Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answering

TL;DR

This paper introduces TopoRAG, a novel framework that enhances reasoning over textual graphs by modeling multi-dimensional topological structures, leading to improved question answering performance.

Contribution

The work proposes lifting textual graphs into cellular complexes and developing a topology-aware retrieval and reasoning mechanism, capturing higher-dimensional dependencies for better inference.

Findings

Outperforms existing methods on textual graph question answering tasks.

Effectively models cycles and relational loops in graphs.

Improves reasoning accuracy through topological context.

Abstract

Retrieval-Augmented Generation (RAG) enhances the reasoning ability of Large Language Models (LLMs) by dynamically integrating external knowledge, thereby mitigating hallucinations and strengthening contextual grounding for structured data such as graphs. Nevertheless, most existing RAG variants for textual graphs concentrate on low-dimensional structures -- treating nodes as entities (0-dimensional) and edges or paths as pairwise or sequential relations (1-dimensional), but overlook cycles, which are crucial for reasoning over relational loops. Such cycles often arise in questions requiring closed-loop inference about similar objects or relative positions. This limitation often results in incomplete contextual grounding and restricted reasoning capability. In this work, we propose Topology-enhanced Retrieval-Augmented Generation (TopoRAG), a novel framework for textual graph question answering that effectively captures higher-dimensional topological and relational dependencies. Specifically, TopoRAG first lifts textual graphs into cellular complexes to model multi-dimensional topological structures. Leveraging these lifted representations, a topology-aware subcomplex retrieval mechanism is proposed to extract cellular complexes relevant to the input query, providing compact and informative topological context. Finally, a multi-dimensional topological reasoning mechanism operates over these complexes to propagate relational information and guide LLMs in performing structured, logic-aware inference. Empirical evaluations demonstrate that our method consistently surpasses existing baselines across diverse textual graph tasks.