ISO-RAG: Isoperimetric Noise Control for Retrieval-Augmented Generation

arXiv:2609.00513v1 Announce Type: new Abstract: Retrieval-Augmented Generation (RAG) mitigates large language models (LLMs) hallucinations, yet conventional dense retrieval struggles with the complex reasoning paths of multi-hop question answering (QA).

Graph-based RAG captures multi-step relationships but suffers from severe semantic drift and high online latency due to noisy global graph traversals.

Thus, we propose ISO-RAG (ISOperimetric Retrieval-Augmented Generation), a geometry-aware RAG framework. By projecting the underlying knowledge graph into a hyperbolic Poincare ball to precompute node-wise isoperimetric profiles, ISO-RAG prunes spurious edges during retrieval, restricting the search space to a strictly localized subgraph.

This topological purification regulates Personalized PageRank (PPR) diffusion driving the retrieval process, ensuring exact and low-latency convergence.

Experiments on multi-hop QA benchmarks demonstrate that ISO-RAG outperforms state-of-the-art baselines by average absolute gains of 10.0% in retrieval recall and 4.3% in downstream exact match, achieving a superior accuracy-efficiency trade-off by fundamentally eliminating the latency bottleneck of global traversals. Our source code is available at https://github.com/ZaiizaiZHANG/ISO-RAG.