稠密检索何时需要非对称几何？共享与双投影的偏差-方差理论
原标题：When Does Dense Retrieval Need Asymmetric Geometry? A Bias-Variance Theory of Shared and Dual Projections
AI 摘要
该论文研究稠密检索中共享投影与双投影的选择问题，提出偏差-方差理论。共享投影产生半正定算子，双投影可实现任意低秩算子，作者推导出精确近似差距并证明局部高斯边界：当方向信号平方超过额外自由度估计成本时双投影风险更低。基于此提出CARS选择器，在多个数据集和嵌入模型上实验，CARS将留出遗憾降低49-96%，几何选择平均准确率达90.1%。
正文节选
When Does Dense Retrieval Need Asymmetric Geometry? A Bias–Variance Theory of Shared and Dual Projections Abstract Dense retrieval powers retrieval-augmented generation, semantic search, and question answering, yet the theoretical basis for choosing between shared and dual query–document projections remains unclear. We introduce a bias–variance theory for low-rank bilinear scoring. Shared projections induce positive-semidefinite operators, whereas dual projections realize arbitrary low-rank oper