Why do reasoning models fail differently at training versus inference?

Two failure modes in the test-time scaling literature look unrelated but share the same underlying mechanism: failed exploration-exploitation balance.

Policy entropy collapse (training time): When RL trains a reasoning model, policy entropy drops over time — the model converges to a narrow repertoire of reasoning paths, sacrificing diversity for short-term reward. The result is a model that's overfit to familiar problem types and struggles to explore novel solution strategies. The fix lives in training: entropy bonuses, diverse critique models, or curriculum design that maintains distributional breadth.

Variance inflation (inference time): When a reasoning model is given an extended thinking budget beyond its optimum, output variance inflates rather than quality improving. The model doesn't converge on the right answer; it oscillates between candidates. The exploration mechanism that training instilled becomes runaway oscillation without the stabilizing feedback of a verifier. The fix lives in inference: parallel sampling instead of sequential extension, confidence-based filtering, or hard token budgets.

Both failures are manifestations of the same underlying problem: the model is neither confidently right nor productively exploring — it's stuck in an uncertain middle state that wastes compute without generating signal. But because they occur at different timescales, the interventions are completely different:

| Failure | Timescale | Mechanism | Fix | |---------|-----------|-----------|-----| | Entropy collapse | Training | Policy over-narrows | Critique diversity, entropy bonuses | | Variance inflation | Inference | Thinking over-extends | Parallel sampling, token limits |

The practical implication: optimizing inference alone (parallel vs sequential, budget allocation) cannot fix a training-time entropy problem. Conversely, training for exploration diversity cannot prevent inference-time variance inflation if the token budget is set too high. Both loops must be managed independently.

Historical vs batch exploration: The Outcome-based Exploration paper adds taxonomic precision to this dual problem. Historical exploration (visiting diverse states during training) improves pass@1 via expanded training signal — this is the training-time fix. Batch exploration (producing diverse outputs at test time) improves pass@k via broader solution coverage — this is the test-time fix. The mechanisms are structurally different: UCB-style bonuses over outcome space for historical exploration, within-batch repetition penalties for batch exploration. This maps the training/test-time dual directly onto concrete algorithmic prescriptions. See Does outcome-based RL diversity loss spread across unsolved problems?.

Training data format as an upstream entropy variable: Does training data format shape reasoning strategy more than domain? adds a third factor upstream of both. Multiple-choice training produces BFS-like (breadth-first, parallel-path) reasoning; free-form training produces DFS-like (depth-first, sequential) reasoning. Format shapes the default exploration profile before any RL training begins. This means entropy collapse is not solely a training-time problem — it can be seeded by format choices in the pre-RL training data. A model pre-trained on free-form data starts the RL phase with a depth-first, collapse-prone default strategy. A model pre-trained on multiple-choice data starts with a more diverse exploration strategy. The intervention sequence is thus: format decisions → exploration profile → RL collapse rate. Managing entropy requires attending to all three.