# Towards Scalable Data Diversification for Language Model Pretraining via Leverage Score Sampling

arXiv: https://arxiv.org/abs/2609.32484 · HTML: https://mlsanity.com/paper/2609.32484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 53 of its 67 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 53)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Bag of Tricks for Efficient Text Classification](https://mlsanity.com/paper/1607.01759/) (2016)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [Nemotron-CC: Transforming Common Crawl into a Refined Long-Horizon Pretraining Dataset](https://mlsanity.com/paper/2412.02595/) (2024)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [OLMES: A Standard for Language Model Evaluations](https://mlsanity.com/paper/2406.08446/) (2024)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [How to Train Data-Efficient LLMs](https://mlsanity.com/paper/2402.09668/) (2024)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Data Diversity Matters for Robust Instruction Tuning](https://mlsanity.com/paper/2311.14736/) (2023)
- [Organize the Web: Constructing Domains Enhances Pre-Training Data Curation](https://mlsanity.com/paper/2502.10341/) (2025)
- [SEAL: Safety-enhanced Aligned LLM Fine-tuning via Bilevel Data Selection](https://mlsanity.com/paper/2410.07471/) (2024)
- [Clustering and Ranking: Diversity-preserved Instruction Selection through Expert-aligned Quality Estimation](https://mlsanity.com/paper/2402.18191/) (2024)
- [Data Selection via Optimal Control for Language Models](https://mlsanity.com/paper/2410.07064/) (2024)
- [Ultra-FineWeb: Efficient Data Filtering and Verification for High-Quality LLM Training Data](https://mlsanity.com/paper/2505.05427/) (2025)
- [Harnessing Diversity for Important Data Selection in Pretraining Large Language Models](https://mlsanity.com/paper/2409.16986/) (2024)
- [Recycling the Web: A Method to Enhance Pre-training Data Quality and Quantity for Language Models](https://mlsanity.com/paper/2506.04689/) (2025)
- [Semantic Diversity in Dialogue with Natural Language Inference](https://mlsanity.com/paper/2205.01497/) (2022)

## Abstract (arXiv)

Data selection for language model pretraining faces a fundamental tension between quality and diversity. While quality filtering is empirically effective, it often induces diversity collapse: by favoring texts similar to high-quality reference corpora (e.g., educational or QA-style data), it systematically excludes valuable data from underrepresented domains. In contrast, diversified selection preserves domain balance and encourages robust downstream performance, yet existing methods either focus on coverage-oriented objectives that indirectly enhance diversity, or directly optimize for diversity via costly covariance matrix recomputation that limits scalability. To address these issues, we introduce Leverage Score Sampling (Lev), which iteratively selects samples that maximally expand the determinantal volume of the embedded data via leverage scores, a computationally efficient criterion that eliminates matrix recomputation and enables scalable selection. Empirically, Lev delivers up to 72× speedup and improves dataset diversity, measured by the Vendi score, by 9.2% over the strong diversification baseline DiSF. On CommonCrawl (CC) web data selection, Lev improves accuracy across seven downstream tasks by up to 1.31% over existing baselines. For domains where robust quality criteria are inherently difficult to define (e.g., code), Lev serves as an effective unsupervised curation alternative: on StarCoderData, the selected subset reduces bits-per-byte by 3.08% over DiSF. Notably, we uncover a cross-domain collapse of quality filtering: CC data filtered by DCLM-fastText fail to retain sufficient code-related content, yielding inferior code performance relative to Lev-selected data. These findings advocate for integrating diversity-aware practices into quality filtering for more effective data curation in language model pretraining.