Future Confidence Distillation in Large Language Models

Sahil Kale

REVIEW 3 major objections 7 minor 22 references

Pre-solution hidden states can predict post-answer confidence

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2026-07-09 04:31 UTC pith:IESYRKHM

load-bearing objection The paper introduces a clean idea — distilling post-solution probe confidence into pre-solution predictors — and backs it with a reasonable experimental sweep. The main recovery result holds up, but the sample-efficiency claim has a real confound and the binary-vs-continuous teacher question isn't cleanly isolated. the 3 major comments →

arxiv 2607.07626 v1 pith:IESYRKHM submitted 2026-07-08 cs.CL cs.AI

Future Confidence Distillation in Large Language Models

Sahil Kale This is my paper

classification cs.CL cs.AI

keywords confidence estimationhidden representationsknowledge distillationcalibrationmetacognitionlinear probesself-knowledgelanguage models

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that a language model's confidence in its own answer is not a single signal but one that evolves over the course of generating a response, and that this temporal evolution can be exploited to build cheaper, better-calibrated confidence estimators. The author first establishes that post-solution confidence (after an answer is generated) is consistently better calibrated than pre-solution confidence (before generation begins), and that linear probes trained on hidden internal representations recover substantially richer confidence information than the model expresses verbally. The central methodological contribution is 'future confidence distillation': a predictor is trained to map pre-solution hidden representations to the confidence estimates produced by a post-solution probe. The author shows that this distilled predictor, which requires only the pre-solution state at inference time and thus avoids the cost of generating a full answer, recovers 32–66% of the calibration improvement that post-solution confidence provides over pre-solution confidence. The method is sample-efficient (effective down to 25 training examples) and transfers across datasets within the same reasoning domain.

Core claim

The core discovery is that confidence-related information encoded in a language model's hidden representations becomes progressively more decodable over the course of answering, and that the richer post-solution confidence signal can be distilled back into a predictor operating on pre-solution representations. This means a model can approximate the quality of its eventual answer before generating it, using only a lightweight probe on early internal states, recovering a substantial fraction of the calibration gap between pre- and post-solution confidence at a fraction of the inference cost.

What carries the argument

Future confidence distillation: a two-stage training procedure where (1) a post-solution correctness probe T is trained on hidden representations extracted after answer generation to produce continuous teacher confidence estimates t_i, and (2) a distilled predictor D (ridge regressor) is trained on pre-solution hidden representations to regress toward those teacher estimates. At inference time, only D is used, operating on pre-solution representations alone.

Load-bearing premise

The distillation framing depends on the post-solution probe's continuous output t_i carrying richer information than the binary correctness label z. If the probe's output is approximately a crisp classifier (near 0 or 1), then regressing toward t_i is effectively the same as training a standard correctness probe on z, and the 'distillation' adds no incremental value beyond what direct supervision on binary labels would provide.

What would settle it

Train a pre-solution predictor directly on binary correctness labels z under the same sample budget and architecture as the distilled predictor. If it matches or exceeds the distilled predictor's calibration and discrimination, the continuous teacher signal provides no incremental information and the distillation mechanism is not the source of the improvement.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Confidence-aware systems (retrieval triggering, tool use, abstention) could use pre-solution distilled predictors to make routing decisions before generating a full answer, saving 2.2–2.5x inference cost compared to post-solution confidence methods.
If confidence-related information is already linearly decodable in intermediate layers (peaking around layers 16–24), this suggests models internally commit to answer reliability well before producing output tokens, raising questions about whether verbalized confidence failures reflect a decoding bottleneck rather than a representational deficit.
The within-domain transfer result implies that confidence predictors could be trained once on a representative benchmark and deployed across new tasks in the same domain without retraining, reducing the data requirements for calibrated confidence estimation.
The failure of cross-domain transfer suggests that metacognitive representations in LLMs are domain-specific rather than universal, which constrains the scope of any general-purpose confidence probe.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The paper does not isolate whether the continuous teacher signal t_i provides information beyond what the binary correctness label z would provide under matched sample budgets. If t_i is approximately a monotone function of z, the distillation target may reduce to binary correctness, and the 'future confidence distillation' framing would not add value over a standard pre-solution correctness probe
The finding that linear probes consistently outperform MLPs and that confidence is most decodable in intermediate layers is consistent with the hypothesis that transformer representations carry confidence information in a linearly accessible subspace that is partially overwritten or transformed during final-layer decoding. This suggests that final-layer representations may be optimized for token p
If the post-solution probe T captures information that emerges during answer generation (e.g., the model encountering difficulties mid-generation), the distilled pre-solution predictor D is effectively learning to anticipate those generation-time signals from the question representation alone. This raises the question of whether D is modeling question difficulty or simulating the generation trajec

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

The paper introduces a clean idea — distilling post-solution probe confidence into pre-solution predictors — and backs it with a reasonable experimental sweep. The main recovery result holds up, but the sample-efficiency claim has a real confound and the binary-vs-continuous teacher question isn't cleanly isolated.

read the letter

This paper does something simple and useful: trains a pre-solution confidence predictor using post-solution probe outputs as soft labels, so you get better calibration without generating a full answer at inference time. The core result in Table 3 is credible — distilled predictors recover 32–66% of the pre-to-post calibration gap across three domains, averaged over five open-source models, with three seeds and confidence intervals. The layer-wise probing analysis (Figure 3) and the verbal-vs-probe comparison (Table 2) are solid supporting work. The within-domain transfer result is a nice addition and the cross-domain negative result is honestly reported. The experimental design is generally careful: label-stratified subsets, validation-based layer selection, multiple metrics. Credit is due for the breadth and honesty of the evaluation. Two problems stand out, one more serious than the other. The serious one is the sample-efficiency claim in §5.4. The paper says distilled predictors outperform pre-solution probes 'with the same supervision budget,' but the teacher probe is always trained on the full ~1080-example split while the baseline pre-solution probe sees only 25–500 examples. So the distilled predictor has indirect access to 4–43× more labeled data through the teacher. The 'same supervision budget' framing is misleading. This doesn't affect Table 3, where both use the full split, but it undermines a key practical claim. The fix is straightforward: train the teacher on the same N examples as the baseline. The second issue is that the paper never isolates whether the continuous teacher signal t_i adds value over binary correctness z. Table 3 compares Pre (logistic on z) against Distilled (ridge on t_i), which conflates the supervision signal with the architecture. Table 8 in the appendix actually shows that with logistic regression, the distilled predictor (0.183 ECE on factual) is worse than the pre-solution probe (0.156) — the advantage appears only with ridge. This means the architecture choice may be doing more work than the distillation target. A matched comparison — same regressor, z vs t_i — would settle this. Minor issues: no code or data shipped, and the PCA dimensionality and layer selection are selected on validation ECE, which is fine but worth noting given the relatively small sample sizes. None of these are fatal. The main result is real, the idea is practical, and the concerns are addressable in revision. This paper is for people working on LLM confidence estimation, calibration, or routing who want a low-cost pre-generation signal. It deserves a serious referee — the core contribution is sound and the gaps are the kind that a good revision closes.

Referee Report

3 major / 7 minor

Summary. This paper introduces 'future confidence distillation,' a method that trains predictors on pre-solution hidden representations using post-solution correctness probe outputs as supervision. The approach is motivated by the observation (established in the paper's first half) that post-solution confidence is better calibrated than pre-solution confidence, and that linear probes on hidden states outperform verbal confidence estimates. The core experimental contribution shows that distilled predictors recover 32–66% of the calibration gap between pre- and post-solution probes while requiring only pre-solution representations at inference time. The paper evaluates five open-source models across nine datasets spanning three domains, with three seeds, and includes sample-efficiency and cross-dataset transfer experiments.

Significance. The paper addresses a practically important problem: reducing the inference cost of calibrated confidence estimation in LLMs. The distillation framework is sensible and the experimental scope is reasonable (five models, nine datasets, three seeds, multiple metrics). The layer-wise probing analysis (Figure 3, Tables 11–13) and the probe architecture ablation (Table 8) are valuable contributions. The cross-domain transfer negative result (Table 16) is a useful and honest finding. The deployment cost comparison (Table 4) provides practical context. The main results in Table 3, where both teacher and baseline use the full training split, are the strongest evidence for the central claim and are not undermined by the sample-efficiency confound.

major comments (3)

§5.4, Figure 4: The sample-efficiency comparison is confounded by unequal total supervision. The text states that the post-solution teacher probe is trained on the full training split (~1080 examples) while the pre-solution baseline it is compared against uses only 25–500 examples. The distilled predictor therefore benefits from information extracted by a teacher trained on 4–43× more labeled data than the baseline. The claim that distilled predictors outperform pre-solution probes 'with the same supervision budget' (§5.4) is not accurate as stated: the total labeled data consumed by the distilled pipeline (teacher + student) exceeds that of the baseline. This affects a key practical sub-claim. The main recovery results in Table 3 are not affected because there both teacher and baseline use the full split. The authors should either (a) re-run the sample-efficiency experiment with the pre
§3.3, Eq. for L_distill; Table 3: The paper does not isolate whether the continuous teacher signal t_i adds value over the binary correctness label z. The distillation target t_i is the output of a post-solution correctness probe trained on z. If t_i is approximately a monotone function of z (near-crisp probabilities), then L_distill reduces to training a pre-solution correctness probe on z, and the 'distillation' framing adds no information beyond standard probing. The paper does not report the distribution of t_i values or include a baseline where the pre-solution predictor regresses directly on z under matched sample budgets. Without this control, the incremental value of the continuous teacher signal over binary correctness is unclear. This matters for the central claim that post-solution probe outputs serve as 'an effective supervisory signal rather than merely a stronger confidence
§5.3, Table 3: The recovery percentages are computed as (Pre − Distilled)/(Pre − Post), but the paper does not report per-model variance or per-dataset breakdowns for the recovery metric. Table 3 reports only domain-averaged values across five models. Given that the five models span 8B–32B parameters and different families, the recovery fraction could vary substantially across models. A per-model or per-dataset breakdown (even in the appendix) would strengthen the claim that the result is robust rather than driven by a subset of models.

minor comments (7)

Table 1: The 'Closed' and 'Open' model groupings aggregate GPT-5.4 with Claude Sonnet 4.6 and five open-source models respectively, but the table does not indicate how many models are in each group or how the aggregation is performed (mean? weighted?). Adding a note clarifying the aggregation method would help.
§5.1: The text states improvements are 'generally modest' for verbal confidence, but Table 1 shows AUROC for Logic on closed models actually decreases from pre (0.73) to post (0.70). This exception should be noted explicitly rather than glossed over.
§C.1: PCA dimensionality is fixed at 128 components. No sensitivity analysis is provided for this choice. A brief note on whether results are robust to this choice would be helpful.
Table 8: The ablation uses 600 training / 400 test examples, which differs from the 60-40 split of 1800 examples (1080/720) used in the main experiments. This difference should be noted, as it may affect the architecture comparison.
§B.3: The maximum generation length for confidence estimation is 32 tokens. For some models or prompts, this may truncate the confidence output. It would be useful to report how often truncation occurred.
Figure 4 caption: 'Pre- and post-solution probes are trained using correctness labels, whereas distilled predictors are trained using post-solution confidences.' This is accurate but does not mention that the teacher probe for the distilled predictor uses the full training split. Adding this would improve transparency when interpreting the figure.
The paper uses 'future confidence' and 'future confidence distillation' throughout. The term 'future' is slightly ambiguous — it could refer to future tokens, future training, or future confidence at inference. A brief clarification in the introduction would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive review. The referee correctly identifies that the main results in Table 3 (where teacher and baseline use the full training split) are not affected by the sample-efficiency confound in Figure 4. We address each major comment below and commit to revisions for all three points.

read point-by-point responses

Referee: §5.4, Figure 4: The sample-efficiency comparison is confounded by unequal total supervision. The post-solution teacher probe is trained on the full training split (~1080 examples) while the pre-solution baseline uses only 25–500 examples. The claim that distilled predictors outperform pre-solution probes 'with the same supervision budget' is not accurate as stated.

Authors: The referee is correct, and we appreciate the precise identification of this confound. The current Figure 4 comparison is unfair because the distilled predictor benefits from a teacher trained on 4–43× more labeled data than the baseline it is compared against. The phrase 'with the same supervision budget' in §5.4 is inaccurate as written because the total labeled data consumed by the distilled pipeline (teacher training + student training) exceeds that of the baseline. We will fix this in two ways. First, we will re-run the sample-efficiency experiment with the pre-solution baseline probe also trained on the full training split, so that the comparison at each x-axis value contrasts a distilled predictor trained on N examples (with a teacher on the full split) against a baseline trained on the full split. This isolates the question of whether distillation helps at all, independent of sample efficiency. Second, we will add an additional comparison where the teacher probe is trained on the same N examples as the student, making the total supervision budget truly matched. We will revise the text to remove the 'same supervision budget' claim and instead characterize the experiment as measuring the student predictor's sample efficiency given a fixed teacher. We note that the main recovery results in Table 3 are unaffected, as the referee acknowledges, since there both teacher and baseline use the full training split. revision: yes
Referee: §3.3, Eq. for L_distill; Table 3: The paper does not isolate whether the continuous teacher signal t_i adds value over the binary correctness label z. If t_i is approximately a monotone function of z, then L_distill reduces to training a pre-solution correctness probe on z, and the 'distillation' framing adds no information beyond standard probing. The paper does not report the distribution of t_i values or include a baseline where the pre-solution predictor regresses directly on z under matched sample budgets.

Authors: This is a fair and important control that we should have included. We will add a baseline where the pre-solution predictor regresses directly on the binary correctness label z (i.e., a standard pre-solution correctness probe) under the same sample budget as the distilled predictor, and we will report the distribution of teacher confidence values t_i across models and domains. We agree that if t_i were approximately a crisp monotone function of z, the distillation framing would add no information. However, we expect the continuous teacher signal carries additional information beyond binary correctness: the post-solution probe is trained on correctness labels but produces calibrated probability estimates that reflect the model's internal confidence given the full answer trajectory, which may encode information about answer quality, partial correctness, or uncertainty that binary z does not capture. The proposed control will directly test this. If the continuous teacher signal does not outperform binary z, we will revise the claim that post-solution probe outputs serve as 'an effective supervisory signal rather than merely a stronger confidence estimate' accordingly. Either way, the control strengthens the paper. revision: yes
Referee: §5.3, Table 3: The recovery percentages are computed as (Pre − Distilled)/(Pre − Post), but the paper does not report per-model variance or per-dataset breakdowns for the recovery metric. Table 3 reports only domain-averaged values across five models. A per-model or per-dataset breakdown would strengthen the claim that the result is robust rather than driven by a subset of models.

Authors: We agree that per-model and per-dataset breakdowns of the recovery metric would strengthen the robustness claim. We will add a table in the appendix reporting recovery percentages for each of the five models individually, along with per-dataset values within each domain. The layer-wise probe results in Tables 11–13 already show that the pre-to-post calibration improvement holds across all five models, which provides indirect evidence that recovery is not driven by a subset. However, the recovery fraction itself could still vary, and we will make this transparent. We will also report per-model 95% confidence intervals for the recovery metric. revision: yes

Circularity Check

0 steps flagged

No significant circularity; the distillation target is a teacher probe output, not the student's own input, and the recovery metric compares against an independent post-solution probe.

full rationale

The paper's central claim is that a distilled predictor D(ℓ) operating on pre-solution representations can recover calibration improvements achieved by a post-solution probe T(ℓ). The derivation chain is: (1) train T(ℓ) on post-solution hidden states h_post using correctness labels z, producing teacher estimates t_i; (2) train D(ℓ) on pre-solution hidden states h_pre to regress toward t_i via L_distill = Σ(ĉ_i − t_i)²; (3) evaluate D(ℓ) on held-out test data against ECE and AUROC. This is not circular: the teacher T(ℓ) and student D(ℓ) operate on different inputs (h_post vs. h_pre), and the evaluation metric (Table 3's 'recovery' percentage) compares D(ℓ) against an independently trained post-solution probe on the test set, not against the training targets. The student does not define its evaluation metric by construction. The sample-efficiency concern (teacher trained on full split while baseline uses N examples) is a valid confound for the §5.4 sub-claim, but it is a methodological fairness issue, not circularity — the distilled predictor's test-set ECE is not tautologically forced by the training procedure. Self-citations (Kale 2025; Kale and Dhami 2025; Kale and Nadadur 2025) appear in the introduction and related work for framing context (self-knowledge, metacognition) but are not load-bearing for the distillation derivation itself, which is self-contained and evaluated against external benchmarks. No step reduces to its inputs by definition.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The paper introduces no new entities (particles, forces, dimensions, etc.). The free parameters are standard ML hyperparameters (PCA dimensionality, layer selection, regularization). The axioms are domain assumptions about probe sufficiency, teacher signal validity, sampling protocol, and quantization effects — all testable but not independently verified in the paper.

free parameters (3)

PCA dimensionality = 128
Fixed at 128 components (§C.1); not tuned per model or dataset, but chosen as a working default rather than derived.
Layer selection = varies (selected by validation ECE)
Operating layer selected per model/dataset/seed using validation ECE (§C.4); this is a hyperparameter chosen on validation data.
Probe regularization = scikit-learn defaults
Ridge regression and logistic regression use default regularization (§C.2, §C.3); stated as 'no hyperparameter tuning' but defaults are still parameter choices.

axioms (4)

domain assumption Linear probes are sufficient to recover confidence-related information from hidden representations
§3.2 and Appendix D justify this empirically (MLPs perform worse), but the choice is also a modeling assumption that constrains what information can be recovered.
domain assumption Post-solution correctness probe outputs serve as a valid teacher signal for pre-solution confidence
§3.3 assumes that t_i = T(h_post) captures confidence-related information worth distilling; this is the core premise of the method.
domain assumption Label-stratified sampling (no accuracy class >65%) does not bias calibration evaluation
§4.3 constructs stratified subsets for stable ECE estimation; the effect of this stratification on generalization is not analyzed.
domain assumption 4-bit quantization does not materially affect hidden-state quality for probing
§B.3 uses 4-bit quantization for all open-source model inference; the impact on probe performance is not assessed.

pith-pipeline@v1.1.0-glm · 22015 in / 2833 out tokens · 394110 ms · 2026-07-09T04:31:55.367982+00:00 · methodology

0 comments

read the original abstract

Reliable confidence estimation is essential for deploying large language models (LLMs) in confidence-aware systems, where downstream decisions such as retrieval, tool use, and adaptive computation depend on accurately estimating answer reliability. Existing approaches, however, largely treat confidence as a property of completed responses, overlooking how confidence-related information evolves throughout the answering process. In this work, we investigate confidence from a temporal perspective by comparing pre-solution Feeling-of-Knowing (FOK) and post-solution Judgement-of-Learning (JOL) confidence estimates across frontier and open-source LLMs. We show that post-solution confidence is consistently better calibrated and more discriminative than pre-solution confidence, while linear probes trained on hidden representations recover substantially richer confidence-related information than models explicitly verbalise. Building on this observation, we introduce future confidence distillation, which trains predictors operating on pre-solution hidden representations using teacher confidence estimates produced by post-solution correctness probes. Despite requiring only pre-solution representations for inference, distilled predictors recover much of the calibration improvement achieved by post-solution confidence, remain highly sample efficient, and transfer across datasets within the same domain. Together, our findings demonstrate that confidence-related information evolves throughout the answering process and can be anticipated before answer generation is complete, enabling significantly more reliable yet low-cost confidence estimation.

Figures

Figures reproduced from arXiv: 2607.07626 by Sahil Kale.

**Figure 2.** Figure 2: Learning future confidence-related information encoded in hidden representations. (a) Hidden-state confidence probing. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 1.** Figure 1: • Prior to answer generation, the model is asked to predict its probability of eventual success, yielding a pre-solution Feeling-of-Knowing (FOK) estimate cpre ∈ [0, 1]. • The model then generates an answer yˆ = f(x), which is evaluated against the reference solution to obtain a correctness label (based on domain) z ∈ [0, 1] or z ∈ {0, 1}. • Finally, the model is prompted to estimate the probability that i… view at source ↗

**Figure 3.** Figure 3: Layer-wise calibration (ECE) of linear probes trained on hidden representations averaged across open-source models. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Calibration (ECE) as a function of training-set size. Pre- and post-solution probes are trained using correctness labels, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Calibration (ECE) as a function of training-set size for cross-dataset transfer within the same domain. Distilled [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

discussion (0)

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