Confidence-Calibrated Inference Expansion for Evaluator-Guided Test-Time Reasoning

Extra inference compute is usually spent on sampling more reasoning chains. We study where inside an existing chain an additional continuation should begin. We define expansion utility, the change in correctness from restarting a chain at a stored step, and measure it at every eligible step for nine models on six benchmarks (41 model and benchmark cells). Restart position matters: steps selected on one set of continuations beat uniform placement when scored on disjoint ones, in held-out audits on 5, 16, and 38 cells (+4.25 points [+2.51, +6.63] in a fresh five-cell audit). A fixed rule that restarts from the last eligible steps, always-last, is a strong baseline: our learned router beats uniform placement but shows no detected gain over it, and on DeepSeek-R1-Distill-Qwen-14B/MATH-500 always-last exceeds the exact self-consistency frontier at matched aggregate generated output by +0.052 [+0.008, +0.098], using 0.774x the aggregate generated output of four-sample self-consistency. Cross-fitted oracle selection still finds held-out headroom beyond declared positional classes, a target for future selectors. Finally, breaking step-label ties by earliest index flips the sign of a pointwise selector's gain over uniform placement in every seed of a five-seed diagnostic with four rollouts per step; randomized ties remove the bias.

Test-time scaling improves language-model reasoning by generating additional candidate solutions, but allocating the same inference budget to every problem is computationally wasteful. Existing adaptive stopping methods commonly rely on confidence, agreement, or answer stability, implicitly assuming that stronger current evidence indicates that further computation is unnecessary. We show that this assumption can fail: checkpoint-level correctness evolves non-monotonically, and observable evidence may strengthen before an answer collapses or weaken before it recovers. Motivated by this mismatch, we introduce Adaptive Evidence Residual Allocation (AERA), a sequential controller that learns whether additional computation is likely to recover a better answer from checkpoint-observable evidence. AERA characterizes cumulative response prefixes using answer-distribution, temporal, re-solving, semantic, and compute features, and repeatedly decides whether to stop or allocate the next response block. Future checkpoint correctness is used only to construct offline supervision and is never available to the controller at inference time. Across GSM8K and GPQA Diamond, AERA identifies question-specific residual opportunities while substantially reducing inference computation. In a frozen-threshold incremental-generation evaluation on 300 untouched GSM8K questions, AERA achieves 92.61% accuracy versus 93.01% with 128 responses while reducing completion tokens by 95.99%. These results suggest that adaptive reasoning should estimate the future value of computation rather than equating present confidence with correctness.

Reasoning language models are increasingly asked not only to answer difficult questions, but also to estimate their likelihood of success. Existing methods typically elicit confidence only once: either before thinking or after answering. We argue that confidence in reasoning models is state-dependent: before thinking, confidence should estimate the chance of the model correctly solving the prompt, while after thinking it should predict whether the realized answer is likely to be correct. This distinction determines the appropriate supervision target: prompt-level success should supervise confidence estimates made after seeing the prompt, while individual answer-level correctness should supervise confidence estimates made after answering. We introduce CALIBER (Calibration Before and After Reasoning), which elicits both estimates and supervises each with the target matched to its information state. Under this unified protocol, CALIBER reduces Expected Calibration Error (ECE) by 52.5% over the strongest single-confidence baseline on BigMathDigits for the 7B model, while achieving the best Brier score and AUROC, and remains within 2.1 points of the best accuracy. Further, on a larger 30B model, CALIBER achieves the best ECE on BigMathDigits while remaining competitive in Brier score and AUROC. Out of distribution, it achieves the best ECE and Brier score on GPQA and TriviaQA, and remains competitive on SimpleQA. Ablations further show that this position-target alignment is most beneficial under distribution shift where it consistently reduces calibration error across all out-of-distribution benchmarks.