LoVeC: Reinforcement Learning for Better Verbalized Confidence in Long-Form Generations

Andreas Vlachos; Caiqi Zhang; Chengzu Li; Nigel Collier; Xiaochen Zhu

arxiv: 2505.23912 · v2 · pith:IOEXB33Wnew · submitted 2025-05-29 · 💻 cs.CL · cs.AI

LoVeC: Reinforcement Learning for Better Verbalized Confidence in Long-Form Generations

Caiqi Zhang , Xiaochen Zhu , Chengzu Li , Nigel Collier , Andreas Vlachos This is my paper

Pith reviewed 2026-05-19 12:39 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords verbalized confidencereinforcement learninghallucination detectionlong-form generationconfidence calibrationlarge language modelsquestion answering

0 comments

The pith

Reinforcement learning trains language models to attach accurate numerical confidence scores to each statement in long-form outputs.

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

The paper sets out to show that reinforcement learning can teach large language models to produce verbalized confidence scores on the fly while generating long-form factual answers. This approach aims to give a direct, interpretable signal of statement factuality without the need for repeated sampling or external checks. A sympathetic reader would care because current methods for spotting hallucinations either demand heavy computation or fail to scale beyond short questions. If the claim holds, models could generate more trustworthy long responses at much lower cost.

Core claim

LoVeC uses reinforcement learning to optimize large language models so they append an on-the-fly numerical confidence score to each generated statement in long-form question answering. In free-form and iterative tagging evaluation settings, the resulting models produce better-calibrated scores than prior verbalized approaches, generalize across domains on three long-form QA datasets, and run approximately twenty times faster than self-consistency baselines while achieving superior calibration.

What carries the argument

The LoVeC reinforcement learning procedure, which directly optimizes the model to generate accurate verbalized numerical confidence scores during the course of long-form generation.

Load-bearing premise

Reinforcement learning can directly optimize verbalized numerical confidence scores to be well-calibrated without relying on post-hoc consistency checks or external verifiers.

What would settle it

Run the trained models on a held-out long-form QA dataset and measure whether the emitted confidence scores correlate more strongly with actual statement accuracy than the scores from non-RL baselines; a clear drop in correlation would falsify the central claim.

Figures

Figures reproduced from arXiv: 2505.23912 by Andreas Vlachos, Caiqi Zhang, Chengzu Li, Nigel Collier, Xiaochen Zhu.

**Figure 2.** Figure 2: GRPO Reward Function Intuitively, we want to reward the model when the confidence ci , and correctness fi for each statement si are close (e.g., high correctness - high confidence and vice versa), and penalize the model when they are far part (e.g., low correctness, high confidence, vice versa). We use a log-base reward as it imposes stronger penalties to miscalibration comparing to simple linear and qua… view at source ↗

**Figure 3.** Figure 3: Running-time Comparison LoVeC is highly efficient on test-time. Our method offers the best test-time efficiency. Confidence scores are generated inline with the answer, requiring no additional sampling or decomposition of responses into atomic claims via external API calls. In contrast, existing state-of-theart sampling-based methods—such as LUQ for long-form generation—incur significant overhead due to … view at source ↗

**Figure 4.** Figure 4: Reliability diagrams for iterative tagging using Llama3-8B-Instruct in sentence-level. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗

**Figure 5.** Figure 5: Token probability distributions when the model is confident. The sentence to tag is: “King’s [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

**Figure 6.** Figure 6: Token probability distributions when the model is uncertain. The sentence to tag is: [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗

**Figure 7.** Figure 7: Comparison of total processing time (in seconds) for WildHallu test set (792 samples) using [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗

read the original abstract

Hallucination remains a major challenge for the safe and trustworthy deployment of large language models (LLMs) in factual content generation. Prior work has explored confidence estimation as an effective approach to hallucination detection, but often relies on post-hoc self-consistency methods that require computationally expensive sampling. Verbalized confidence offers a more efficient alternative, but existing approaches are largely limited to short-form question answering (QA) tasks and do not generalize well to open-ended generation. In this paper, we propose LoVeC (Long-form Verbalized Confidence), a novel reinforcement learning based method that trains LLMs to append an on-the-fly numerical confidence score to each generated statement during long-form generation. The confidence score serves as a direct and interpretable signal of the factuality of generation. We introduce two evaluation settings, free-form tagging and iterative tagging, to assess different verbalized confidence estimation methods. Experiments on three long-form QA datasets show that our RL-trained models achieve better calibration and generalize robustly across domains. Also, our method is highly efficient, being 20 times faster than traditional self-consistency methods while achieving better calibration.

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

LoVeC applies RL to train LLMs to verbalize numerical confidence scores in long-form generation, delivering claimed calibration gains and a 20x speedup, but the reward signal details are missing.

read the letter

LoVeC trains LLMs with reinforcement learning to append numerical confidence scores to statements as they generate long-form answers. This is the core advance over earlier verbalized confidence work that stayed in short-form QA. The RL step lets the model learn to produce these scores on the fly instead of relying on post-hoc sampling. They introduce free-form and iterative tagging setups to measure the output, then test on three long-form QA datasets. The reported results show better calibration than the baselines they compare against, plus solid generalization across domains. The practical edge is the speed: roughly 20 times faster than self-consistency while still improving calibration. That efficiency angle is the clearest win for anyone who wants to avoid heavy sampling at inference time. The soft spot is the reward formulation for the RL training. To push the model toward well-calibrated scores, the reward has to reflect how factual each statement actually is. In long-form settings that signal normally requires ground-truth references, human labels, or an auxiliary verifier during training. The abstract gives no information on how the reward is built, so the premise of direct optimization without external components does not fully hold up. The results also omit error bars, significance tests, or a full list of baselines, which leaves the size of the gains harder to judge. This paper is for groups working on efficient hallucination detection and trustworthy long-form generation. Readers who care about calibration methods that run cheaply at inference time will get the most from the efficiency numbers. I would send it for peer review so the reward design and experimental details can be checked directly.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes LoVeC, a reinforcement learning method to train LLMs to append on-the-fly numerical confidence scores to each statement during long-form generation. It introduces free-form and iterative tagging evaluation settings and reports experiments on three long-form QA datasets showing improved calibration, robust cross-domain generalization, and a 20x inference-time speedup relative to self-consistency baselines.

Significance. If the central results are confirmed, the work would demonstrate that RL can be used to internalize calibration directly into the generation process for open-ended outputs, offering a more efficient alternative to sampling-based methods. The efficiency advantage at inference time would be a notable practical contribution for trustworthy long-form generation.

major comments (2)

[Abstract] Abstract: The central claim of improved calibration via RL-trained verbalized confidence rests on the reward formulation, yet no details are provided on how the scalar reward per statement is computed (e.g., whether it uses ground-truth references, an auxiliary verifier, or another LLM). This information is load-bearing for assessing whether the method truly avoids external verifiers and for interpreting the reported 20x speedup.
[Experiments] Experiments section: The abstract states that RL-trained models achieve better calibration and generalize robustly, but provides no information on the calibration metric (e.g., ECE or Brier score), the exact baselines, number of runs, error bars, or statistical significance tests. These omissions prevent verification of the quantitative claims.

minor comments (1)

[Evaluation Settings] Clarify the precise difference between the free-form tagging and iterative tagging protocols with an illustrative example of a generated statement and its tagged confidence score.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive feedback on our manuscript. We have carefully reviewed each major comment and provide detailed responses below. We agree that additional clarifications are warranted and will revise the manuscript accordingly to improve clarity and verifiability.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim of improved calibration via RL-trained verbalized confidence rests on the reward formulation, yet no details are provided on how the scalar reward per statement is computed (e.g., whether it uses ground-truth references, an auxiliary verifier, or another LLM). This information is load-bearing for assessing whether the method truly avoids external verifiers and for interpreting the reported 20x speedup.

Authors: We agree that the abstract would benefit from a concise description of the reward computation to make the central claims more self-contained. In Section 3.2 of the manuscript, the per-statement scalar reward is computed by comparing each generated statement against ground-truth references from the QA datasets via an automated factuality verifier (details in Appendix B). This verifier is used exclusively during RL training; at inference time the model generates verbalized confidence scores without any external components. This distinction is what enables the reported 20x speedup relative to sampling-based self-consistency. We will add a brief clause to the abstract summarizing the reward source and the training-versus-inference distinction. revision: yes
Referee: [Experiments] Experiments section: The abstract states that RL-trained models achieve better calibration and generalize robustly, but provides no information on the calibration metric (e.g., ECE or Brier score), the exact baselines, number of runs, error bars, or statistical significance tests. These omissions prevent verification of the quantitative claims.

Authors: We thank the referee for noting these gaps. Section 4.1 defines the primary calibration metric as Expected Calibration Error (ECE) with 10 equal-width bins; Brier score is reported as a secondary metric in the appendix. The main baselines are self-consistency sampling at 5, 10, and 20 samples, plus a verbalized-confidence baseline without RL. All quantitative results are averaged over 5 independent training runs with different random seeds; error bars show standard deviation. Statistical significance between LoVeC and the strongest baseline is assessed via paired t-tests (p < 0.05 reported in Table 2 and Appendix C). We will explicitly restate these experimental details in the main experiments section and ensure they appear in the abstract where space permits. revision: yes

Circularity Check

0 steps flagged

No significant circularity in LoVeC derivation chain

full rationale

The paper introduces an RL-based training procedure to produce verbalized numerical confidence scores during long-form generation. The RL objective optimizes for factuality signals in the generated statements, while evaluation relies on separate calibration metrics computed over held-out long-form QA datasets. These components do not reduce to each other by construction: the reward formulation during training is not shown to be identical to the post-training calibration scores, and no equations or self-citations are presented that would make the reported improvements tautological. The method is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The approach implicitly assumes RL can shape verbalized confidence without external supervision.

axioms (1)

domain assumption Reinforcement learning can optimize verbalized confidence scores to match actual factuality in long-form text
Central to the LoVeC training procedure described in the abstract.

pith-pipeline@v0.9.0 · 5736 in / 1145 out tokens · 29282 ms · 2026-05-19T12:39:46.685010+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 unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We design this confidence reward rconf for an output y using binary cross-entropy loss as below... rconf = λ · 1/n 1⊤ (1 + f ⊙ log(c) − (1 − f) ⊙ log(1 − c) / Rmax)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We explore both on-policy and off-policy RL methods, including DPO, ORPO, and GRPO

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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