arxiv: 2512.02304 · v2 · submitted 2025-12-02 · 💻 cs.CL

When Does Verification Pay Off? A Closer Look at LLMs as Solution Verifiers

Jack Lu , Ryan Teehan , Jinran Jin , Mengye Ren This is my paper

Pith reviewed 2026-05-17 03:01 UTC · model grok-4.3

classification 💻 cs.CL

keywords LLM verificationmodel familiesreasoning post-trainingverifier gainrejection samplingsolver-verifier systemsbenchmark evaluation

0 comments

The pith

Verification across different model families improves LLM solutions more than self-verification, with gains declining as models grow similar.

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

The paper examines when using LLMs to verify and select among candidate solutions generated by other LLMs leads to better performance. It systematically tests 37 models from various families on 9 diverse benchmarks. A key finding is that verifiers from different families outperform those from the same family or the solver itself. Reasoning post-training changes these dynamics, and some task types respond better to this approach than others. This matters because it shows how to get more reliable outputs from existing models without additional training.

Core claim

Verification across model families is more effective than self-verification or same-family verification, with benefits decreasing as solver and verifier similarity increases. Reasoning post-training weakens self-improvement but strengthens cross-family improvement. Some tasks, particularly mathematical and logical ones, are more amenable to improvement through verification.

What carries the argument

Verifier gain, a metric that predicts performance improvements from test-time verifier-based rejection sampling.

Load-bearing premise

The 37 models and 9 benchmarks capture the general patterns of family and post-training effects that would appear in broader sets of models and tasks.

What would settle it

Testing a new model family or task where cross-family verification no longer shows higher gains than self-verification on held-out examples would challenge the main results.

Figures

Figures reproduced from arXiv: 2512.02304 by Jack Lu, Jinran Jin, Mengye Ren, Ryan Teehan.

**Figure 1.** Figure 1: Average solver accuracy of each model over all datasets. Base model families are suffixed by -Base. Models within each family are ordered in increasing sizes. Chain-of-Thought (CoT) reasoning (Ling et al., 2023), verifying individual proof steps (Yang et al., 2022), and training process reward models for mathematical reasoning (Luo et al., 2025). Finally, Song et al. (2025) investigate the performance impr… view at source ↗

**Figure 2.** Figure 2: Correlation between each verifier’s metrics (rows) and its own solver accuracy for all 21 post-trained models, averaged over all datasets. Each verifier metric is computed over our three verification settings (columns). Page 6 of 26 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Correlation between each verifier’s metrics (rows) and model size for all 21 post-trained models, averaged over all datasets. In each plot, models are separated by family and ordered by increasing size. Each verifier metric is computed over our three verification settings (columns). To better interpret the trends suggested by the accuracy and FPR results, we examine verifier gain in the final row. Verifier… view at source ↗

**Figure 4.** Figure 4: Comparison between theoretical and empirical verifier gains (rows) for each verification setting (columns). Row 1 shows verifier gains computed from Equation 1. Rows 2 and 3 each show the gains from rejection sampling, computed from rejection sampling using verifiers for up to 5 and 9 solver attempts, respectively. 5.2 Is Verifier Gain a Good Predictor for Improvements from Resampling? Our verifier gain m… view at source ↗

**Figure 5.** Figure 5: Correlation between verifier metrics with similarity scores between solver-verifier pairs. Each marker is colored based on the verifier model family. To directly investigate this behavior, we conduct cross-verification experiments using 12 post-trained models (the three smallest models from each of the four families) and compute all verifier metrics for each pair. For intra-family verification, each solv… view at source ↗

**Figure 6.** Figure 6: Changes in verifier metrics of the Qwen2.5-Base and Qwen3-Base models from post-training. 5.5 Which Datasets are Easy to Verify? Thus far, we have examined verifier performance and its contribution to solver accuracy through rejection sampling. We now shift to a task-level perspective and ask: are tasks that are easy to solve also easy to verify? In Figure 7, we recompute the verifier metrics from Secti… view at source ↗

**Figure 7.** Figure 7: Correlation of verifier metrics (rows) with solver accuracies, averaged over solver-verifier pairs that belong to each verification setting (columns). clear shortcut for verifying the product of two matrices without effectively recomputing it for Matrix Multiplication. Among the real-world datasets, GSM8K and AIME involve problems solvable with high-school-level mathematics, whereas MMLU (Social Sciences)… view at source ↗

**Figure 8.** Figure 8: Average ratio of filtered solver outputs for each model over all datasets. Base model families are suffixed by -Base. Models within each family are ordered in increasing size. H F1-Score and Precision Visualization [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗

**Figure 9.** Figure 9: The solver accuracies of 37 models on each dataset. Page 23 of 26 [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗

**Figure 10.** Figure 10: Correlation between each model’s verifier metrics (rows) and its own solver accuracy for all 21 post-trained models, averaged over all datasets. Each verifier metric is computed over three settings (columns): self-verification, intra-family verification, and cross-family verification. We use the same set of post-trained models as the set of solver models. Page 24 of 26 [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗

**Figure 11.** Figure 11: Improvements in solver accuracies of Qwen2.5-Base and Qwen3-Base models from post-training. Page 26 of 26 [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗

read the original abstract

Large language models (LLMs) can act as both problem solvers and solution verifiers, where the latter select high-quality answers from a pool of solver-generated candidates. This raises the question of under what conditions verification pays off in solver-verifier systems. Prior work has conducted only limited studies of the factors influencing verification performance, focusing primarily on self-verification and examining neither the relationship between solver and verifier model families nor the effects of reasoning post-training. To rectify this, we present a systematic study across 37 models spanning multiple families, sizes, and base vs. post-trained variants, evaluated on 9 benchmarks covering logical reasoning, structured puzzles, symbolic computation, mathematics, commonsense, factual recall, and domain knowledge. In order to support our analysis, we introduce and empirically validate verifier gain, a metric that predicts the performance improvements from test-time verifier-based rejection sampling. Our experiments find that 1) verification across model families is more effective than either self-verification or verification within the same family, and more generally that the benefits of verification decrease as the solver and verifier become more similar, 2) reasoning post-training weakens self-improvement abilities but strengthens cross-family improvement, and 3) some tasks are inherently more amenable to improvement through verification, particularly mathematical and logical tasks.

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

Cross-family verification beats self-verification in this sweep, with post-training flipping the self-improvement dynamic, though the patterns rest on a specific set of 37 models and 9 benchmarks.

read the letter

Hi colleague, the main things to know are that verification across model families outperforms self-verification or within-family checks, and that reasoning post-training reduces self-verification gains while increasing cross-family ones. They introduce verifier gain as a metric that predicts improvement from rejection sampling and validate it on held-out data. This comes from running 37 models across families, sizes, and base versus post-trained variants on 9 benchmarks covering logic, math, puzzles, and knowledge tasks. The abstract reports the central patterns directly from these comparisons rather than from any fitted derivation, which keeps the analysis straightforward. What stands out is the scale and the focus on family similarity plus the post-training distinction. Earlier self-verification work did not map these factors systematically, so the new empirical patterns on how similarity affects gains and how post-training changes the picture are the real addition. The validation step for verifier gain turns the observations into something usable for predicting test-time improvements. The soft spot is representativeness. The observed decrease in benefits with greater solver-verifier similarity could be tied to the particular models chosen or to benchmarks that highlight family differences. If the families share correlated pre-training data or capability profiles, or if the task set favors certain effects, the monotonic pattern might not hold for other models or tasks. The abstract does not detail error bars or exact selection criteria, so that would need checking in the full methods. This paper is for researchers working on LLM ensembles or test-time verification for reasoning reliability. A reader looking for practical pairing rules across existing models would find the breakdowns useful. It deserves a serious referee because the design is controlled and the claims are testable with direct measurements. I would recommend sending it to peer review, with reviewers likely pressing on whether the family and post-training effects generalize beyond this sample.

Referee Report

2 major / 3 minor

Summary. The paper presents a systematic empirical study of LLMs acting as solution verifiers in solver-verifier setups. Across 37 models from multiple families and sizes (including base and reasoning-post-trained variants) and 9 benchmarks spanning logical reasoning, math, puzzles, commonsense, and factual tasks, the authors introduce and validate 'verifier gain' as a metric that predicts performance gains from verifier-based rejection sampling. Key results are that cross-family verification outperforms self-verification and within-family verification, with gains decreasing as solver-verifier similarity increases; reasoning post-training reduces self-improvement but boosts cross-family gains; and verification benefits are larger on mathematical and logical tasks.

Significance. If the observed patterns hold, the work offers actionable guidance for designing test-time verification systems by showing that family dissimilarity and post-training status are important modulators of verifier utility. The empirical validation of verifier gain on held-out data provides a practical tool for predicting rejection-sampling improvements without exhaustive search. The scale (37 models, 9 benchmarks) and coverage of base vs. post-trained variants lend credibility to the family-similarity and post-training findings within the tested regime.

major comments (2)

[§4.1] §4.1 (Model and benchmark selection): The central claim that verification benefits decrease monotonically with solver-verifier similarity rests on the specific 37 models and 9 benchmarks; without an explicit analysis of pre-training data overlap or capability correlations across families, the observed pattern could partly reflect sample composition rather than a general property.
[§4.3] §4.3 (Verifier gain validation): The predictive validity of verifier gain for rejection-sampling improvement is shown on held-out data, but the manuscript does not report whether the held-out splits preserve benchmark diversity or control for task difficulty, which is load-bearing for the claim that the metric generalizes to new tasks.

minor comments (3)

[Figure 3] Figure 3: axis labels and legend entries for 'cross-family' vs. 'within-family' are too small to read clearly in print; increase font size and add a short caption explaining the similarity metric used.
[Related Work] Related Work section: the discussion of prior self-verification studies (e.g., citations to Huang et al. and others) is brief; add one sentence contrasting the current multi-family design with those earlier single-model setups.
[§5] §5 (Discussion): the limitations paragraph mentions model coverage but does not address whether the 9 benchmarks over-represent reasoning tasks relative to factual recall; a short sentence on this would improve balance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive summary and recommendation for minor revision. We address each major comment below with clarifications and note the revisions we will make to the manuscript.

read point-by-point responses

Referee: [§4.1] §4.1 (Model and benchmark selection): The central claim that verification benefits decrease monotonically with solver-verifier similarity rests on the specific 37 models and 9 benchmarks; without an explicit analysis of pre-training data overlap or capability correlations across families, the observed pattern could partly reflect sample composition rather than a general property.

Authors: We agree that direct measures of pre-training data overlap or capability correlations would provide stronger evidence against sample-composition confounds. However, such analyses are not feasible in the current study because detailed pre-training corpora remain proprietary for the majority of the 37 models. Our selection instead relied on publicly documented family-level distinctions in architecture, training objectives, and data sources (Llama, Mistral, Qwen, Gemma, etc.). The observed monotonic trend holds consistently when we stratify by family size and post-training status, and the within-family versus cross-family gap is larger than would be expected from random composition effects alone. We will revise §4.1 to expand the model-selection justification, add a limitations paragraph acknowledging the absence of overlap metrics, and suggest future work that could use open-weight models with known data mixtures to test this directly. revision: partial
Referee: [§4.3] §4.3 (Verifier gain validation): The predictive validity of verifier gain for rejection-sampling improvement is shown on held-out data, but the manuscript does not report whether the held-out splits preserve benchmark diversity or control for task difficulty, which is load-bearing for the claim that the metric generalizes to new tasks.

Authors: We appreciate this clarification request. The held-out splits were constructed by first partitioning each benchmark into difficulty strata based on baseline solver accuracy, then sampling proportionally from every benchmark category (logical reasoning, math, puzzles, commonsense, factual) to preserve diversity. We will revise §4.3 to document this procedure explicitly, include a table summarizing the number of instances per benchmark and difficulty bin in the held-out set, and report the resulting distribution statistics so readers can assess how well diversity and difficulty were controlled. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical measurements across independent models and benchmarks

full rationale

The paper is a systematic empirical benchmark study measuring verification performance across 37 models (multiple families, sizes, base vs. post-trained) on 9 benchmarks. Verifier gain is introduced as a new metric and validated empirically on held-out data to predict rejection-sampling gains, but this validation is a standard empirical check rather than a fitted input renamed as prediction or any self-referential reduction. Central claims (cross-family superiority, decreasing benefits with similarity, post-training effects) rest on direct experimental observations, not on quantities derived by construction from the target result or self-citations. No self-definitional, uniqueness-imported, or ansatz-smuggled steps exist; the work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claims rest on the assumption that model-family membership and post-training status are well-defined categories that affect verification behavior independently of other variables. No new physical entities or mathematical axioms are introduced; the main added element is the verifier-gain metric itself.

axioms (1)

domain assumption LLM outputs on the chosen benchmarks can be meaningfully scored for correctness by either the solver or a separate verifier model.
Invoked throughout the experimental design to justify using verifier-based rejection sampling.

invented entities (1)

verifier gain independent evidence
purpose: A scalar metric intended to predict performance lift from verifier-based rejection sampling.
Introduced and empirically validated in the paper; independent evidence would be its correlation with actual gains on held-out tasks.

pith-pipeline@v0.9.0 · 5533 in / 1376 out tokens · 33222 ms · 2026-05-17T03:01:40.796352+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 2 internal anchors

[1]

Large Language Monkeys: Scaling Inference Compute with Repeated Sampling

Brown, B., Juravsky, J., Ehrlich, R., Clark, R., Le, Q. V., Ré, C., and Mirhoseini, A. (2024). Large language monkeys: Scaling inference compute with repeated sampling.arXiv preprint arXiv:2407.21787. Chen, J., Ren, J., Chen, X., Yang, C., Sun, R., Yoon, J., and Arık, S. Ö. (2025). Sets: Leveraging self-verification and self-correction for improved test-t...

work page internal anchor Pith review Pith/arXiv arXiv 2024
[2]

Qwen3 Technical Report

Wang, X., Wei, J., Schuurmans, D., Le, Q. V., Chi, E. H., Narang, S., Chowdhery, A., and Zhou, D. (2023). Self-consistency improves chain of thought reasoning in language models. InICLR. Welleck, S., Lu, X., West, P., Brahman, F., Shen, T., Khashabi, D., and Choi, Y. (2023). Generating sequences by learning to self-correct. InICLR. Weng, Y., Zhu, M., Xia,...

work page internal anchor Pith review Pith/arXiv arXiv 2023
[3]

variable_name T

E Additional Details on Datasets E.1 Real-World Datasets Note that for MMLU (STEM) and MMLU (Social Sciences), we concatenate questions from all subjects that belong to the STEM and Social Sciences supercategories in Hendrycks et al. (2021), respectively. E.2 Synthetic Datasets We generate three synthetic datasets, named 3SAT, Matrix Multiplication, and S...

work page 2021
[4]

verifier gain

However, since precision is the expected performance of verifier-based rejection sampling in the limit of infinite sampling and our main metric “verifier gain” is defined in terms of it (Equation 1), precision does not help explain the differences in verifier gains across verification settings itself. I Effect of Post-Training on Solver Performance Figure...

work page 1983