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

arXiv:2602.19240v1 Announce Type: new 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-dimensiona

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Sen Zhao, Lincheng Zhou, Yue Chen, Ding Zou · · 1 min read · 2 views
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arXiv:2602.19240v1 Announce Type: new 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.

Executive Summary

The article proposes Topology-enhanced Retrieval-Augmented Generation (TopoRAG), a novel framework for textual graph question answering that captures higher-dimensional topological and relational dependencies. TopoRAG lifts textual graphs into cellular complexes, extracts relevant subcomplexes, and performs multi-dimensional topological reasoning to guide Large Language Models (LLMs) in structured inference. Empirical evaluations demonstrate that TopoRAG surpasses existing baselines across diverse textual graph tasks, enhancing the reasoning ability of LLMs and mitigating hallucinations.

Key Points

  • ▸ Introduction of TopoRAG, a novel framework for textual graph question answering
  • ▸ Lifting textual graphs into cellular complexes to model multi-dimensional topological structures
  • ▸ Topology-aware subcomplex retrieval mechanism for extracting relevant cellular complexes

Merits

Enhanced Reasoning Ability

TopoRAG's ability to capture higher-dimensional topological and relational dependencies enhances the reasoning ability of LLMs, leading to more accurate and informative responses.

Demerits

Computational Complexity

The lifting of textual graphs into cellular complexes and the topology-aware subcomplex retrieval mechanism may increase computational complexity, potentially limiting the scalability of TopoRAG.

Expert Commentary

The introduction of TopoRAG represents a significant advancement in the field of textual graph question answering, as it addresses the limitation of existing Retrieval-Augmented Generation (RAG) variants in capturing higher-dimensional topological and relational dependencies. The use of cellular complexes and topology-aware subcomplex retrieval mechanisms demonstrates a nuanced understanding of the complexities involved in reasoning over relational loops. However, further research is needed to fully explore the potential applications and implications of TopoRAG, particularly in areas like explainability and transparency.

Recommendations

  • ✓ Further evaluation of TopoRAG on a wider range of textual graph tasks to assess its generalizability and robustness
  • ✓ Investigation into the potential applications of TopoRAG in areas like natural language processing, knowledge graph-based question answering, and decision support systems

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