Reranker Optimization via Geodesic Distances on k-NN Manifolds

Abstract

Current neural reranking approaches for retrieval-augmented generation (RAG) rely on cross- encoders or large language models (LLMs), requiring substantial computational resources and exhibiting latencies of 3–5 seconds per query. We propose Maniscope, a geometric reranking method that computes geodesic distances on k-nearest neighbor (k-NN) manifolds constructed over retrieved document candidates. This approach combines global cosine similarity with local manifold geometry to capture neighborhood coherence within the candidate set that global pairwise similarity alone cannot model. Evaluated on 15 BEIR benchmark datasets (∼25,000 queries spanning scientific, biomedical, financial, web search, and fact-verification domains), Maniscope achieves 0.9806 average NDCG@10, ranking best on 13 of 15 datasets and outperforming HNSW (0.9673) and three established graph-diffusion baselines (0.7326–0.7630) at 13 ms average latency, 1.8× faster than HNSW (23.7 ms). The algorithm requires O(N D + M 2 D + M k log k) complexity with M ≪ N . Code and data are released as open source.