Personality Without a Person: Within-Respondent Structure in Humans and LLM Personas

Do Large Language Models (LLMs) possess stable, latent personality traits, or is their apparent personality merely a product of how questionnaires are structured? While LLMs often produce aggregate scores that mimic human population norms, it remains unclear whether these responses reflect an underlying psychological structure or a superficial alignment with group-level stereotypes.

The author introduces a novel geometric representation for personality questionnaires. Instead of relying on aggregate scores, which discard how responses to different dimensions co-vary, the study constructs an Item-Dimension correlation matrix for each respondent. This matrix is treated as a point on the manifold of symmetric positive definite (SPD) matrices. By mapping these matrices to a tangent space, the author can analyze the internal structure of a single response set. The study tests the robustness of this structure by manipulating the order of questionnaire items for both human participants and four frontier LLMs (GPT-4o, DeepSeek-V3, Claude Haiku 4.5, and Claude Sonnet 4.6) prompted with specific personas.

Human personality structure is robust: individual correlation matrices remain stable across sessions that share no items, order, or context, and these geometric features significantly predict real-world outcomes like GPA. In contrast, LLM persona structure is entirely frame-dependent. When item order is randomized, the geometric structure of LLM responses collapses to chance. However, if all instances are realigned to a shared random order, the structure recovers. This V-shaped collapse-recovery pattern demonstrates that LLM personas are not latent traits but group-level statistical templates. The study further confirms this by showing that a null model—generating responses item-by-item with no internal structure—perfectly replicates the LLM behavior.