AI 中文总结
代数检索通过数学查询组合搜索策略，基于PEM实现对比评分、重排序和加权排序，在Vaswani基准上验证了执行等价性。
AI 中文摘要
代数检索（Algebraic Retrieval）让AI智能体在查询时组合搜索策略。相关性标准、资格约束和排序偏好可以在一个数学查询中共同表达。查询表面暴露了可用的操作，因此智能体可以针对当前问题组合这些操作，并在检查结果后修改程序。我们评估的是执行等价性，而非智能体行为或检索质量。基于程序化嵌入调制（Programmatic Embedding Modulation, PEM），该技术在检索期间暴露向量和分数运算，我们演示了对比评分、候选池重排序和加权排序作为可组合查询，并配有可执行的SQL和PyTerrier对应实现。在公开的包含11,429篇文档的Vaswani基准上，每个程序的实现选择相同的文档集，分数差异低于1e-6；有一对并列的排序在不同评分路径下顺序不同。
英文摘要
Algebraic Retrieval lets AI agents compose search strategies at query time. Relevance criteria, eligibility constraints, and ranking preferences can be expressed together in a mathematical query. The query surface exposes available operations, so an agent can combine them for the question at hand and revise a program after inspecting results. We evaluate execution parity, not agent behavior or retrieval quality. Building on Programmatic Embedding Modulation (PEM), which exposes vector and score arithmetic during retrieval, we demonstrate contrastive scoring, candidate-pool reranking, and weighted ranking as composable queries, alongside executable SQL and PyTerrier counterparts. On the public 11,429-document Vaswani fixture, each program's implementations select the same document set with score differences below 1e-6; one tied pair orders differently across scoring paths.
Comments5 pages, 1 figure. Code and reproducible examples: https://github.com/algebraicretrieval/algebraicretrieval
