Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming

Diversity-aware retrieval is essential for Retrieval-Augmented Generation (RAG), yet existing methods lack theoretical guarantees and face scalability issues as the number of retrieved passages $k$ increases. We propose a principled formulation of diversity retrieval as a cardinality-constrained binary quadratic programming (CCBQP), which explicitly balances relevance and semantic diversity through an interpretable trade-off parameter. Inspired by recent advances in combinatorial optimization, we develop a non-convex tight continuous relaxation and a Frank--Wolfe based algorithm with landscape analysis and convergence guarantees. Extensive experiments demonstrate that our method consistently dominates baselines on the relevance-diversity Pareto frontier, while achieving significant speedup.

Decentralized Complete Dictionary Learning via $\ell^{4}$-Norm Maximization

With the rapid development of information technologies, centralized data processing is subject to many limitations, such as computational overheads, communication delays, and data privacy leakage. Decentralized data processing over networked terminal nodes becomes an important technology in the era of big data. Dictionary learning is a powerful representation learning method to exploit the low-dimensional structure from the high-dimensional data. By exploiting the low-dimensional structure, the storage and the processing overhead of data can be effectively reduced. In this paper, we propose a novel decentralized complete dictionary learning algorithm, which is based on $\ell^{4}$-norm maximization. Compared with existing decentralized dictionary learning algorithms, comprehensive numerical experiments show that the novel algorithm has significant advantages in terms of per-iteration computational complexity, communication cost, and convergence rate in many scenarios. Moreover, a rigorous theoretical analysis shows that the dictionaries learned by the proposed algorithm can converge to the one learned by a centralized dictionary learning algorithm at a linear rate with high probability under certain conditions.