The Crowded Embedding Space: A Mean-Field Mechanism for Emergent Marginalization in Retrieval-Augmented Agents
This work provides a theoretical foundation for understanding emergent marginalization in retrieval-augmented agents, which is critical for fairness in AI systems that rely on dense retrieval.
The paper shows that in retrieval-augmented generative agents, high document density for majority interests can geometrically crowd out minority content from top-k results, leading to catastrophic performance collapse for minority goals. The authors prove that optimizing for local retrieval accuracy drives the system to self-organize into a state that exclusively serves majority interests.
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.