signal-to-noise

Graph RAG Matrix Modeling and Stable Hop Count Derivation

Spectral analysis of adjacency matrices reveals the optimal diffusion depth that maximizes signal-to-noise ratio in knowledge graph retrieval

Graph-based Retrieval Augmented Generation traverses knowledge graphs to gather context for language-model prompts. Each additional hop `h` in `A^h` can add useful context but also amplify noise through irrelevant paths. This paper models diffusion as matrix exponentiation with decay, derives signal-to-noise behavior by hop count using spectral decomposition, and identifies an optimal hop count `h*`. Across four enterprise knowledge graphs, the derived `h*` reduced hallucination rate by 43% versus fixed-depth traversal.