Do LLMs Transfer Structural Knowledge? Probing Structural Inference as a Cognitive Capability in LLMs

Structural knowledge refers to relational patterns that capture an underlying organization beyond the specific entities and contexts in which those relations occur. While recent studies have examined cognitive biases and reasoning behaviors in large language models (LLMs), whether LLMs can infer such structures from natural language and transfer them across contexts remains unclear. We introduce INSTILL, a framework for INvestigating the STructural Inference in LLMs through tasks that require transferring structural knowledge. Each task presents a reference context and four candidate contexts, only one of which preserves the underlying relational structure of the reference. Drawing on five representative structure families motivated by cognitive science, INSTILL constructs diverse structural patterns and contextualizes them as cognitive scenarios grounded in nine domains spanning spatial, social, comparative, and temporal relations. These tasks require models to infer the latent structure from natural language and generalize it across contexts with different entities, relationships, or domains. INSTILL enables controlled analysis of how structural inference varies across structure families, domain congruency, and increasing structure sizes. Our results show that several recent models maintain stable structural inference across domain shifts and increasing structure sizes, whereas smaller variants of the same model families exhibit larger performance drops and greater sensitivity to domain congruency and local relational patterns.