Exploring the Potential of Topological Data Analysis for Explainable Large Language Models: A Scoping Review

Petar Sekuloski (), Dimitar Kitanovski, Igor Goshev, Kostadin Mishev, Monika Simjanoska Misheva and Vesna Dimitrievska Ristovska
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Petar Sekuloski: Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, 1000 Skopje, North Macedonia
Dimitar Kitanovski: Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, 1000 Skopje, North Macedonia
Igor Goshev: Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, 1000 Skopje, North Macedonia
Kostadin Mishev: Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, 1000 Skopje, North Macedonia
Monika Simjanoska Misheva: Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, 1000 Skopje, North Macedonia
Vesna Dimitrievska Ristovska: Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, 1000 Skopje, North Macedonia

Mathematics, 2026, vol. 14, issue 2, 1-35

Abstract: Large language models (LLMs) have become central to modern artificial intelligence, yet their internal decision-making processes remain difficult to interpret. As interest grows in making these models more transparent and reliable, topological data analysis (TDA) has emerged as a promising mathematical approach for exploring their structure. This scoping review maps the current landscape of research where TDA tools—such as persistent homology and Mapper—are used to examine LLM components like attention patterns, latent representations, and training dynamics. By analyzing topological features across layers and tasks, these methods provide new ways to understand how language models generalize, respond to unfamiliar inputs, and shift under fine-tuning. The review also considers how TDA-based techniques contribute to broader goals in interpretability and robustness, especially in detecting hallucinations, out-of-distribution behavior, and representational collapse. Overall, the findings suggest that TDA offers a rigorous and versatile framework for studying LLMs, helping researchers uncover deeper patterns in how these models learn and reason.

Keywords: topological data analysis; persistent homology; mapper; large language models; explainability; interpretability; robustness; representation learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2026
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