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

2026-02-22

AI Summary

Existing retrieval-augmented generation (RAG) approaches for textual graph question answering typically overlook high-dimensional topological structures—such as loops—thereby limiting their reasoning capabilities. This work addresses this limitation by modeling textual graphs as cellular complexes and introduces, for the first time, a topology-aware subcomplex retrieval mechanism coupled with multidimensional reasoning, transcending the constraints of conventional node-edge low-dimensional representations. By effectively integrating cellular complex construction, topology-aware retrieval, and large language models, the proposed method achieves significant performance gains across multiple textual graph question-answering benchmarks, notably outperforming existing baselines in tasks requiring cyclic reasoning and structured question answering.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• graph question answering
• retrieval-augmented generation
• topological reasoning
• cycles
• relational loops

Innovation

• cellular complexes
• topological reasoning
• Retrieval-Augmented Generation
• graph question answering
• higher-dimensional topology