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

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.

Accepted to EMNLP 2026. An earlier version was accepted to 3rd DATA-FM workshop at ICLR 2026

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2603.13790 [cs.LG]

(or arXiv:2603.13790v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.13790 Focus to learn more arXiv-issued DOI via DataCite

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