# BiMix: A Bivariate Data Mixing Law for Language Model Pretraining

arXiv: https://arxiv.org/abs/2405.14908 · HTML: https://mlsanity.com/paper/2405.14908/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2024.

## Built on by (most cited first, 25 of 25)

- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [A Survey of Multimodal Large Language Model from A Data-centric Perspective](https://mlsanity.com/paper/2405.16640/) (2024)
- [Scaling Laws for Optimal Data Mixtures](https://mlsanity.com/paper/2507.09404/) (2025)
- [CMR Scaling Law: Predicting Critical Mixture Ratios for Continual Pre-training of Language Models](https://mlsanity.com/paper/2407.17467/) (2024)
- [AutoScale: Scale-Aware Data Mixing for Pre-Training LLMs](https://mlsanity.com/paper/2407.20177/) (2024)
- [A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules](https://mlsanity.com/paper/2503.12811/) (2025)
- [ATLAS: Adaptive Transfer Scaling Laws for Multilingual Pretraining, Finetuning, and Decoding the Curse of Multilinguality](https://mlsanity.com/paper/2510.22037/) (2025)
- [The Synergy between Data and Multi-Modal Large Language Models: A Survey from Co-Development Perspective](https://mlsanity.com/paper/2407.08583/) (2024)
- [AgentMonitor: A Plug-and-Play Framework for Predictive and Secure Multi-Agent Systems](https://mlsanity.com/paper/2408.14972/) (2024)
- [Data Mixture Optimization: A Multi-fidelity Multi-scale Bayesian Framework](https://mlsanity.com/paper/2503.21023/) (2025)
- [MergeMix: Optimizing Mid-Training Data Mixtures via Learnable Model Merging](https://mlsanity.com/paper/2601.17858/) (2026)
- [DUET: Optimizing Training Data Mixtures via Feedback from Unseen Evaluation Tasks](https://mlsanity.com/paper/2502.00270/) (2025)
- [Measuring Fingerprints of Web-filtered Text Datasets and Fingerprint Propagation Through Training](https://mlsanity.com/paper/2412.02857/) (2024)
- [Towards Compositional Generalization of LLMs via Skill Taxonomy Guided Data Synthesis](https://mlsanity.com/paper/2601.03676/) (2026)
- [R&B: Domain Regrouping and Data Mixture Balancing for Efficient Foundation Model Training](https://mlsanity.com/paper/2505.00358/) (2025)
- [Demystifying Data Organization for Enhanced LLM Training](https://mlsanity.com/paper/2605.30334/) (2026)
- [DaMo: Data Mixing Optimizer in Fine-tuning Multimodal LLMs for Mobile Phone Agents](https://mlsanity.com/paper/2510.19336/) (2025)
- [Repetition Mismatch: Why Data Mixture Experiments Don't Scale and How to Fix Them](https://mlsanity.com/paper/2606.07597/) (2026)
- [Capacity-Aware Mixture Law Enables Efficient LLM Data Optimization](https://mlsanity.com/paper/2603.08022/) (2026)
- [DataProphet: Demystifying Supervision Data Generalization in Multimodal LLMs](https://mlsanity.com/paper/2603.19688/) (2026)
- [Data Mixing as Mixture Experiment: Response Surface Methodology and Optimal Design for Large Language Model Pretraining](https://mlsanity.com/paper/2608.23922/) (2026)
- [Knowledge Transfer Scaling Laws for 3D Medical Imaging](https://mlsanity.com/paper/2605.06859/) (2026)
- [Harnessing the Potential of Optimizing Data Mixtures via Bayesian Domain Reweighting](https://mlsanity.com/paper/2607.27928/) (2026)
- [When do data mixtures improve scaling laws? Insights from high-dimensional regression](https://mlsanity.com/paper/2609.38011/) (2026)
- [Selecting Repetition Counts Across Model Scales in Data-Constrained Pretraining](https://mlsanity.com/paper/2610.05126/) (2026)

## Abstract (arXiv)

Large language models have demonstrated remarkable capabilities across various tasks, primarily attributed to the utilization of diversely sourced data. However, the impact of pretraining data composition on model performance remains poorly understood. This paper introduces BiMix, a novel bivariate data mixing law that models the joint scaling behavior of domain proportions and data volume in LLM pretraining. BiMix provides a systematic framework for understanding and optimizing data mixtures across diverse domains. Through extensive experiments on two large-scale datasets, we demonstrate BiMix's high accuracy in loss extrapolation (mean relative error < 0.2%) and its generalization to unseen mixtures (R2 > 0.97). Optimization of domain proportions yields superior model performance compared to existing methods. Furthermore, we establish entropy-based measures as efficient proxies for data mixing, offering a computationally lightweight strategy. Our work contributes both theoretical insights into data mixing dynamics and practical tools for enhancing LLM training efficiency, paving the way for more effective scaling strategies in language model development.