provide visual analysis of the learned mixing strategy. Overall, CausalMix offers a causal and interpretable framework for optimizing LLM data mixtures.

Zinan Tang, Yukun Zhang, Shaomian Zheng +6

Tsinghua University · Ant Group · Renmin University of China

Data Mixture Optimization LLM Training

Jun 12, 2026cs.LG

FastMix: Fast Data Mixture Optimization via Gradient Descent

While large and diverse datasets have driven recent advances in large models, identifying the optimal data mixture for pre-training and post-training remains a significant open problem. We address this challenge with FASTMIX, a novel framework that automates data mixture discovery while training only a single proxy model. Instead of relying on predefined heuristics or resource-intensive simulations, FASTMIX jointly optimizes mixture coefficients and model parameters, substantially improving efficiency and scalability over prior approaches. At the core of FASTMIX is a reformulation of mixture selection as a bilevel optimization problem. Under this reformulation, we show that optimizing mixture ratios is mathematically equivalent to assigning per-source loss weights under uniform source sampling. This embeds the mixture coefficients directly into the differentiable iterative optimization objective, enabling efficient, gradient-based optimization of both mixture and model. To solve the optimization problem, FASTMIX implements an approximate iterative optimization procedure, alternating between (i) updating model parameters on data sampled according to current mixture ratios (inner loop) and (ii) updating mixture ratios based on validation feedback (outer loop). Across pre- and post-training, FASTMIX outperforms baselines while drastically reducing search cost. Code (https://github.com/hrtan/fastmix)

Haoru Tan, Sitong Wu, Yanfeng Chen +5

University of Hong Kong · 2Hunyuan LLM, Tencent · 3Chinese University of Hong Kong

Language Model Pretraining Data Mixture Optimization Language Model Post-Training

Jun 6, 2026cs.LG

Explaining Data Mixing Scaling Laws

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.

Rui Dai, Shuran Zheng

Beijing Institute of Technology · IIIS, Tsinghua University

Data Mixture Optimization Neural Scaling Laws

Jun 3, 2026cs.LG

TANDEM: Bi-Level Data Mixture Optimization with Twin Networks

The capabilities of large language models (LLMs) significantly depend on training data drawn from various domains. Optimizing domain-specific mixture ratios can be modeled as a bi-level optimization problem, which we simplify into a single-level penalized form and solve with twin networks: a proxy model trained on primary data and a dynamically updated reference model trained with additional data. Our proposed method, Twin Networks for bi-level DatA mixturE optiMization (TANDEM), measures the data efficacy through the difference between the twin models and up-weights domains that benefit more from the additional data. TANDEM provides theoretical guarantees and wider applicability, compared to prior approaches. Furthermore, our bi-level perspective suggests new settings to study domain reweighting such as data-restricted scenarios and supervised fine-tuning, where optimized mixture ratios significantly improve the performance. Extensive experiments validate TANDEM's effectiveness in all scenarios.

Jiaxing Wang, Deping Xiang, Jin Xu +9

University of Oxford · Renmin University of China · University of Chinese Academy of Sciences

Bilevel Optimization Data Mixture Optimization

May 29, 2026cs.LG

Repetition Mismatch: Why Data Mixture Experiments Don't Scale and How to Fix Them

Pre-training data mixtures are commonly tuned by running small-scale experiments and extrapolating to the target training budget. When high-quality data is scarce and must be repeated, this extrapolation frequently fails, but the source of the failure has not been isolated. We show that a primary culprit is a repetition mismatch: because high-quality datasets are small, their repetition rate changes as the training budget grows, shifting the optimal mixture in ways that small-scale proxy experiments do not anticipate. A subsampling procedure that matches the target repetition rate controls for this effect. In a two-source setting combining limited high-quality data with web crawl, a single repetition-controlled experiment using only 1/16 of the target tokens recovers a mixture within 0.10 of the optimum on Wiki-Text for a 1.17B parameter model, compared to an error of 0.85 without repetition control. Achieving comparable accuracy without repetition control requires multiple training horizons, consuming 19%, 44%, and 94% of the target token budget when using the results from two, three, and four horizons respectively. With three data sources, the larger mixture space requires more than a single experiment to constrain, but the approach remains effective: at the 757M scale, just two repetition-controlled horizons recover the optimal mixture, outperforming baselines that instead require the full two-source experiments to construct. Our results reveal that repetition dynamics, not scale alone, shape whether small-scale mixture experiments generalize. More broadly, they suggest that data repetition deserves treatment as a first-class variable in mixture optimization, rather than an inconvenient side effect of limited data.

Kevin Zhou, Lisa Alazraki, Kris Cao +1

Imperial College London · Cohere

Language Model Pretraining Data Mixture Optimization Data Repetition in Language Model Training

May 20, 2026cs.CV

Closed Loop Dynamic Driving Data Mixture for Real-Synthetic Co-Training

Data scaling is fundamental to modern deep learning, and grows increasingly critical as autonomous driving shifts to end-to-end learning. Real-world driving data is expensive to annotate and scene-biased, making real-synthetic co-training with near-infinite synthetic data a promising direction. However, naively incorporating all available synthetic data is inefficient and leads to distribution shifts, and optimizing data mixture under practical training budgets remains a critical yet under-explored problem. In this sense, we claim that the mixture of training data requires clear guidance in terms of scene types and quantities. Particularly in this work, we conceptualize the data mixture approximately as a dynamic optimization process that iteratively adjusts the training data mixture to maximize model performance, guided by closed-loop evaluation feedback, and propose AutoScale, a fully automated closed-loop data engine unifying scene representation, data mixture optimization and retrieval, as well as model training and evaluation. Specifically, we propose Graph Regularized AutoEncoder (Graph-RAE) for driving scene representations, introduce Cluster-aware Gradient Ascent (Cluster-GA) for cluster-wise importance estimation and reweighting, and perform cluster-guided vector retrieval to select high-value samples. Experiments on NavSim demonstrate that AutoScale outperforms vanilla co-training and cross-domain baselines, achieving better performance with fewer synthetic samples under constrained budgets.

Hongzhi Ruan, Pei Liu, Weiliang Ma +5

Li Auto · HKUST (GZ) · HKUST

Autonomous Driving Datasets Synthetic Data Augmentation End-to-End Autonomous Driving Adaptive Sampling Data Mixture Optimization

May 12, 2026cs.LG

Scaling Laws for Mixture Pretraining Under Data Constraints

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.

Anastasiia Sedova, Skyler Seto, Natalie Schluter +1

Apple · ITU

Language Model Pretraining Language Model Scaling Laws Data Mixture Optimization LLM Training Data Repetition in Language Model Training

May 11, 2026cs.LG

DynaMiCS: Fine-tuning LLMs with Performance Constraints using Dynamic Mixtures

Multi-domain fine-tuning of large language models requires improving performance on target domains while preserving previous capabilities, such as general knowledge, instruction following, or safety evaluations. Existing data mixing strategies rely on fixed heuristics or adaptive rules that cannot explicitly enforce preservation of such capabilities. We propose DynaMiCS, a dynamic mixture optimizer that casts multi-domain fine-tuning as a constrained optimization problem. At each update, DynaMiCS performs short domain-specific probing runs to estimate a slope matrix of local cross-domain effects, capturing how training on each fine-tuning dataset affects each evaluation domain. These estimates are then used to compute mixture weights through optimization over the probability simplex, with the objective of improving target-domain performance while keeping constrained-domain metrics within a specified tolerance of reference levels. Because these effects are measured by finite differences rather than gradients, targets and constraints need not be differentiable, or present in the fine-tuning data, and can be specified directly as benchmark accuracies. Across scenarios with varying numbers of target and constrained domains, and with loss- or accuracy-based objectives, DynaMiCS achieves stronger target-domain improvements and higher constraint satisfaction than static, dynamic, similarity-based and probing-based alternatives, without a reference model, per-example scoring, or manually tuned weights.

Eleonora Gualdoni, Sonia Laguna, Louis Bethune +3

Apple

Fine-Tuning LLM Fine-Tuning Data Mixture Optimization

May 4, 2026cs.CL

InfoLaw: Information Scaling Laws for Large Language Models with Quality-Weighted Mixture Data and Repetition

Upweighting high-quality data in LLM pretraining often improves performance, but in datalimited regimes, especially under overtraining, stronger upweighting increases repetition and can degrade performance. However, standard scaling laws do not reliably extrapolate across mixture recipes or under repetitions, making the selection for optimal data recipes at scaling underdetermined. To solve this, we introduce InfoLaw (Information Scaling Laws), a data-aware scaling framework that predicts loss from consumed tokens, model size, data mixture weights, and repetition. The key idea is to model pretraining as information accumulation, where quality controls information density and repetition induces scaledependent diminishing returns. We first collect the model performance after training on datasets that vary in scale, quality distribution, and repetition level. Then we build up the modeling for information so that information accurately predicts those model performance. InfoLaw predicts performance on unseen data recipes and larger scale runs (up to 7B, 425B tokens) with 0.15% mean and 0.96% max absolute error in loss, and it extrapolates reliably across overtraining levels, enabling efficient data-recipe selection under varying compute budgets.

Fengze Liu, Weidong Zhou, Binbin Liu +7

1ByteDance · 2UC Santa Cruz

Language Model Pretraining Language Model Scaling Laws Data Mixture Optimization Data Repetition in Language Model Training

Apr 27, 2026cs.LG

GEM: Geometric Entropy Mixing for Optimal LLM Data Curation

LLM pre-training efficacy increasingly depends on data composition rather than sheer volume. Yet, optimal mixing is hindered by categorization flaws: human taxonomies suffer from ontological misalignment, and Euclidean clustering fails to address embedding anisotropy. We introduce GEM (Geometric Entropy Mixing), a framework reformulating data curation as a variational problem on the hypersphere augmented with a mixing-balance regularizer. By decoupling the generative prior and optimizing the objective via a provable MM (Minorize-Maximize) algorithm, GEM effectively counteracts the cluster collapse to discover balanced semantic structures invisible to Euclidean heuristics. We employ teacher-student distillation to scale this geometric fidelity to web-scale corpora and introduce the Geometric Influence Score (GIS) for interpretable taxonomy generation. Experiments with 1.1B-parameter models demonstrate that GEM establishes a new state-of-the-art when integrated into mixing strategies like DoReMi and RegMix, improving average downstream accuracy by up to 1.2% and offering a robust coordinate system for predictable data mixing.

Yue Min, Ziyun Qiao, Ruining Chen +1

Wizard Quant, Beijing, China · The Hong Kong University of Science and Technology, Hong Kong SAR, China · Peking University, Beijing, China +1

Language Model Pretraining Training Data Curation Geometric Representation Learning Data Mixture Optimization

Mar 27, 2026cs.LG

DataFlex: A Unified Framework for Data-Centric Dynamic Training of Large Language Models

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.

Hao Liang, Zhengyang Zhao, Mingrui Chen +22

Peking University · Institute for Advanced Algorithms Research, Shanghai

Training Data Selection Data Mixture Optimization LLM Training

Mar 17, 2026cs.CL

Domain Mixture Design via Log-Likelihood Differences for Aligning Language Models with a Target Model

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.

Ryo Kishino, Riku Shiomi, Hiroaki Yamagiwa +2

1Kyoto University · 2RIKEN

Language Model Pretraining LLM Alignment Data Mixture Optimization

Sep 26, 2025math.OC

Mixtures Closest to a Given Measure: A Semidefinite Programming Approach

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.

Srećko Đurašinović, Jean-Bernard Lasserre, Victor Magron

College of Computing and Data Science, NTU, Singapore · LAAS-CNRS, Toulouse, France · Toulouse School of Economics +1

Semidefinite Programming Data Mixture Optimization

Aug 16, 2025cs.LG

DynamixSFT: Dynamic Mixture Optimization of Instruction Tuning Collections

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.

Haebin Shin, Lei Ji, Xiao Liu +4

University of Michigan · Microsoft Research · KAIST AI +1

Multi-Armed Bandits Instruction Tuning Data Mixture Optimization