# Reranker Optimization via Geodesic Distances on k-NN Manifolds

arXiv: https://arxiv.org/abs/2602.15860 · HTML: https://mlsanity.com/paper/2602.15860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Placed in

- Retrieval-augmented generation / [Generation and context integration](https://mlsanity.com/rag/generation-and-context-integration/)

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [Atlas: Few-shot Learning with Retrieval Augmented Language Models](https://mlsanity.com/paper/2208.03299/) (2022)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Passage Re-ranking with BERT](https://mlsanity.com/paper/1901.04085/) (2019)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [Are Neural Ranking Models Robust?](https://mlsanity.com/paper/2108.05018/) (2021)

## Abstract (arXiv)

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 semantic structure that flat Euclidean metrics miss. Evaluating on eight BEIR benchmark datasets (1,233 queries), Maniscope outperforms HNSW graph-based baseline on the three hardest datasets (NFCorpus: +7.0%, TREC-COVID: +1.6%, AorB: +2.8% NDCG@3) while being 3.2x faster (4.7 ms vs 14.8 ms average). Compared to cross-encoder rerankers, Maniscope achieves within 2% accuracy at 10-45x lower latency. On TREC-COVID, LLM-Reranker provides only +0.5% NDCG@3 improvement over Maniscope at 840x higher latency, positioning Maniscope as a practical alternative for real-time RAG deployment. The method requires O(N D + M^2 D + M k log k) complexity where M << N , enabling sub-10 ms latency. We plan to release Maniscope as open-source software.