Know Thy Reasoner: Not All Language Models Explore Alike

Compute scaling for LLM reasoning trades off exploring solution approaches (breadth) against refining promising ones (depth), yet why a given trade-off works, and why it often fails to transfer across models, remains unclear. We argue that the optimal strategy depends on the model's diversity profile, the spread of probability mass across solution approaches, and that this must be characterized before any exploration strategy is adopted. We formalize this with a framework decomposing reasoning uncertainty, deriving when depth-based refinement outperforms parallel sampling, and validate it across three model families at both inference and training. Our central finding is that the diversity regime dictates the strategy: low-diversity aligned models benefit from depth-based refinement with lightweight intrinsic signals, whereas high-diversity base models are often harmed by it, and instead need breadth or stronger signals to compensate.