Capable yet Parsimonious: Extracting and Characterizing Hidden Chain-of-Thought in Frontier Models

The rapid capability gains of frontier language models are widely attributed to improved reasoning abilities, yet this cannot be verified as raw CoT traces in closed-source systems are hidden. By registering a simple custom tool through a standard API feature, we induce frontier models to externalize intermediate reasoning. Because these traces may reflect post-hoc rationalization rather than genuine reasoning, we first evaluate against native CoT on open-source models and extend to closed-source frontier models including GPT-6 Astra. We find that the extracted reasoning matches native reasoning performance and substantially outperforms no-reasoning baselines, across competition mathematics, science, and code generation. We then characterize how frontier models structure their intermediate reasoning. Across token efficiency, reasoning-step types, and induced reasoning trees, we identify systematic differences in how models externalize, compress, and organize reasoning. We find that Astra exhibits token-efficient directed reasoning, selecting a correct trajectory earlier, while resolving elementary steps internally and externalizing only crucial reasoning. These findings provide a behavioral lens on frontier-model reasoning beyond benchmark scores.

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Test-time scaling has emerged as a key inference strategy for reasoning models, where a model generates a large number of candidate solutions in the hope of finding at least one correct solution. Running all candidate solutions to completion can be computationally demanding, so recent work prunes the candidate pool after generating only a short prefix, committing further computation only to the surviving candidates. Existing pruning strategies divide broadly into two categories: Quality-based methods assign a score to each partial solution and discard those predicted to ultimately lead to an incorrect final solution, while diversity-based methods select partial solutions that follow different reasoning trajectories and are therefore likely to cover different final solutions. The tension between these two objectives is an instance of exploration versus exploitation, yet little to no prior work on pruning exposes this trade-off directly, let alone optimizes it. In this paper, we introduce a pruning procedure that addresses this trade-off directly by optimizing pass@k over the selected solution pool. In particular, it chooses the pool to maximize the probability that at least one of its partial solutions, when continued to completion, yields a correct answer. Because this objective simultaneously rewards high-quality partial solutions and penalizes redundancy among them, quality and diversity are naturally balanced by the criterion itself rather than through separate ad-hoc design choices. On eight open-weight reasoning models, our method outperforms existing quality-based and diversity-based pruning strategies. The gains are particularly pronounced when the pruning procedure keeps a moderate number of partial solutions for continued generation, highlighting the value of directly balancing quality and diversity during pruning.

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