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

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 \textbf{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 $65\times$ speedup and improves dataset diversity, measured by the Vendi score, by $9.2\%$ over the strong diversification baseline \textbf{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.