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

arXiv: https://arxiv.org/abs/2512.02304 · HTML: https://mlsanity.com/paper/2512.02304/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 50 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 30 of 43)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Deductive Verification of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2306.03872/) (2023)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Small Language Models Need Strong Verifiers to Self-Correct Reasoning](https://mlsanity.com/paper/2404.17140/) (2024)

## Built on by (most cited first, 15 of 15)

- [Learning to Self-Verify Makes Language Models Better Reasoners](https://mlsanity.com/paper/2602.07594/) (2026)
- [V1: Unifying Generation and Self-Verification for Parallel Reasoners](https://mlsanity.com/paper/2603.04304/) (2026)
- [More Convincing, Not More Correct: Self-Play Reward Hacking of Reference-Free LLM Judges](https://mlsanity.com/paper/2607.05904/) (2026)
- [Squeeze Evolve: Unified Multi-Model Orchestration for Verifier-Free Evolution](https://mlsanity.com/paper/2604.07725/) (2026)
- [The Hidden Signal of Verifier Strictness: Controlling and Improving Step-Wise Verification via Selective Latent Steering](https://mlsanity.com/paper/2605.20745/) (2026)
- [The Verifier is the Curriculum: Precision Sets the Return on Search in Code Self-Distillation](https://mlsanity.com/paper/2607.09709/) (2026)
- [LLM-as-a-Judge Scores Are Unreliable Optimization Signals in Closed-Loop Table Recognition](https://mlsanity.com/paper/2607.13347/) (2026)
- [Oracle Gap and Signal Fidelity: A Fixed-Pool Diagnostic for Test-Time Collaboration](https://mlsanity.com/paper/2607.17531/) (2026)
- [Verify, Repair, Repeat, or Stop? Robust Stopping for Noisy Verify-Repair Loops in LLM Agents](https://mlsanity.com/paper/2607.17641/) (2026)
- [Peer-Predictive Self-Training for Language Model Reasoning](https://mlsanity.com/paper/2604.13356/) (2026)
- [Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling](https://mlsanity.com/paper/2606.19354/) (2026)
- [HyperThink: Text-to-Parameter Hypernetworks for Efficient Reasoning](https://mlsanity.com/paper/2610.03039/) (2026)
- [The Same Zero: Why Identical ASR Can Imply Different Guarantees in LLM-Agent Security](https://mlsanity.com/paper/2610.04504/) (2026)
- [Review Rarely Beats the Stronger Model: Separating Verification from Capability Transfer in LLM Pipelines](https://mlsanity.com/paper/2610.15897/) (2026)
- [Verifier-Harness Co-Evolution for Training-Free Self-Improvement on Open-Ended Tasks](https://mlsanity.com/paper/2610.17609/) (2026)

## Abstract (arXiv)

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.