# The Crowded Embedding Space: A Mean-Field Mechanism for Emergent Marginalization in Retrieval-Augmented Agents

arXiv: https://arxiv.org/abs/2606.28343 · HTML: https://mlsanity.com/paper/2606.28343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agentic RAG, agents and memory, one of 15 directions in Retrieval-augmented generation.
- Builds on 43 of its 57 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

- Retrieval-augmented generation / [Agentic RAG, agents and memory](https://mlsanity.com/rag/agentic-rag-agents-and-memory/)
- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 30 of 43)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [In-Context Retrieval-Augmented Language Models](https://mlsanity.com/paper/2302.00083/) (2023)
- [Passage Re-ranking with BERT](https://mlsanity.com/paper/1901.04085/) (2019)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Sentence-T5: Scalable Sentence Encoders from Pre-trained Text-to-Text Models](https://mlsanity.com/paper/2108.08877/) (2021)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [FreshLLMs: Refreshing Large Language Models with Search Engine Augmentation](https://mlsanity.com/paper/2310.03214/) (2023)
- [Benchmarking Large Language Models in Retrieval-Augmented Generation](https://mlsanity.com/paper/2309.01431/) (2023)
- [Representation Degeneration Problem in Training Natural Language Generation Models](https://mlsanity.com/paper/1907.12009/) (2019)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1802.05438/) (2018)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [A Tale of Tails: Model Collapse as a Change of Scaling Laws](https://mlsanity.com/paper/2402.07043/) (2024)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [On the Theoretical Limitations of Embedding-Based Retrieval](https://mlsanity.com/paper/2508.21038/) (2025)
- [A Survey on the Fairness of Recommender Systems](https://mlsanity.com/paper/2206.03761/) (2022)
- [Bias and Unfairness in Information Retrieval Systems: New Challenges in the LLM Era](https://mlsanity.com/paper/2404.11457/) (2024)
- [Ranking with Fairness Constraints](https://mlsanity.com/paper/1704.06840/) (2017)
- [Controlling Fairness and Bias in Dynamic Learning-to-Rank](https://mlsanity.com/paper/2005.14713/) (2020)
- [Anisotropy Is Inherent to Self-Attention in Transformers](https://mlsanity.com/paper/2401.12143/) (2024)

## Abstract (arXiv)

Retrieval-augmented generative agents rely on retrieval for grounding, yet are typically evaluated on a query-by-query basis. This isolates interactions that are geometrically coupled in a shared embedding space. For example, we show that the high document density required to serve majority interests (e.g., generic "Crime" movies) can geometrically overcrowd the retrieval neighborhood of a semantically similar minority (e.g., "Film Noir"), effectively expelling minority content from top-k results. We introduce a formal framework to analyze how such goal collisions in dense retrieval induce fundamental performance limits and emergent fairness issues inherent to spatial crowding. In our static analysis, we demonstrate that for a fixed embedding space, a phase transition occurs where minority user goals suffer a catastrophic collapse in performance as the density of majority goals increases. We then extend this to a dynamic model and derive a non-linear Fokker-Planck equation that governs the evolution of document embeddings as the agent updates them to maximize retrieval accuracy. Our analysis reveals that this local relevance objective triggers an emergent global mechanism that systematically marginalizes minority interests. We prove that such objectives drive the system to self-organize into a state that exclusively serves majority interests. These results provide a theoretical foundation for understanding a critical grounding failure mode in retrieval-augmented agents.