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Variation in Verification: Understanding Verification Dynamics in Large Language Models

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Systematically studies how problem difficulty, generator capability, and verifier generation capability shape generative (CoT + verdict) verification accuracy across math, knowledge, and NL reasoning, and draws implications for verification-augmented test-time scaling.

Problem

Understanding what factors determine whether LLM generative verifiers correctly accept or reject candidate solutions without reference answers, and how these factors affect verifier-based test-time scaling.

Approach

Decomposes verification performance into TPR and TNR and varies problem difficulty (model-agnostic average pass rate), generator pass rate, and verifier generation capability in a controlled grid of 15 models over 12 benchmarks, finding that difficulty mainly drives TPR, generator strength mainly drives TNR, and verifier capability correlates with accuracy in difficulty-dependent (linear, saturate

Key results

• Verifier TPR increases steadily as problems get easier, while TNR shows no predictable trend with difficulty; 39.1% of verification false negatives on hard problems contain reference-answer mistakes.
• As generator capability increases, TNR drops substantially (e.g., Qwen2.5-72B verifier TNR falls from 0.68 on Llama-3.1-8B solutions to 0.17 on Qwen3-32B solutions in math) while TPR rises only slightly.
• With GPT-4o as fixed verifier, Gemma2-9B's post-verification pass rate nearly matches Gemma2-27B, shrinking the gap from 10.3% to 2.5% (75.7% closed).

Surprising findings

• Verifiers achieve below-random accuracy on hard natural language reasoning problems, and verifier generation capability shows no meaningful relation to accuracy there.
• Strong verifiers (GPT-4o) offer limited advantage over 7B verifiers in regimes where the gap narrows, since both provide minimal verification gain.

Limitations

• Experiments restricted to verifiable problems with objective ground-truth answers, though the authors argue insights should extend to other domains.
• Mostly relies on greedy-decoded, instruction-tuned models; reasoning models evaluated only in a supplementary way.
• Large-scale interpretability analyses depend on LLM-as-judge labels (GPT-4.1-mini).

Experimental setup

Datasets: GSM8K MATH500 OlympiadBench AIME24 AIME25 AMC23 Minerva-Math BBEH Multi-step Arithmetic MMLU-Pro ReClor FOLIO GPQA Diamond

Benchmarks: GSM8K MATH500 OlympiadBench AIME24 AIME25 AMC23 Minerva-Math BBEH Multi-step Arithmetic MMLU-Pro ReClor FOLIO GPQA Diamond

Metrics: true positive rate true negative rate balanced accuracy pass rate verification gain

Baselines: GPT-4o

Builds on: LLM-as-a-judge Math-Verify locally weighted regression

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