Confidence Is Not a Reranker

TL;DR for operators

A reasoning model can have a useful estimate of how likely its current answer is to be correct without having enough information to reliably identify the best answer among several alternatives. That distinction is the central result of this paper.

A lightweight classifier reading the model’s hidden state immediately before its final answer produces substantially better calibrated confidence than the model’s own stated score. Yet when that same signal is used to pick one answer from many sampled traces, its advantage over majority voting is small and remains far below the oracle that knows whether any candidate is correct.

The authors then use those internal probabilities as training targets. Their Probe-guided Self-Distillation method substantially improves the model’s reported confidence in and out of domain, and the resulting model no longer needs the probe at inference time.

For production systems, the result supports confidence as an input to abstention, escalation, routing, and weighted aggregation. It provides much weaker support for using confidence to rerank candidates as though the highest-confidence answer were reliably the right one. Building the training data still requires white-box access to model hidden states, and the evidence is limited to two open-weight reasoning-model families on factual short-answer QA.

A confidence score can answer one question without answering another

Suppose a system generates several candidate answers to the same question. The system now has at least two decisions to make.

First, how much should it trust an answer? That determines whether the system proceeds, abstains, escalates to a human, or invokes another model.

Second, which candidate should it choose?

Those decisions are easy to collapse into one idea of “confidence.” If a model can estimate when it is likely to be correct, it seems reasonable to expect the highest-confidence candidate to be the best candidate.

The evidence from Xi and colleagues shows why that inference is unsafe.¹

On Qwen3-14B answering TriviaQA with 32 sampled traces, choosing the answer with the highest internal confidence reaches 0.778 accuracy. Majority voting reaches 0.771. An oracle that can identify a correct candidate whenever one exists reaches 0.879.

The gap is informative. The confidence signal contains enough information to improve probability estimates substantially, but not enough to recover most of the answers that a perfect selector could have recovered.

That is the paper’s most consequential measurement result: calibration and answer-selection power are different properties of a confidence signal.

A calibrated score means that answers assigned, for example, roughly 70% confidence are correct roughly 70% of the time. It does not imply that, within a group of competing answers, the 70% candidate can be reliably distinguished from every lower-scored alternative.

The model’s hidden state is better calibrated than its stated confidence

The authors test Qwen3-14B and Ministral-3-8B-Reasoning-2512 across TriviaQA, EntityQuestions, NQ-open, and SimpleQA-Verified.

For each reasoning trace, they train an L2-regularized logistic probe on the hidden state immediately before the final answer. The probe estimates the probability that the trace is correct.

Across the main comparisons, this internal signal is dramatically better calibrated than the confidence the model verbalizes itself.

For Qwen3-14B on TriviaQA, verbalized confidence has expected calibration error of 0.178. The probe reduces it to 0.015. On EntityQuestions, ECE falls from 0.529 to 0.014. On SimpleQA, where Qwen’s answer accuracy is only 0.066, verbal ECE is 0.661 while probe ECE is 0.075.

The same pattern appears for Ministral. Its TriviaQA ECE falls from 0.247 to 0.014, and its EntityQuestions ECE from 0.627 to 0.024.

These results are not merely rescaling. The probe also improves AUROC, meaning it better discriminates correct from incorrect traces. Post-hoc calibration methods can improve the probability scale on the distribution where they are fitted, but they do not create new ranking information.

The harder result is that this stronger trace-level signal still does not become a correspondingly strong best-of-N selector. Better measurement of correctness probability does not close the candidate-recovery gap.

Probe-SD moves the signal into the model

A probe is useful diagnostically, but retaining an auxiliary hidden-state classifier in the serving path complicates deployment.

The paper’s second contribution is Probe-guided Self-Distillation, or Probe-SD.

For each retained training trace, the probe converts the pre-answer hidden state into a probability,

which is then mapped to an integer confidence score from 1 to 100. The model’s original stated confidence is replaced with this probe-derived value, and the authors supervised-finetune a same-family base checkpoint on 10,000 selected traces.

The important point is where the supervision operates. The reasoning trace and answer are not replaced with a new answer selected by the probe. Instead, the confidence attached to that particular trace is relabeled using the internal correctness estimate.

After training, the student reports calibrated confidence directly. The probe is no longer required at inference time.

For Qwen3-14B, Probe-SD reduces ECE from 0.178 to 0.024 on the in-domain TriviaQA evaluation and from 0.542 to 0.113 averaged across the three out-of-domain datasets. Ministral moves from 0.247 to 0.044 in domain and from 0.634 to 0.129 out of domain.

Post-hoc isotonic calibration does slightly better than Probe-SD on the distribution where it is fitted for Qwen—0.013 versus 0.024 ECE—but deteriorates to 0.274 out of domain and leaves AUROC essentially unchanged. Probe-SD therefore appears to be learning a more transferable confidence behavior rather than only correcting the numerical scale of existing scores.

The ablation separates calibration gains from accuracy gains

The component ablation is particularly useful because it prevents a common misreading of the finetuning result.

With full Probe-SD on Qwen, in-domain ECE is 0.024 and out-of-domain ECE is 0.113. Removing only the confidence-weighted loss raises those values modestly to 0.033 and 0.129.

Removing probe relabeling changes the result much more sharply: ECE rises to 0.159 in domain and 0.522 out of domain.

Answer accuracy barely moves across these variants.

That makes probe relabeling the main supported mechanism behind the calibration improvement. The modest answer-accuracy gain seen for the Base-initialized Probe-SD students comes from a different source.

The authors’ factual-recall audit attributes 93.7% of Qwen’s 2.36-point accuracy gain and 73.0% of Ministral’s 3.56-point gain to better retrieval of the gold fact into the reasoning trace. In other words, initialization appears to affect factual accessibility, while probe-derived labels affect confidence calibration.

Those should be treated as separate mechanisms.

Use confidence to weight decisions, not to manufacture an oracle

The clearest production use follows from that separation.

If a model reports a probability that better tracks its empirical correctness rate, a system can set more meaningful thresholds for abstention, human review, secondary-model escalation, or other costly actions.

The paper also gives limited evidence for multi-sample aggregation. On Qwen3-14B TriviaQA with 16 samples, confidence-weighted voting reaches 79.05% accuracy, compared with 78.59% for majority voting and 77.75% for simply choosing the maximum-confidence sample.

The gains are modest, but the ordering fits the broader result. Confidence appears more useful when it modulates evidence across samples than when it is asked to identify one supposedly definitive answer.

Cognaptus infers a narrower deployment rule from this: treat calibrated confidence as a control signal for downstream policy, not as proof that the model can locate the correct candidate whenever one was generated.

That distinction matters most for systems that attach different costs to accepting, escalating, retrying, or abstaining.

White-box training access is still the entry price

Probe-SD simplifies the inference path, not the data-construction path.

Training requires access to internal hidden states, a model-specific probe, validation-based probe configuration, sampled traces, correctness labels, and a subsequent finetuning stage. A team working only through a closed text API cannot reproduce this pipeline from outputs alone.

The evidence base is also narrow in ways that affect deployment claims. The experiments cover two open-weight model families, with sizes up to 14B, and four factual QA benchmarks with short, checkable answers. Long-form generation, subjective evaluation, larger closed models, and more reasoning-intensive domains remain untested.

Ranking quality also weakens on low-base-rate tasks. Calibration cannot repair a candidate pool in which the correct answer was never generated.

Finally, the paper does not run a controlled online-reinforcement-learning baseline. It shows that supervised finetuning can produce calibrated confidence behavior in this setting; it does not establish that Probe-SD is generally equivalent to RL-based confidence training.

Confidence becomes more useful once its job is defined

The paper narrows what model confidence should be expected to do.

A well-calibrated internal signal can estimate the reliability of a reasoning trace while remaining only a modest candidate selector. That signal can also be distilled into the model’s own reported confidence, substantially improving calibration without keeping an auxiliary probe in the serving path.

For operators, the valuable shift is conceptual before it is architectural. Confidence can govern how much authority an answer receives without being trusted to identify the best answer among every set of alternatives.

That makes calibration useful for policy. It does not make confidence omniscient.

Cognaptus: Automate the Present, Incubate the Future.