# MA-DPR: Manifold-aware Distance Metrics for Dense Passage Retrieval

arXiv: https://arxiv.org/abs/2509.13562 · HTML: https://mlsanity.com/paper/2509.13562/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2025.

## Built on by (most cited first, 9 of 9)

- [Semantic XPath: Structured Agentic Memory Access for Conversational AI](https://mlsanity.com/paper/2603.01160/) (2026)
- [Bayesian Active Learning with Gaussian Processes Guided by LLM Relevance Scoring for Dense Passage Retrieval](https://mlsanity.com/paper/2604.17906/) (2026)
- [Evaluating Scene-based In-Situ Item Labeling for Immersive Conversational Recommendation](https://mlsanity.com/paper/2604.09698/) (2026)
- [Goal-Oriented Reasoning for RAG-based Memory in Conversational Agentic LLM Systems](https://mlsanity.com/paper/2605.12213/) (2026)
- [SafeGEO: Understanding Generative Engine Optimization Risks in Recommendation Agents](https://mlsanity.com/paper/2606.28356/) (2026)
- [Temporal Order Matters for Agentic Memory: Segment Trees for Long-Horizon Agents](https://mlsanity.com/paper/2606.04555/) (2026)
- [SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry](https://mlsanity.com/paper/2603.01168/) (2026)
- [MicroVerse: An Instrument for Measuring Self-Authored Identity Drift in Long-Horizon Multi-Agent Language-Model Simulations](https://mlsanity.com/paper/2608.15844/) (2026)
- [Have I Scene This Before? Spatially Grounded Conversational Memory for Complex Queries in Egocentric Assistants](https://mlsanity.com/paper/2610.05526/) (2026)

## Abstract (arXiv)

Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold. However, our experiments across DPR benchmarks suggest that embeddings often lie on lower-dimensional, non-linear manifolds, especially in out-of-distribution (OOD) settings, where cosine and Euclidean distance fail to capture semantic similarity. To address this limitation, we propose a manifold-aware distance metric for DPR (MA-DPR) that models the intrinsic manifold structure of passages using a nearest neighbor graph and measures query-passage distance based on their shortest path in this graph. We show that MA-DPR outperforms Euclidean and cosine distances by up to 26% on OOD passage retrieval with comparable in-distribution performance across various embedding models while incurring a minimal increase in query inference time. Empirical evidence suggests that manifold-aware distance allows DPR to leverage context from related neighboring passages, making it effective even in the absence of direct semantic overlap. MADPR can be applied to a wide range of dense embedding and retrieval tasks, offering potential benefits across a wide spectrum of domains.