A Wasserstein Barycenter Index For Efficient Rank Fusion

Information retrieval pipelines routinely aggregate diverse base rankers, e.g., lexical, sparse, and dense, to exploit their complementary strengths. Classical fusion methods score query-document pairs pointwise and, therefore, typically ignore the relationships among retrieved documents in the embedding space. As a result, they treat near-duplicate clusters and genuinely complementary subsets alike. In this work, we recast rank fusion as a Restricted Support Wasserstein Barycenter (RSWB) problem that jointly optimizes the retrieved set and its ranking order. We then fix the support set and cast RSWB as a set-function objective. We further show that it is monotone and restricted submodular, yielding approximation guarantees for greedy maximization. However, the greedy algorithm requires an exhaustive search over the entire corpus during the marginal-gain computation step. Therefore, we approximate the marginal gain using an approximate nearest neighbor (ANN) index amenable to dot-product approximation. This reduces each greedy step to an approximate ANN search, enabling sublinear retrieval via off-the-shelf indices such as DiskANN and Faiss. Our experiments show that the proposed method achieves favorable trade-offs among ranking accuracy, corpus geometry, and query latency.