用信息投影方法高效筛选大模型训练数据，兼顾质量与多样性。
Greedy Information Projection for LLM Data Selection
- 通过最大化数据与任务信号的互信息来选样本
- 仅用少量数据就达到全量数据的微调效果
- 适合需要高效微调的科研与工程场景
我们提出一种名为「贪心信息投影」（Greedy Information Projection, GIP）的训练数据选择框架，用于大语言模型的微调。GIP 将数据选择建模为最大化选定样本子集与任务相关查询信号之间的互信息，查询信号可来自模型质量判断、元数据等。该框架基于数据和查询嵌入定义闭式互信息目标，自然平衡了质量与多样性。优化过程等价于将查询嵌入矩阵投影到所选数据张成的空间，提供了质量与多样性协同出现的几何解释。在此基础上，我们采用快速贪心匹配追踪算法，结合高效的投影更新机制。在指令遵循和数学推理数据集上，GIP 能选出极小规模的样本子集，实现与全数据微调相当的性能，同时仅使用极少的样本和计算资源，统一了质量感知与多样性感知的数据选择策略，显著提升微调效率。
原文摘要 · Abstract (English)
We present \emph{Greedy Information Projection} (\textsc{GIP}), a principled framework for choosing training examples for large language model fine-tuning. \textsc{GIP} casts selection as maximizing mutual information between a subset of examples and task-specific query signals, which may originate from LLM quality judgments, metadata, or other sources. The framework involves optimizing a closed-form mutual information objective defined using both data and query embeddings, naturally balancing {\it quality} and {\it diversity}. Optimizing this score is equivalent to maximizing the projection of the query embedding matrix onto the span of the selected data, which provides a geometric explanation for the co-emergence of quality and diversity. Building on this view, we employ a fast greedy matching-pursuit procedure with efficient projection-based updates. On instruction-following and mathematical reasoning datasets, \textsc{GIP} selects small subsets that match full-data fine-tuning while using only a fraction of examples and compute, unifying quality-aware and diversity-aware selection for efficient fine-tuning.
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