arxiv: 2605.12446 · v1 · submitted 2026-05-12 · 💻 cs.LG · cs.CL

Recognition: 2 theorem links

· Lean Theorem

ORCE: Order-Aware Alignment of Verbalized Confidence in Large Language Models

Chao Chen, Chen Li, Jiawei Zhou, Songzhu Zheng, Xiaoling Hu

Pith reviewed 2026-05-13 05:57 UTC · model grok-4.3

classification 💻 cs.LG cs.CL

keywords verbalized confidenceLLM calibrationdecoupled frameworksampling surrogaterank-based RLfailure prediction

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The pith

Decoupling answer generation from confidence estimation improves calibration of verbalized confidence in LLMs while preserving accuracy.

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

Large language models often state high confidence even when wrong, creating a need for better verbalized confidence calibration. The paper introduces a decoupled framework that generates the answer first and then estimates confidence on the fixed question-answer pair. This separation prevents confidence optimization from interfering with answer quality. It constructs a sampling-based surrogate from multiple completions to estimate correctness likelihood and uses rank-based reinforcement learning to assign higher verbalized confidence to more likely correct responses. A sympathetic reader would care because this enables more reliable uncertainty signals for real-world LLM deployment without sacrificing performance.

Core claim

The central claim is that decoupling answer generation from confidence estimation and optimizing the relative ordering of verbalized confidence using rank-based objectives on a sampling surrogate leads to improved calibration and failure prediction while largely preserving answer accuracy on reasoning and knowledge-intensive benchmarks.

What carries the argument

The order-aware alignment framework that decouples answer generation and applies rank-based RL to align verbalized confidence with a sampling-based correctness surrogate.

If this is right

Better calibration of verbalized confidence scores.
Improved failure prediction performance.
Answer accuracy remains largely intact.
More reliable user-facing uncertainty estimates without token logit access.

Where Pith is reading between the lines

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

This approach could extend to calibrating other LLM outputs like explanations or plans.
Reducing reliance on ground truth for confidence training might enable self-supervised improvements.
In practice, this could help in applications where overconfident answers lead to costly mistakes.

Load-bearing premise

The sampling-based surrogate from multiple model completions provides an accurate proxy for the actual correctness likelihood of responses.

What would settle it

If the ranks assigned by the sampling surrogate do not correlate with actual correctness rates across diverse benchmarks, the optimization would fail to align confidence properly.

Figures

Figures reproduced from arXiv: 2605.12446 by Chao Chen, Chen Li, Jiawei Zhou, Songzhu Zheng, Xiaoling Hu.

**Figure 2.** Figure 2: Comparison between local rank matching (NRD) and global Spearman alignment. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.

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

ORCE decouples answer generation from verbalized confidence and uses rank RL on sampling surrogates to improve calibration while holding accuracy steady, though the surrogate's accuracy as a correctness proxy is the main open question.

read the letter

The main thing here is the strict decoupling: generate the answer first, then estimate verbalized confidence on the fixed pair, and train the ordering of those statements with rank-based RL driven by a sampling surrogate for correctness likelihood. This avoids the interference that joint training often creates between accuracy and calibration objectives. The experiments on reasoning and knowledge benchmarks report better calibration and failure prediction with answer accuracy mostly preserved, which is the practical payoff they emphasize. The order-aware rank objective is a reasonable fit for natural-language confidence outputs. The soft spot is the sampling surrogate. If the model repeats the same wrong answer across draws, as it often does on knowledge tasks, the frequency signal can assign high likelihood to errors and the RL then aligns confidence to the wrong ordering. The abstract does not show a direct check of how well the surrogate correlates with ground-truth labels, so the reported gains could partly be artifacts of optimizing a noisy proxy. I would want to see that correlation table or ablation in the full paper before treating the calibration numbers as robust. This is for people working on LLM reliability where verbalized confidence matters more than logit access. A reader who needs a concrete technique to try on standard benchmarks will get usable ideas from the method and results. It deserves peer review because the claims are specific and the setup is testable, even if the surrogate assumption needs referee scrutiny.

Referee Report

2 major / 2 minor

Summary. The paper proposes ORCE, a decoupled order-aware framework for verbalized confidence calibration in LLMs. Answers are generated and fixed first, after which confidence is estimated on the question-answer pair via a sampling-based surrogate derived from multiple completions to approximate correctness likelihood; rank-based RL then optimizes verbalized confidence to respect the surrogate ordering. Experiments on reasoning and knowledge-intensive benchmarks report improved calibration and failure prediction while largely preserving answer accuracy.

Significance. If the sampling surrogate reliably tracks true correctness, the decoupled design and rank-based objective could provide a practical route to better verbalized confidence without the interference that joint optimization often introduces, while the reported preservation of accuracy is a useful empirical outcome.

major comments (2)

[§3 (surrogate construction)] §3 (surrogate construction): The sampling-based surrogate for per-response correctness likelihood is constructed from multiple completions but is never directly validated against ground-truth correctness labels. This assumption is load-bearing for the central claim, because on knowledge-intensive tasks models frequently repeat the same incorrect answer; the resulting surrogate can assign high likelihood to errors, so the rank objective may optimize a mis-specified target rather than genuine alignment.
[Experimental results (Section 5)] Experimental results (Section 5): Reported calibration gains are presented without ablations or correlation analysis showing that surrogate scores track actual correctness; if the surrogate-rank correlation is weak, the observed improvements could be artifacts of optimizing a noisy proxy rather than evidence of improved alignment.

minor comments (2)

[Abstract] Abstract: The phrase 'order-aware' is introduced without a one-sentence definition; adding a brief gloss would help readers immediately distinguish the contribution from standard ranking losses.
[Notation] Notation: Ensure the symbol for the surrogate likelihood (e.g., p̂_correct) is used consistently when describing both the sampling procedure and the RL reward.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment below and indicate the revisions we will make to strengthen the paper.

read point-by-point responses

Referee: [§3 (surrogate construction)] §3 (surrogate construction): The sampling-based surrogate for per-response correctness likelihood is constructed from multiple completions but is never directly validated against ground-truth correctness labels. This assumption is load-bearing for the central claim, because on knowledge-intensive tasks models frequently repeat the same incorrect answer; the resulting surrogate can assign high likelihood to errors, so the rank objective may optimize a mis-specified target rather than genuine alignment.

Authors: We acknowledge that the current manuscript does not include a direct empirical validation of the sampling-based surrogate against ground-truth correctness labels. The surrogate is constructed by drawing multiple completions from the model to estimate the likelihood of producing the correct answer for a fixed question-answer pair, serving as a practical proxy when direct supervision is unavailable. While repetition of incorrect answers is indeed possible on knowledge-intensive tasks, the rank-based RL objective operates on relative ordering rather than absolute values, which can still promote better calibration even with a noisy proxy. To address this concern, we will add a correlation analysis (including Spearman rank correlation and scatter plots) between surrogate scores and actual correctness labels across the benchmarks in a new subsection of Section 3 or an appendix in the revised manuscript. revision: yes
Referee: [Experimental results (Section 5)] Experimental results (Section 5): Reported calibration gains are presented without ablations or correlation analysis showing that surrogate scores track actual correctness; if the surrogate-rank correlation is weak, the observed improvements could be artifacts of optimizing a noisy proxy rather than evidence of improved alignment.

Authors: We agree that the experimental section would benefit from explicit ablations and correlation metrics linking surrogate scores to ground-truth correctness. The reported results show consistent gains in calibration and failure prediction with minimal impact on accuracy, which provides indirect support for the approach. However, to rule out the possibility that improvements stem from a weak proxy, we will add (i) correlation coefficients and visualizations between surrogate scores and correctness, and (ii) ablation studies removing or varying the rank-based objective in the revised Section 5. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation chain relies on an external sampling-based surrogate constructed from multiple independent model completions to estimate correctness likelihood, followed by rank-based RL optimization that aligns verbalized confidence ordering to this proxy. This is not equivalent to the inputs by construction: the surrogate is generated separately from the final verbalized outputs, the RL objective is a relative ranking loss rather than a direct fit to ground-truth labels or to the confidence values themselves, and claimed improvements are measured against external benchmarks using actual correctness. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or described framework; the approach remains self-contained with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that multiple sampled completions form a reliable surrogate for correctness likelihood and that conditioning confidence estimation on a fixed answer does not lose critical information.

axioms (1)

domain assumption Sampling multiple model completions yields a usable surrogate for the likelihood that a given answer is correct
This surrogate is used to construct the rank-based training signal for confidence alignment.

pith-pipeline@v0.9.0 · 5515 in / 1062 out tokens · 32065 ms · 2026-05-13T05:57:04.080004+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes
we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_strictMono_of_one_lt echoes
Spearman correlation reward ... RSC(c, κ;C, K) = rs(C∪{c},K∪{κ})−rs(C,K)

Reference graph

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