高密度检索空间会挤压少数兴趣,导致系统自动排斥小众内容。
The Crowded Embedding Space: A Mean-Field Mechanism for Emergent Marginalization in Retrieval-Augmented Agents
- 用平均场理论分析嵌入空间拥挤对检索的影响
- 多数用户需求增加时,少数用户性能骤降,出现相变现象
- 揭示了检索增强型智能体的隐性不公平机制,适合研究者参考
检索增强型生成智能体依赖检索进行事实锚定,但通常以单个查询为单位评估,忽略了嵌入空间中几何耦合的交互。例如,为满足大多数用户对通用主题(如“犯罪片”)的需求而引入的高文档密度,会几何上挤占语义相似的小众主题(如“黑色电影”)的检索邻域,使其难以进入 top-k 结果。本文提出一个形式化框架,分析密集检索中的目标冲突如何引发固有的性能极限与涌现公平性问题。静态分析表明,在固定嵌入空间下,当多数目标密度上升时,少数用户目标性能发生灾难性崩溃,出现相变。进一步扩展至动态模型,推导出非线性 Fokker-Planck 方程,描述智能体更新嵌入以最大化检索准确率时的演化过程。分析发现,局部相关性目标触发了一种涌现的全局机制,系统性地边缘化少数兴趣。证明此类目标促使系统自我组织为仅服务多数利益的状态。该研究为检索增强型智能体的关键接地失效模式提供了理论基础。
原文摘要 · Abstract (English)
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.
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