# Optimizing Pre-Training Data Mixtures with Mixtures of Data Expert Models

arXiv: https://arxiv.org/abs/2502.15950 · HTML: https://mlsanity.com/paper/2502.15950/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [WiC: the Word-in-Context Dataset for Evaluating Context-Sensitive Meaning Representations](https://mlsanity.com/paper/1808.09121/) (2018)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [DoGE: Domain Reweighting with Generalization Estimation](https://mlsanity.com/paper/2310.15393/) (2023)
- [Efficient Online Data Mixing For Language Model Pre-Training](https://mlsanity.com/paper/2312.02406/) (2023)
- [The Vizier Gaussian Process Bandit Algorithm](https://mlsanity.com/paper/2408.11527/) (2024)
- [Scalable Data Ablation Approximations for Language Models through Modular Training and Merging](https://mlsanity.com/paper/2410.15661/) (2024)
- [Geometric and computational hardness of bilevel programming](https://mlsanity.com/paper/2407.12372/) (2024)
- [Completeness in the Polynomial Hierarchy for many natural Problems in Bilevel and Robust Optimization](https://mlsanity.com/paper/2311.10540/) (2023)

## Built on by (most cited first, 5 of 5)

- [MergeMix: Optimizing Mid-Training Data Mixtures via Learnable Model Merging](https://mlsanity.com/paper/2601.17858/) (2026)
- [RegMix-D: Dynamic Data Mixing via Proxy Training Trajectories](https://mlsanity.com/paper/2606.18663/) (2026)
- [Laguna M.1/XS.2 Technical Report](https://mlsanity.com/paper/2605.27605/) (2026)
- [Harnessing the Potential of Optimizing Data Mixtures via Bayesian Domain Reweighting](https://mlsanity.com/paper/2607.27928/) (2026)
- [Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesics](https://mlsanity.com/paper/2609.09099/) (2026)

## Abstract (arXiv)

We propose a method to optimize language model pre-training data mixtures through efficient approximation of the cross-entropy loss corresponding to each candidate mixture via a Mixture of Data Experts (MDE). We use this approximation as a source of additional features in a regression model, trained from observations of model loss for a small number of mixtures. Experiments with Transformer decoder-only language models in the range of 70M to 1B parameters on the SlimPajama dataset show that our method achieves significantly better performance than approaches that train regression models using only the mixture rates as input features. Combining this improved optimization method with an objective that takes into account cross-entropy on end task data leads to superior performance on few-shot downstream evaluations. We also provide theoretical insights on why aggregation of data expert predictions can provide good approximations to model losses for data mixtures.