检索引导微调作为噪声估计：风险界与架构分析
Retrieval-Guided Fine-Tuning as Noisy Estimation: Risk bounds and Architectural Analysis
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中文总结 AI 辅助
本研究将检索引导微调建模为多任务线性回归中的噪声估计问题，证明其风险界优于仅目标训练，并揭示线性自注意力前向传播的固定聚合是性能不稳定的根源，而OLS代理则保持最优风险。
中文摘要 AI 辅助
检索引导微调（RAG-FT）将检索到的数据直接纳入训练目标，但训练过程中噪声检索的统计后果在理论上仍未被充分刻画。我们通过在多任务线性回归框架中将RAG-FT建模为估计问题来研究这一问题，使用单层线性自注意力的OLS代理以获得有限样本风险界。在同方差检索噪声下，我们证明检索失败随任务分离度相对于噪声呈指数衰减，并推导出RAG-FT实现比仅目标训练和全语料训练更低风险的显式有限样本条件。随后，我们引入距离比例噪声（DPN）模型，其中检索质量随排名下降，并在相同检索过程下比较两种估计器：OLS代理和线性自注意力的字面、均匀权重前向传播。我们证明注意力估计器的偏差在精确检索下也发散为$\Theta(n^{2q})$，而OLS风险对每个噪声指数$q>0$保持为$\Theta(d/n)$。这些结果将不稳定性定位于字面LSA前向传播的固定、未加权聚合，而非噪声检索本身，通过可靠性重新加权可经验性地消除这种不稳定性。我们通过DPN模型的直接模拟验证了预测的速率分离。
英文摘要
Retrieval-Guided Fine-Tuning (RAG-FT) incorporates retrieved data directly into the training objective, but the statistical consequences of noisy retrieval during training remain theoretically undercharacterized. We study this question by modeling RAG-FT as an estimation problem in a multi-task linear regression framework, using an OLS proxy for single-layer linear self-attention to obtain finite-sample risk bounds. Under homoscedastic retrieval noise, we show that retrieval failure decays exponentially with task separation relative to noise, and derive explicit finite-sample conditions under which RAG-FT achieves lower risk than both target-only and full-corpus training. We then introduce a Distance-Proportional Noise (DPN) model, in which retrieval quality degrades with rank, and compare two estimators under the same retrieval process: the OLS proxy and the literal, uniform-weight forward pass of linear self-attention. We prove that the attention estimator's bias diverges as $Θ(n^{2q})$ even under exact retrieval, while OLS risk remains $Θ(d/n)$ for every noise exponent $q>0$. These results locate the instability not in noisy retrieval itself, but in the fixed, unweighted aggregation of the literal LSA forward pass, which reweighting by reliability empirically removes. We validate the predicted rate separation through direct simulation of the DPN model.
发表机构
- Indian Institute of Technology Delhi（印度理工学院德里分校）
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。
