High-Dimensional Concentration and Retrieval Instability in Embedding Spaces: Implications for Retrieval-Augmented Generation

Modern LLMs excel at reasoning and instruction following, enabling users to express complex and diverse information needs. However, conventional retrievers largely rely on surface-level matching between queries and documents, resulting in a growing gap between how users express their needs and how retrievers interpret them. In this paper, we present GEM, a generative embedding model that augments retrieval through its own knowledge by explicitly reasoning about user intent and relevance criteria. GEM unifies generation and embedding within a single model: it first reasons over the query, then appends an embedding token to encode the enriched context for retrieval. \zhili{Evaluated on reasoning-intensive and instruction-following retrieval tasks, GEM demonstrates the effectiveness of its reasoning-augmented retrieval, outperforming its non-reasoning variant and matching baselines using substantially larger models.} Furthermore, GEM's generative nature allows test-time compute scaling via prompting to further enhance retrieval performance. Our code is available at: https://anonymous.4open.science/r/GEM.

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.

Dense vector retrieval is the practical backbone of Retrieval- Augmented Generation (RAG), but similarity search can suffer from precision limitations. Conversely, utility-based approaches leveraging LLM re-ranking often achieve superior performance but are computationally prohibitive and prone to noise inherent in perplexity estimation. We propose Utility-Aligned Embeddings (UAE), a framework designed to merge these advantages into a practical, high-performance retrieval method. We formulate retrieval as a distribution matching problem, training a bi-encoder to imitate a utility distribution derived from perplexity reduction using a Utility-Modulated InfoNCE objective. This approach injects graded utility signals directly into the embedding space without requiring test-time LLM inference. On the QASPER benchmark, UAE improves retrieval Recall@1 by 30.59%, MAP by 30.16% and Token F1 by 17.3% over the strong semantic baseline BGE-Base. Crucially, UAE is over 180x faster than the efficient LLM re-ranking methods preserving competitive performance, demonstrating that aligning retrieval with generative utility yields reliable contexts at scale.