Learning to Think on Hypergraph: HyperCoT for Structure-Guided N-ary Knowledge Graph Completion

N -ary knowledge graph completion (KGC) aims to infer missing components in facts with multiple entities under distinct semantic roles, commonly formulated as a knowledge hypergraph link prediction task. Most embeddingbased approaches score individual hyperedges relying on enriched structural representations, but overlook intermediate propagation states containing complementary local and global structural evidence. Despite their capability to generate chain-of-thought (CoT) representations for the classical KGC task, large language models (LLMs) struggle with hypergraph structure involving multiple facts, while current hypergraph QA methods only provide LLMs with a single query signal rather than path-level evidence. These limitations hinder the transferability of existing methods, especially those leveraging LLMs, to solve the knowledge hypergraph link prediction problem. To bridge this gap, we propose HyperCoT, a structureaware approach that models multi-hop structural reasoning as a depth-sensitive progressive evidence accumulation process. It constructs a Graphical Chain-of-Thought (Graph-CoT) by aggregating role-aware hyperedge states along strongly correlated reasoning paths, and injects the resulting path-level structural evidence into each token in query and candidate entities to prompt LLMs. Experiments on three realworld datasets demonstrate that HyperCoT consistently outperforms strong n-ary KGC baselines, particularly in high arity and structural sparsity scenarios, meanwhile yielding interpretable multi-hop reasoning traces. * *Corresponding author. Question). Given the following incomplete fact, which factory best satisfies all structural role constraints?