arxiv: 2604.05306 · v2 · submitted 2026-04-07 · 💻 cs.LG · cs.AI· cs.CL

Recognition: no theorem link

LLMs Should Express Uncertainty Explicitly

Junyu Guo , Shangding Gu , Ming Jin , Costas Spanos , Javad Lavaei

Authors on Pith no claims yet

Pith reviewed 2026-05-15 07:08 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL

keywords large language modelsuncertainty estimationself-assessmentpost-trainingfactual reasoningoverconfidenceretrieval augmented generationconfidence calibration

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The pith

Post-training lets LLMs explicitly signal uncertainty either during or after reasoning.

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

The paper tests whether large language models can be trained after pretraining to express uncertainty in their own outputs instead of always sounding confident. It compares two placements for the signal: a verbalized confidence score once reasoning finishes, or an marker inserted while reasoning is still underway whenever the current state looks unreliable. Both approaches cut the rate of overconfident wrong answers on factual tasks, raise overall answer quality, and let uncertainty detection trigger retrieval-augmented generation for better final outputs. A reader would care because explicit uncertainty markers give users and downstream systems a concrete way to know when an answer might need checking or extra information.

Core claim

The paper claims that post-training LLMs to produce either an end-of-reasoning verbalized confidence score or a during-reasoning <uncertain> marker reduces overconfident errors and improves answer quality on factual reasoning tasks. The end-of-reasoning version sharpens an existing confidence-related structure in the pretrained model, while the during-reasoning version teaches the model to flag high-risk steps with parameter changes concentrated in late layers.

What carries the argument

Two explicit self-assessment mechanisms: verbalized end-of-reasoning confidence scores and during-reasoning <uncertain> token emission.

Load-bearing premise

That post-training on these uncertainty signals will make the model reflect genuine internal uncertainty rather than simply learning to output the markers without changing its actual reasoning.

What would settle it

An evaluation on held-out factual questions showing that the trained models still produce high-confidence incorrect answers at the same rate as the base model.

Figures

Figures reproduced from arXiv: 2604.05306 by Costas Spanos, Javad Lavaei, Junyu Guo, Ming Jin, Shangding Gu.

**Figure 2.** Figure 2: Mechanistic evidence for verbalized confidence calibration. Calibration sharpens late-layer [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Final-layer PCA of the confidence-token hidden state, colored by verbalized confidence. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: First <uncertain> emission position as a fraction of response length [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Probe performance peaks in the middle layers. Hidden-State Probe for Retrieval Triggering. To convert <uncertain> emission into an actual retrieval decision, we train a linear probe on emitted examples to predict whether the final answer is wrong. The probe uses span-aware hidden-state features around the first emitted <uncertain> span together with a small set of scalar response features [PITH_FULL_IMAGE… view at source ↗

**Figure 6.** Figure 6: Token-level KL by position type. Both objectives concentrate distributional change at their [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Layer-wise CKA between base and calibrated models. Verbal calibration preserves [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: KL mass fractions by token type. These plots complement the main-text boxplots by showing total KL allocation rather than per-token enrichment. Because reasoning spans are much longer than uncertainty spans, raw mass fractions should be interpreted together with the per-token statistics in the main text [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗

**Figure 9.** Figure 9: Hidden-state patching at the signal position versus reasoning positions. In both interfaces, patching the reasoning trace is at least as disruptive as patching the signal token itself, which is consistent with uncertainty being assembled across the trajectory and only exposed at the designated output position. (a) Verbal model. Drift is concentrated in value/output projections and MLP projections, with mi… view at source ↗

**Figure 10.** Figure 10: Relative Frobenius weight drift across layers and module types. Both calibrated models show similar update structure in parameter space, with the largest changes in v_proj, o_proj, and MLP projection layers. This makes the difference in representation geometry especially noteworthy: similar magnitudes of weight drift yield very different geometric consequences. does not by itself define the full uncertain… view at source ↗

**Figure 11.** Figure 11: Mechanism-to-behavior linkage for the verbal model. Localization-related features predict per-example confidence shifts with cross-validated R2 = 0.51, indicating that the strength of the learned confidence mechanism varies meaningfully across examples rather than appearing only as a population-level average [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗

**Figure 12.** Figure 12: Mechanism-to-utility linkage for the special model. Under the current proxy utility target, the special model shows weak and unstable within-subset linkage. This likely reflects a mismatch between the current utility proxy and the model’s operative mechanism, which is more naturally framed as a binary emission decision than as graded variation within already-emitting examples. This produces an informative… view at source ↗

**Figure 13.** Figure 13: Detailed binned routing view for verbalized confidence calibration. In the base model, [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗

**Figure 14.** Figure 14: Final-layer PCA of the confidence-token hidden state, grouped by outcome type. In [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗

**Figure 15.** Figure 15: Training dynamics and calibration quality of the calibrated Llama-3-8B model. [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗

**Figure 16.** Figure 16: Qualitative examples of epistemic and aleatoric errors before and after GRPO calibration [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗

**Figure 17.** Figure 17: Qualitative examples for the <uncertain> token checkpoint, which signals uncertainty via a discrete trainable token rather than a verbalized confidence score. Epistemic errors (Examples 1–2) occur when the model produces a wrong answer without emitting <uncertain> in the reasoning chain; the baseline (Example 1) never uses the token, while the trained model (Example 2) still fails to trigger it for short,… view at source ↗

read the original abstract

Large language models (LLMs) often produce confident yet incorrect answers, which can lead to risky failures in real-world applications. We study whether post-training can make a model's self-assessment explicit: when the model is uncertain, can it be trained to signal so within its own response? A central design question is where in the response this signal should be exposed -- during reasoning, while the answer is still being formed, or at the end, once the answer has been produced. We study both. For end-of-reasoning self-assessment, we train the model to verbalize a confidence score for its response, with the aim of high confidence on correct answers and low confidence on incorrect ones. For during-reasoning self-assessment, we train the model to emit the marker <uncertain> whenever its current reasoning state appears unreliable. Across factual reasoning tasks, both forms sharply reduce overconfident errors while improving answer quality, and both can be used as triggers for retrieval augmented generation (RAG) to improve the final response. We further analyze their internal mechanisms: end-of-reasoning verbalized confidence sharpens a confidence-related structure already present in the pretrained model, whereas during-reasoning <uncertain> emission teaches the model to mark high-risk reasoning steps, with parameter changes concentrated in the model's late layers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper trains LLMs to emit explicit uncertainty signals either mid-reasoning or at the end and shows both can trigger RAG, but the abstract's strong claims rest on unreported numbers.

read the letter

The core new piece is the direct comparison between training a model to verbalize a confidence score after reasoning and training it to insert an marker while reasoning is still happening. The internal analysis that ties the during-reasoning version to late-layer changes is also fresh relative to earlier calibration work. Both approaches are then used as simple triggers for retrieval, which is a clean, deployable idea for cutting down on overconfident factual errors. That part is practical and worth testing further. The main weakness is that the abstract asserts sharp drops in overconfident mistakes and better answer quality without any numbers, baselines, dataset sizes, or training details. Without those, it is impossible to judge whether the gains are real, large, or just artifacts of the chosen tasks. The stress-test concern also lands: because the training signal is final-answer correctness, the model could learn to emit the marker or score based on surface features rather than any genuine internal uncertainty readout. The late-layer concentration does not distinguish those two stories. Generalization beyond the factual tasks tested is not addressed either. This is the kind of work that belongs in a reading group for people focused on reliable LLM deployment and calibration. It is not yet ready for citation in its current form because the evidence is missing, but the question it asks is worth a serious referee's time once the quantitative results and controls are added.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes two post-training approaches for LLMs to make uncertainty explicit: verbalizing a confidence score at the end of reasoning (high on correct answers, low on incorrect) and emitting an <uncertain> marker during reasoning when the current state appears unreliable. It claims both sharply reduce overconfident errors and improve answer quality on factual reasoning tasks, that the signals can trigger RAG to improve final responses, and that the methods operate via distinct internal mechanisms (sharpening existing confidence structures for verbalized scores versus late-layer changes for marking high-risk steps).

Significance. If the empirical claims hold and the signals genuinely track internal reasoning reliability rather than surface correlations, the work would be significant for improving LLM trustworthiness in applications where overconfident errors carry risk. The two methods offer practical, deployable ways to surface uncertainty and the mechanistic analysis provides insight into how post-training affects model internals differently for each approach.

major comments (1)

[Internal mechanisms analysis] Internal mechanisms analysis: The reported concentration of parameter changes in late layers for <uncertain> emission is consistent with marking high-risk steps but does not distinguish this from the model learning a direct input-to-marker mapping based solely on final-answer correctness labels. Since supervision derives from answer correctness rather than any internal uncertainty estimate, additional evidence (such as representation probing or OOD tests) is required to support the claim that the training produces explicit self-assessment of reasoning reliability.

minor comments (1)

[Abstract] Abstract: Claims of 'sharp reductions' in overconfident errors and quality improvements are stated without any quantitative metrics, baselines, dataset sizes, or statistical details; these should be added to the abstract to allow immediate assessment of effect sizes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment on the internal mechanisms analysis point by point below. We agree that additional evidence would strengthen the claims and will incorporate it in the revision.

read point-by-point responses

Referee: Internal mechanisms analysis: The reported concentration of parameter changes in late layers for <uncertain> emission is consistent with marking high-risk steps but does not distinguish this from the model learning a direct input-to-marker mapping based solely on final-answer correctness labels. Since supervision derives from answer correctness rather than any internal uncertainty estimate, additional evidence (such as representation probing or OOD tests) is required to support the claim that the training produces explicit self-assessment of reasoning reliability.

Authors: We agree that the supervision signal originates from final-answer correctness labels, which in principle permits a direct input-to-marker mapping. However, the observed concentration of parameter changes in late layers (which integrate higher-level reasoning rather than surface mappings) and the fact that the marker is emitted at intermediate reasoning steps (not solely at the end) provide evidence that the model is responding to reasoning-state reliability. To further distinguish these possibilities, we will add representation probing experiments and OOD tests in the revised manuscript demonstrating that <uncertain> activations correlate with internal uncertainty signals beyond what final correctness alone would predict. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on empirical training outcomes

full rationale

The paper presents an empirical study of post-training LLMs to emit explicit uncertainty signals (verbalized confidence scores or <uncertain> markers). All central claims are supported by experimental results on factual reasoning tasks rather than any mathematical derivation, fitted parameter, or self-referential definition. No equations appear in the provided text, and no load-bearing step reduces to a self-citation chain or input-by-construction. The training signal (answer correctness) is external to the model's internal representations, so the reported improvements do not constitute a circular re-labeling of the same data. This is the expected non-finding for a purely empirical methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The approach appears to rest on standard supervised fine-tuning assumptions rather than new axioms or invented entities.

pith-pipeline@v0.9.0 · 5541 in / 1171 out tokens · 62522 ms · 2026-05-15T07:08:14.584073+00:00 · methodology

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Forward citations

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Reference graph

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