Inference-time thinking improves the performance of large language models, but aggregate outcomes do not reveal whether models use available evidence more effectively or seek information that could improve future decisions. We distinguish these responses by measuring action preference, thinking length, and reported confidence under matched uncertainty. Ten open-weight models completed matched horizon-style two-armed bandit trials in thinking and non-thinking modes. A cognitive model separated value-guided action and uncertainty-independent choice noise from two behavioral signatures of exploration: a UCB-like preference for the less-known arm and Thompson-like choice variability that increases with total uncertainty. On average, thinking strengthened value-guided action and reduced uncertainty-independent choice noise, without producing UCB-like exploration or strengthening Thompson-like exploration. Outside action, the information-imbalanced history condition, which also displayed more observations than the matched balanced condition, was associated with greater thinking length. Reported confidence became more sensitive to decision difficulty and more strongly associated with chosen task evidence. We interpret these thinking-length and reported-confidence patterns as consistent with metacognitive control and metacognitive monitoring, respectively, without establishing either process. Decoder sweeps, especially temperature, altered choice noise and thinking length but did not reproduce the joint cross-output pattern. In this controlled decision setting, thinking improved how models acted on current evidence, while neither measured signature supported a shift toward a more information-seeking policy.
On-policy distillation (OPD) has become a key paradigm in LLM post-training, yet its training dynamics remain poorly understood. We present a systematic study examining the role, pathologies, and regulations of OPD. We first clarify the role of OPD as an exploration catalyst: it steers the student toward correct reasoning paths via dense token-level guidance, without expanding capability ceiling. We confirm this by showing that prompt diversity matters more than per-problem sampling numbers, and critically, that the effectiveness of OPD hinges entirely on the quality of its guiding signal. This dependency exposes two pathologies that derail exploration. The Student-Teacher Mismatch occurs when a large teacher-student distributional gap causes the guiding signal to misalign with task correctness, steering exploration in counterproductive directions. Length Exploitation arises when the aggregated token-level objective creates length-dependent shortcuts, allowing the student to game the reward landscape through response truncation or redundant padding, exploring degenerate length modes rather than reasoning strategies. To tame these pathologies, we investigate lightweight signal regulations: advantage clipping and log-scale compression, ensuring exploration is guided by faithful signals. Experiments across seven benchmarks demonstrate that these regulations alleviate length exploitation and enable effective distillation, stably surpassing OPD variants and RLVR baselines, thereby confirming that well-regulated signal quality, rather than mere teacher scale, governs successful exploration in OPD.