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This study investigates the dual nature of LLM personas by analyzing the geometric structure of responses to psychometric questionnaires, revealing that persona expression consists of both frame-dependent geometric features and frame-robust aggregated traits. The research shows that while aggregated features degrade significantly under randomized question orderings, geometric features exhibit a pronounced collapse when frames are misaligned but can recover substantially when shared frames are used. These findings suggest that understanding LLM personas requires a nuanced approach that considers both the stability of aggregated traits and the variability of geometric representations, challenging traditional static trait models.
Persona expression in LLMs reveals a surprising duality: while aggregated traits are stable, their geometric representations are highly sensitive to context, collapsing under misalignment.
Evaluations of LLM personas via psychometric questionnaires typically rely on aggregate scores, discarding within-instance correlation structure. We test whether this geometric structure is intrinsic or frame-dependent. Constructing within-instance correlation matrices from IPIP-50 responses, we analyze geometry on SPD manifolds under manipulated question orderings in GPT-4o simulating American and Chinese-American personas. We find that persona expression comprises two dissociable components: aggregated features (Big Five scores) degrade under randomization (21% drop) but are frame-robust; geometric features (SPD manifold) collapse under frame misalignment (42% drop) but recover substantially (to 84%) under shared frames, surpassing aggregated features (76%). This collapse-recovery pattern reveals that persona geometry is not intrinsic but a frame-dependent coordination pattern encoding information invisible to aggregation. Our findings establish a dual-nature framework for LLM personas, frame-dependent geometry versus frame-robust aggregates, necessitating frame-aware evaluation and challenging static trait conceptions.
