HypoSpace: Evaluating LLM Creativity as Set-Valued Hypothesis Generators under Underdetermination

As language models are increasingly used in scientific workflows, evaluating their ability to propose sets of explanations-not just a single correct answer-becomes critical. Many scientific problems are underdetermined: multiple, mechanistically distinct hypotheses are consistent with the same observations. We introduce HypoSpace, a diagnostic suite that treats LLMs as samplers of finite hypothesis sets and measures three complementary indicators: Validity (precision of proposals consistent with observations), Uniqueness (non-redundancy among proposals), and Recovery (coverage of the enumerated admissible set). We instantiate HypoSpace in three structured domains with deterministic validators and exactly enumerated hypothesis spaces: (i) causal graphs from perturbations, (ii) gravity-constrained 3D voxel reconstruction from top-down projections, and (iii) Boolean genetic interactions. Across instruction-tuned and reasoning-focused models, Validity often remains high while Uniqueness and Recovery degrade as the admissible space grows, revealing mode collapse that is invisible to correctness-only metrics. HypoSpace offers a controlled probe-rather than a leaderboard-for methods that explicitly explore and cover admissible explanation spaces. Code is available at: https://github.com/CTT-Pavilion/_HypoSpace.