GAM-RAG: Gain-Adaptive Memory for Evolving Retrieval in Retrieval-Augmented Generation

Retrieval-Augmented Generation (RAG) grounds large language models with external evidence, but many implementations rely on pre-built indices that remain static after construction. Related queries therefore repeat similar multi-hop traversal, increasing latency and compute. Motivated by \emph{schema}-based learning in cognitive neuroscience, we propose GAM-RAG, a training-free framework that accumulates retrieval experience from recurring or related queries and updates retrieval memory over time. GAM-RAG builds a lightweight, relation-free hierarchical index whose links capture potential co-occurrence rather than fixed semantic relations. During inference, successful retrieval episodes provide sentence-level feedback, updating sentence memories so evidence useful for similar reasoning types becomes easier to activate later. To balance stability and adaptability under noisy feedback, we introduce an uncertainty-aware, \emph{Kalman}-inspired gain rule that jointly updates memory states and perplexity-based uncertainty estimates. It applies fast updates for reliable novel signals and conservative refinement for stable or noisy memories. We provide a theoretical analysis of the update dynamics, and empirically show that GAM-RAG improves average performance by 3.95\% over the strongest baseline and by 8.19\% with 5-turn memory, while reducing inference cost by 61\%.\footnote{Our code and datasets are available at: \url{https://anonymous.4open.science/r/GAM_RAG-2EF6}.}