Abstract
Dense vector retrieval is essential for semantic queries within Natural Language Processing, particularly in knowledge-intensive applications like Retrieval-Augmented Generation (RAG). The ability to retrieve vectors that satisfy both similarity and diversity substantially enhances system performance. Although the Maximal Marginal Relevance (MMR) algorithm is widely used to balance these objectives, its reliance on a manually tuned parameter leads to optimization fluctuations and unpredictable retrieval results. Furthermore, there is a lack of sufficient theoretical analysis on the joint optimization of similarity and diversity in vector retrieval. To address these challenges, this paper introduces a novel approach that characterizes both constraints simultaneously by maximizing the similarity between the query vector and the sum of the selected candidate vectors. We formally define this optimization problem, Vectors Retrieval with Similarity and Diversity (VRSD) , and prove that it is