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

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.

Modern AI assistants answer questions by looking up information in large digital libraries of documents. We usually test these systems one question at a time, but a single assistant serves millions of users sharing the same library. We asked what happens when popular interests and niche interests have to compete for room in that shared space. We built a mathematical model that treats users and documents as crowds in a shared landscape, where nearby documents compete to be retrieved. First, we found that once popular content crosses a critical density, niche topics get pushed out of search results suddenly rather than gradually — for example, searches for "Film Noir" movies can collapse simply because generic "Crime" movies are abundant nearby. Second, when the assistant learns from user feedback over time, it reshapes its library to serve popular interests and erases niche ones, even though no one designed it to be unfair. This reveals a form of unfairness that doesn't come from biased data or biased rules — it is a byproduct of geometry and learning itself. Our work gives designers an early-warning signal before a library hits this tipping point, and suggests safeguards such as filtering by topic before searching. It also shows that testing these systems one question at a time misses a failure mode that only appears at scale.