Trust but Verify: Prover-Verifier Deliberation for Selective LLM Prediction

Baotong Zhang; Dean Foster; Jo\~ao Sedoc

arxiv: 2605.25133 · v1 · pith:6EVRZHAMnew · submitted 2026-05-24 · 💻 cs.AI · cs.CL

Trust but Verify: Prover-Verifier Deliberation for Selective LLM Prediction

Jo\~ao Sedoc , Baotong Zhang , Dean Foster This is my paper

Pith reviewed 2026-06-30 11:07 UTC · model grok-4.3

classification 💻 cs.AI cs.CL

keywords prover-verifier deliberationselective predictionLLM confidence estimationinteractive verificationGPQA DiamondAccept No Changeargument defensibility

0 comments

The pith

Prover-verifier deliberation produces Accept + No Change answers that show a roughly 30 percentage point precision advantage over the rest on GPQA Diamond.

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

The paper introduces an interactive protocol in which one language model defends an answer with checkable sub-claims while another issues targeted challenges and returns Accept, Challenge, or Reject. The central empirical result is that answers accepted without revision form a high-confidence subset whose precision exceeds the complement by about 30 points. A sympathetic reader would care because the protocol supplies a structured way to abstain on uncertain cases rather than forcing every output to be reported. The authors evaluate the approach across model pairs and benchmarks and contrast it with self-consistency and debate baselines to argue that the signal is distinct.

Core claim

Prover-verifier deliberation (PVD) lets a frozen prover defend a candidate answer through checkable sub-claims while a verifier issues challenges and returns Accept, Challenge, or Reject; the Accept + No Change (ANC) cases are treated as the high-confidence subset. On GPQA Diamond this subset exhibits roughly 30 percentage points higher precision than the non-ANC complement. The same gap transfers across some model families when verifier strictness and domain competence are adequate, yet collapses or inverts when the verifier is outside its effective region. The protocol is shown to supply an argument-defensibility signal distinct from self-consistency, universal self-consistency, multi-agen

What carries the argument

Prover-verifier deliberation (PVD) protocol: a prover generates checkable sub-claims defending a candidate answer and a verifier returns Accept, Challenge, or Reject; the Accept + No Change (ANC) subset is used for selective high-confidence reporting.

If this is right

ANC subsets can be reported while the system abstains on the remaining cases, raising overall precision of delivered answers.
High HC-Prec gaps transfer across some model families provided the verifier remains competent in the domain.
Verifier strictness and domain competence control the size of the selection gap.
Weaker prover-verifier pairings can produce zero or negative gaps on harder sets such as Humanity's Last Exam.
The argument-defensibility signal differs from those produced by self-consistency, debate, or Reflexion.

Where Pith is reading between the lines

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

If the independence premise holds, the protocol could be combined with existing calibration methods to further enlarge the precision gap.
The approach might extend to open-ended generation tasks if sub-claims can be formulated for non-multiple-choice answers.
Deployment would require monitoring verifier competence on each new domain to avoid signal collapse.
The coverage-precision trade-off could be tuned by adjusting verifier strictness rather than by post-hoc thresholds.

Load-bearing premise

The verifier's challenges and Accept/Reject decisions supply an independent signal of answer correctness that is not reducible to model-specific biases or simpler self-consistency checks.

What would settle it

An experiment in which the precision gap between ANC and non-ANC disappears when the verifier is replaced by a model that performs only self-consistency checks or issues random challenges would show the signal is not independent.

Figures

Figures reproduced from arXiv: 2605.25133 by Baotong Zhang, Dean Foster, Jo\~ao Sedoc.

read the original abstract

Reliably knowing when a language model is correct is almost as important as being correct. We introduce prover-verifier deliberation (PVD), an inference-time protocol grounded in interactive proof theory, as a mechanism for selective prediction: the protocol produces both an answer and a structured confidence verdict, allowing a system to report high-confidence answers while abstaining on uncertain cases. In each dialogue, a prover defends a candidate answer through checkable sub-claims while a verifier issues targeted challenges and returns \textsc{Accept}, \textsc{Challenge}, or \textsc{Reject}. Because frozen language models are imperfect provers and verifiers operating over a noisy channel, formal soundness and completeness guarantees do not transfer; instead, we characterize the protocol empirically through its coverage-precision behavior. Our main experiment uses Claude Sonnet 4.6 as prover and Claude Haiku 4.5 as verifier on GPQA Diamond. Questions accepted with no answer revision, which we call Accept + No Change (ANC), are reported as the high-confidence subset; we evaluate this subset by its precision and coverage. ANC separates reliable from unreliable answers, yielding a $\sim$30pp HC-Prec gap over the non-ANC complement. Robustness experiments with GPT and Gemini pairings show that high HC-Prec can transfer across model families, while verifier strictness and domain competence largely determine the size of the selection gap. On Humanity's Last Exam, weaker prover-verifier pairings can collapse or invert the ANC signal, illustrating a practical failure mode when the verifier operates outside its effective region. Comparisons with self-consistency, universal self-consistency, multi-agent debate, and Reflexion suggest that prover-verifier deliberation supplies a distinct argument-defensibility signal for selective prediction.

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

PVD produces a 30pp precision gap on GPQA via the ANC subset, but the gap size tracks model competence matching more than the interactive protocol itself.

read the letter

The paper's main result is that Accept + No Change answers from a prover-verifier exchange form a high-confidence subset with about 30 points higher precision than the rest on GPQA Diamond. That empirical separation is the concrete thing to evaluate.

The protocol itself is new: a prover breaks an answer into checkable sub-claims, the verifier issues targeted challenges, and the final Accept/Reject plus whether the answer changed defines the filter. Framing selective prediction this way, rather than through self-consistency scores or debate, is a clear difference from the baselines cited. The cross-family runs with GPT and Gemini pairs, plus the explicit failure cases on Humanity's Last Exam when the verifier is too weak, are useful additions.

The soft spot is whether the verifier's Accept/Reject decisions supply an independent signal or simply reflect that a stronger model is better at spotting weak answers from a similar model. The largest reported gap uses same-family Claude models, and the paper itself notes that verifier strictness and domain competence drive the gap size. Without matched controls on total forward passes or prompt templates that remove the interactive framing, the 30pp number could shrink or disappear. The abstract comparisons to self-consistency and multi-agent debate are mentioned but lack the detail needed to judge how distinct the signal actually is.

This is for researchers working on inference-time methods for LLM reliability and abstention. The setup is concrete enough, and the documented limits are honest enough, that the work deserves referee attention rather than a desk reject.

Referee Report

2 major / 2 minor

Summary. The paper introduces prover-verifier deliberation (PVD), an inference-time interactive protocol in which a prover defends a candidate answer via checkable sub-claims and a verifier issues targeted challenges, returning Accept, Challenge, or Reject. On GPQA Diamond with Claude Sonnet 4.6 as prover and Haiku 4.5 as verifier, the Accept + No Change (ANC) subset is treated as the high-confidence set and exhibits an approximately 30 percentage-point precision advantage over the non-ANC complement. The work reports cross-family transfer with GPT and Gemini pairings, compares PVD against self-consistency, universal self-consistency, multi-agent debate and Reflexion, and documents collapse or inversion of the ANC signal on Humanity's Last Exam when verifier competence is mismatched.

Significance. If the ANC precision gap reflects an argument-defensibility signal that is not reducible to self-consistency or shared model biases, the protocol supplies a new, structured mechanism for selective prediction whose coverage-precision behavior can be characterized empirically even though formal soundness guarantees do not transfer. The cross-family robustness results and explicit identification of a competence-mismatch failure mode are concrete strengths.

major comments (2)

[Main GPQA experiment] Main GPQA experiment (abstract and § on empirical results): the central ~30pp HC-Prec gap is obtained with same-family Claude models; the manuscript must demonstrate that this separation is not an artifact of correlated rejection patterns induced by shared training data. An explicit control that replaces the interactive verifier with a non-interactive self-consistency check using an identical number of forward passes and prompt templates stripped of dialogue framing is required to isolate the contribution of the prover-verifier structure.
[Robustness and failure-mode sections] Robustness and failure-mode sections: the claim that verifier strictness and domain competence determine gap size is load-bearing for the practical takeaway, yet the reported collapse on Humanity's Last Exam with weaker pairings is presented without quantitative controls that hold the number of model calls fixed across conditions. Without such matched-compute ablations, it remains unclear whether the observed inversion is protocol-specific or simply a capability mismatch.

minor comments (2)

[Methods] Notation for Accept + No Change (ANC) is introduced in the abstract but should be defined with an explicit equation or pseudocode block in the methods section to avoid ambiguity when readers compare ANC to other selection criteria.
[Results] The abstract states that comparisons 'suggest that prover-verifier deliberation supplies a distinct argument-defensibility signal'; the corresponding results table or figure should report the exact precision and coverage numbers for each baseline under identical question sets so that the distinctness claim can be verified numerically.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The requested controls will help strengthen the isolation of the prover-verifier contribution and the interpretation of failure modes. We address each major comment below.

read point-by-point responses

Referee: [Main GPQA experiment] Main GPQA experiment (abstract and § on empirical results): the central ~30pp HC-Prec gap is obtained with same-family Claude models; the manuscript must demonstrate that this separation is not an artifact of correlated rejection patterns induced by shared training data. An explicit control that replaces the interactive verifier with a non-interactive self-consistency check using an identical number of forward passes and prompt templates stripped of dialogue framing is required to isolate the contribution of the prover-verifier structure.

Authors: We agree that a precisely matched non-interactive control is needed to rule out artifacts from shared training data. While the manuscript already compares PVD against self-consistency and universal self-consistency (which use multiple forward passes), those baselines do not strip dialogue framing from the prompts. We will add the requested ablation—replacing the interactive verifier with a non-interactive self-consistency check that uses an identical number of forward passes and stripped prompt templates—in the revised manuscript. revision: yes
Referee: [Robustness and failure-mode sections] Robustness and failure-mode sections: the claim that verifier strictness and domain competence determine gap size is load-bearing for the practical takeaway, yet the reported collapse on Humanity's Last Exam with weaker pairings is presented without quantitative controls that hold the number of model calls fixed across conditions. Without such matched-compute ablations, it remains unclear whether the observed inversion is protocol-specific or simply a capability mismatch.

Authors: The HLE results are meant to demonstrate the practical importance of verifier competence. We acknowledge that the current version does not explicitly hold the total number of model calls fixed when varying pairings. We will add matched-compute ablations that keep the number of forward passes constant across conditions in the revision, allowing clearer attribution of signal collapse or inversion to the protocol versus capability mismatch. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical coverage-precision results on external benchmarks with no reductive equations or self-referential definitions.

full rationale

The paper introduces an inference-time protocol (PVD) and evaluates it empirically via ANC subset precision/coverage on GPQA Diamond and other benchmarks. The central ~30pp HC-Prec gap is a direct measurement of the selected subset versus complement; no equations, fitted parameters, or derivations reduce this gap to an input by construction. Formal proof theory is invoked only as motivation, with explicit statement that soundness guarantees do not transfer. Comparisons to self-consistency, debate, and Reflexion are external empirical baselines. No self-citation load-bearing steps, ansatzes, or uniqueness theorems appear in the provided text. The result is self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the empirical behavior of current LLMs as imperfect provers and verifiers; no free parameters, new entities, or additional axioms beyond standard benchmark evaluation are introduced.

axioms (1)

domain assumption Frozen language models can function as provers and verifiers over a noisy channel sufficiently well for empirical characterization of coverage-precision tradeoffs.
The abstract explicitly states that formal soundness guarantees do not transfer and relies instead on empirical results.

pith-pipeline@v0.9.1-grok · 5849 in / 1232 out tokens · 42197 ms · 2026-06-30T11:07:11.720662+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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That is one round

Generate one [PROVER] block, then one [VERIFIER] block. That is one round
[38]

Do not Accept or Reject on the first round

The verifier MUST Challenge in round 1 –- pick the single weakest or least justified sub-claim and demand rigorous justification. Do not Accept or Reject on the first round
[39]

From round 2 onwards: if the verifier Challenges, generate the next [PROVER] block (responding to that specific challenge only), then another [VERIFIER] block
[40]

Stop when the verifier issues Accept or Reject, or after {fatigue} rounds (forced Reject –- output FINAL_VERDICT: Reject(fatigue))
[41]

Accept only when every sub-claim is specific, the logic is airtight, and there is nothing left worth probing

The verifier must be genuinely adversarial –- default to Challenge. Accept only when every sub-claim is specific, the logic is airtight, and there is nothing left worth probing. Reject if there is a clear logical flaw or factual error
[42]

answer":

The prover may revise its answer if a challenge exposes a mistake. Use this exact format for each block: [PROVER] { "answer": "A" | "B" | "C" | "D", "statement": "one sentence explaining your choice", "subclaims": ["atomic claim 1", "atomic claim 2", ...], "reasoning": "step-by-step explanation" 18 } [/PROVER] [VERIFIER] { "verdict": "Accept" | "Reject" |...
[43]

Retroviruses have an RNA genome, not a DNA genome
[44]

To sequence a retroviral genome, RNA must first be reverse-transcribed into cDNA
[45]

Real-time PCR (RT-qPCR) is the gold-standard molecular diagnostic method for RNA viruses
[46]

Option A is incorrect: direct DNA sequencing is inappropriate for an RNA retrovirus without reverse transcription
[47]

RNA must first be reverse-transcribed into cDNA before sequencing

Option C is incorrect: IgG ELISA detects antibody response (serological), not the virus itself. Verifier — Round 1verdict:CHALLENGE Reasoning:The fundamentals are sound, but sub-claim 2 requires further justification. Modern sequencing platforms (Nanopore, Illumina) can directly sequence RNA without reverse transcription. The prover has not explained why ...
[48]

Direct RNA sequencing exists but is not the standard validated workflow for clinical outbreak diagnostic kit design under current regulatory norms
[49]

cDNA sequencing via reverse transcription is the established, reproducible, and validated method for characterizing RNA virus genomes in diagnostic contexts
[50]

Real-time PCR

“Real-time PCR” in clinical virology is understood to mean real-time RT-PCR, as standard qPCR cannot amplify RNA templates
[51]

real-time PCR

Option D is the only choice that correctly combines RNA-to-cDNA conversion with a sensitive, quantitative, closed-tube molecular detection method. Verifier — Round 2verdict:ACCEPT Reasoning:The prover now correctly distinguishes between what is technically possible (direct RNA sequencing exists) and what is standard validated clinical practice (cDNA seque...
[52]

Institutional review board (IRB) approvals or equivalent for research with human subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or ...

[1] [1]

Humanity's Last Exam

Center for AI Safety, Scale AI, and HLE Contributors Consortium. A benchmark of expert-level academic questions to assess AI capabilities.Nature, 649:1139–1146, 2026. doi: 10.1038/ s41586-025-09962-4. URLhttps://arxiv.org/abs/2501.14249

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[2] [2]

X. Chen, R. Aksitov, U. Alon, J. Ren, K. Xiao, P. Yin, S. Prakash, C. Sutton, X. Wang, and D. Zhou. Universal self-consistency for large language models. InICML 2024 Workshop on In-Context Learning, 2024. URLhttps://openreview.net/forum?id=LjsjHF7nAN

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Do not Accept or Reject on the first round

The verifier MUST Challenge in round 1 –- pick the single weakest or least justified sub-claim and demand rigorous justification. Do not Accept or Reject on the first round

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From round 2 onwards: if the verifier Challenges, generate the next [PROVER] block (responding to that specific challenge only), then another [VERIFIER] block

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answer":

The prover may revise its answer if a challenge exposes a mistake. Use this exact format for each block: [PROVER] { "answer": "A" | "B" | "C" | "D", "statement": "one sentence explaining your choice", "subclaims": ["atomic claim 1", "atomic claim 2", ...], "reasoning": "step-by-step explanation" 18 } [/PROVER] [VERIFIER] { "verdict": "Accept" | "Reject" |...

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Retroviruses have an RNA genome, not a DNA genome

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Option A is incorrect: direct DNA sequencing is inappropriate for an RNA retrovirus without reverse transcription

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RNA must first be reverse-transcribed into cDNA before sequencing

Option C is incorrect: IgG ELISA detects antibody response (serological), not the virus itself. Verifier — Round 1verdict:CHALLENGE Reasoning:The fundamentals are sound, but sub-claim 2 requires further justification. Modern sequencing platforms (Nanopore, Illumina) can directly sequence RNA without reverse transcription. The prover has not explained why ...

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Direct RNA sequencing exists but is not the standard validated workflow for clinical outbreak diagnostic kit design under current regulatory norms

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cDNA sequencing via reverse transcription is the established, reproducible, and validated method for characterizing RNA virus genomes in diagnostic contexts

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Real-time PCR

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real-time PCR

Option D is the only choice that correctly combines RNA-to-cDNA conversion with a sensitive, quantitative, closed-tube molecular detection method. Verifier — Round 2verdict:ACCEPT Reasoning:The prover now correctly distinguishes between what is technically possible (direct RNA sequencing exists) and what is standard validated clinical practice (cDNA seque...

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Institutional review board (IRB) approvals or equivalent for research with human subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or ...