CogArena: A Multimethod Evaluation of Cognitive Ability Structure in Large Language Models
LLM cognitive scores are increasingly summarized as per-ability profiles whose dimensions should converge across tasks, respond selectively to matched interventions, and generalize beyond the models used to define them. We introduce CogArena, a procedurally generated 13-paradigm benchmark built around a multimethod framework for determining when cognitive-task scores warrant dimensional labels across five theory-motivated groupings. Across 55 open-weight models, nearly all paradigm correlations are positive and a common axis explains about half the variance. The within-grouping advantage is small, scoring-sensitive, and uncertain across model families. In a separately frozen, fully crossed study across 12 models from six families, targeted scaffolds show a small matched-grouping advantage, but no scaffold-specific contrast survives multiplicity correction and selectivity does not improve held-out-family prediction. The frozen confirmation criterion fails. A post-hoc alternate-wording replication produces a smaller positive estimate and again fails. Together, these results support a boundary conclusion. Theory-aligned prompting produces a small in-battery diagonal tendency, but the present evidence does not establish stable five-dimensional profiles. CogArena provides a workflow joining behavioral signatures, covariance, matched interventions, and out-of-family prediction before cognitive labels are attached to model scores.