# Training Dense Retrievers with Multiple Positive Passages

arXiv: https://arxiv.org/abs/2602.12727 · HTML: https://mlsanity.com/paper/2602.12727/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [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)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [Atlas: Few-shot Learning with Retrieval Augmented Language Models](https://mlsanity.com/paper/2208.03299/) (2022)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [In-Context Retrieval-Augmented Language Models](https://mlsanity.com/paper/2302.00083/) (2023)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Passage Re-ranking with BERT](https://mlsanity.com/paper/1901.04085/) (2019)
- [RocketQA: An Optimized Training Approach to Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2010.08191/) (2020)
- [Large Language Models are Effective Text Rankers with Pairwise Ranking Prompting](https://mlsanity.com/paper/2306.17563/) (2023)
- [Overview of the TREC 2019 deep learning track](https://mlsanity.com/paper/2003.07820/) (2020)
- [Overview of the TREC 2020 deep learning track](https://mlsanity.com/paper/2102.07662/) (2021)
- [Condenser: a Pre-training Architecture for Dense Retrieval](https://mlsanity.com/paper/2104.08253/) (2021)
- [Optimizing Dense Retrieval Model Training with Hard Negatives](https://mlsanity.com/paper/2104.08051/) (2021)
- [RetroMAE: Pre-Training Retrieval-oriented Language Models Via Masked Auto-Encoder](https://mlsanity.com/paper/2205.12035/) (2022)
- [Re2G: Retrieve, Rerank, Generate](https://mlsanity.com/paper/2207.06300/) (2022)
- [SimLM: Pre-training with Representation Bottleneck for Dense Passage Retrieval](https://mlsanity.com/paper/2207.02578/) (2022)
- [Tevatron: An Efficient and Flexible Toolkit for Dense Retrieval](https://mlsanity.com/paper/2203.05765/) (2022)
- [Retrieval-Enhanced Machine Learning](https://mlsanity.com/paper/2205.01230/) (2022)
- [Improving Pairwise Ranking for Multi-label Image Classification](https://mlsanity.com/paper/1704.03135/) (2017)
- [Unsupervised Dense Retrieval with Relevance-Aware Contrastive Pre-Training](https://mlsanity.com/paper/2306.03166/) (2023)
- [Cascade Ranking for Operational E-commerce Search](https://mlsanity.com/paper/1706.02093/) (2017)
- [RetroMAE-2: Duplex Masked Auto-Encoder For Pre-Training Retrieval-Oriented Language Models](https://mlsanity.com/paper/2305.02564/) (2023)
- [Hard Negatives or False Negatives: Correcting Pooling Bias in Training Neural Ranking Models](https://mlsanity.com/paper/2209.05072/) (2022)
- [Unleashing the Power of LLMs in Dense Retrieval with Query Likelihood Modeling](https://mlsanity.com/paper/2504.05216/) (2025)

## Built on by (most cited first, 1 of 1)

- [Rethinking Reasoning-Intensive Retrieval: Evaluating and Advancing Retrievers in Agentic Search Systems](https://mlsanity.com/paper/2605.04018/) (2026)

## Abstract (arXiv)

Modern knowledge-intensive systems, such as retrieval-augmented generation (RAG), rely on effective retrievers to establish the performance ceiling for downstream modules. However, retriever training has been bottlenecked by sparse, single-positive annotations, which lead to false-negative noise and suboptimal supervision. While the advent of large language models (LLMs) makes it feasible to collect comprehensive multi-positive relevance labels at scale, the optimal strategy for incorporating these dense signals into training remains poorly understood. In this paper, we present a systematic study of multi-positive optimization objectives for retriever training. We unify representative objectives, including Joint Likelihood (JointLH), Summed Marginal Likelihood (SumMargLH), and Log-Sum-Exp Pairwise (LSEPair) loss, under a shared contrastive learning framework. Our theoretical analysis characterizes their distinct gradient behaviors, revealing how each allocates probability mass across positive document sets. Empirically, we conduct extensive evaluations on Natural Questions, MS MARCO, and the BEIR benchmark across two realistic regimes: homogeneous LLM-annotated data and heterogeneous mixtures of human and LLM labels. Our results show that LSEPair consistently achieves superior robustness and performance across settings, while JointLH and SumMargLH exhibit high sensitivity to the quality of positives. Furthermore, we find that the simple strategy of random sampling (Rand1LH) serves as a reliable baseline. By aligning theoretical insights with empirical findings, we provide practical design principles for leveraging dense, LLM-augmented supervision to enhance retriever effectiveness.