# Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance

arXiv: https://arxiv.org/abs/2403.16952 · HTML: https://mlsanity.com/paper/2403.16952/

## Key facts

- Cited by 184 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 74 references that are in the map.
- First posted on arXiv 25 Mar 2024.

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [CCNet: Extracting High Quality Monolingual Datasets from Web Crawl Data](https://mlsanity.com/paper/1911.00359/) (2019)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Effective Long-Context Scaling of Foundation Models](https://mlsanity.com/paper/2309.16039/) (2023)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)

## Built on by (most cited first, 30 of 184)

- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Organize the Web: Constructing Domains Enhances Pre-Training Data Curation](https://mlsanity.com/paper/2502.10341/) (2025)
- [A Survey of Multimodal Large Language Model from A Data-centric Perspective](https://mlsanity.com/paper/2405.16640/) (2024)
- [Archon: An Architecture Search Framework for Inference-Time Techniques](https://mlsanity.com/paper/2409.15254/) (2024)
- [Scaling Laws for Optimal Data Mixtures](https://mlsanity.com/paper/2507.09404/) (2025)
- [Scaling Laws for Predicting Downstream Performance in LLMs](https://mlsanity.com/paper/2410.08527/) (2024)
- [Adaptive Data Optimization: Dynamic Sample Selection with Scaling Laws](https://mlsanity.com/paper/2410.11820/) (2024)
- [D-CPT Law: Domain-specific Continual Pre-Training Scaling Law for Large Language Models](https://mlsanity.com/paper/2406.01375/) (2024)
- [Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Models](https://mlsanity.com/paper/2412.02980/) (2024)
- [Aioli: A Unified Optimization Framework for Language Model Data Mixing](https://mlsanity.com/paper/2411.05735/) (2024)
- [Towards Neural Scaling Laws for Time Series Foundation Models](https://mlsanity.com/paper/2410.12360/) (2024)
- [Parallel Scaling Law for Language Models](https://mlsanity.com/paper/2505.10475/) (2025)
- [MoDoMoDo: Multi-Domain Data Mixtures for Multimodal LLM Reinforcement Learning](https://mlsanity.com/paper/2505.24871/) (2025)
- [MiniPLM: Knowledge Distillation for Pre-Training Language Models](https://mlsanity.com/paper/2410.17215/) (2024)
- [DDK: Distilling Domain Knowledge for Efficient Large Language Models](https://mlsanity.com/paper/2407.16154/) (2024)
- [Demystifying Synthetic Data in LLM Pre-training: A Systematic Study of Scaling Laws, Benefits, and Pitfalls](https://mlsanity.com/paper/2510.01631/) (2025)
- [CMR Scaling Law: Predicting Critical Mixture Ratios for Continual Pre-training of Language Models](https://mlsanity.com/paper/2407.17467/) (2024)
- [Learning to See Before Seeing: Demystifying LLM Visual Priors from Language Pre-training](https://mlsanity.com/paper/2509.26625/) (2025)
- [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)
- [E-RayZer: Self-supervised 3D Reconstruction as Spatial Visual Pre-training](https://mlsanity.com/paper/2512.10950/) (2025)
- [Structured Scaling of AI Discovery Across Diverse Scientific Domains](https://mlsanity.com/paper/2604.19341/) (2026)
- [Meta-rater: A Multi-dimensional Data Selection Method for Pre-training Language Models](https://mlsanity.com/paper/2504.14194/) (2025)
- [MagicGUI: A Foundational Mobile GUI Agent with Scalable Data Pipeline and Reinforcement Fine-tuning](https://mlsanity.com/paper/2508.03700/) (2025)
- [Phoenix: A Motion-based Self-Reflection Framework for Fine-grained Robotic Action Correction](https://mlsanity.com/paper/2504.14588/) (2025)
- [QuaDMix: Quality-Diversity Balanced Data Selection for Efficient LLM Pretraining](https://mlsanity.com/paper/2504.16511/) (2025)
- [Data Mixing Can Induce Phase Transitions in Knowledge Acquisition](https://mlsanity.com/paper/2505.18091/) (2025)
- [Loss-to-Loss Prediction: Scaling Laws for All Datasets](https://mlsanity.com/paper/2411.12925/) (2024)

## Abstract (arXiv)

Pretraining data of large language models composes multiple domains (e.g., web texts, academic papers, codes), whose mixture proportions crucially impact the competence of outcome models. While existing endeavors rely on heuristics or qualitative strategies to tune the proportions, we discover the quantitative predictability of model performance regarding the mixture proportions in function forms, which we refer to as the data mixing laws. Fitting such functions on sample mixtures unveils model performance on unseen mixtures before actual runs, thus guiding the selection of an ideal data mixture. Furthermore, we propose nested use of the scaling laws of training steps, model sizes, and our data mixing law to enable predicting the performance of large models trained on massive data under various mixtures with only small-scale training. Moreover, experimental results verify that our method effectively optimizes the training mixture of a 1B model trained for 100B tokens in RedPajama, reaching a performance comparable to the one trained for 48% more steps on the default mixture. Extending the application of data mixing laws to continual training accurately predicts the critical mixture proportion that avoids catastrophic forgetting and outlooks the potential for dynamic data schedules