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

arXiv:2609.00513 · cs.AI · Submitted 2026-09-01 · Read on arXiv

cs.AI

Submitted: 2026-09-01

Updated: 2026-09-01

Code: https://github.com/ZaiizaiZHANG/ISO-RAG

License: http://creativecommons.org/licenses/by/4.0/

The gist: 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

Terminology

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.

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