Aligning the Query Space: Greedy Information Projection for Language Model Data Selection

Victor Ye Dong, Kuan-Yun Lee, Jiamei Shuai, Shengfei Liu, Yi Liu, Jian Jiao


Abstract
Data selection for language models is often framed as balancing example quality and diversity. We argue that both are consequences of a more fundamental principle: selected examples should preserve the downstream query space induced by instructions, task signals, or retrieval needs. We present Greedy Information Projection (GIP), a query-aligned method that requires only candidate embeddings and a score signal from LLM judgments, metadata, or intrinsic geometry. GIP greedily selects examples whose embedding span explains the largest residual component of task/query scores, yielding a fast matching-pursuit selector. A Gaussian projection view connects this update to maximizing mutual information, equivalently minimizing the residual volume of the query subspace left unexplained by selected data; this explains how quality and diversity emerge from one objective. Empirically, GIP matches or surpasses full-data fine-tuning using small instruction and reasoning subsets, while pretraining and RAG passage-selection experiments show that the same residual principle transfers beyond supervised fine-tuning.
Anthology ID:
2026.emnlp-main.1814
Volume:
Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
Month:
October
Year:
2026
Address:
Budapest, Hungary
Editors:
Hung-Yi Lee, Sunipa Dev, Jessy Li, Desmond Elliott
Venue:
EMNLP
SIG:
SIGDAT
Publisher:
Association for Computational Linguistics
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Pages:
41334–41361
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URL:
https://aclanthology.org/2026.emnlp-main.1814/
DOI:
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Cite (ACL):
Victor Ye Dong, Kuan-Yun Lee, Jiamei Shuai, Shengfei Liu, Yi Liu, and Jian Jiao. 2026. Aligning the Query Space: Greedy Information Projection for Language Model Data Selection. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 41334–41361, Budapest, Hungary. Association for Computational Linguistics.
Cite (Informal):
Aligning the Query Space: Greedy Information Projection for Language Model Data Selection (Dong et al., EMNLP 2026)
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https://aclanthology.org/2026.emnlp-main.1814.pdf