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Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification

ICML 2025 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Shows that simply scaling a minimalist sampling-based search (random sampling plus Gemini self-verification with rewriting and pairwise tie-breaking) lets Gemini v1.5 Pro surpass o1-Preview on AIME, MATH, and LiveBench, and introduces a verification benchmark exposing weak out-of-box verification of frontier models.

Problem

Test-time compute scaling via sampling-based search depends on selecting the best candidate without ground-truth verifiers; it is unclear how performance scales with number of samples and verification effort, and how well models can self-verify.

Approach

Scale a minimalist sampling-based search with random sampling and LM self-verification (rewriting responses as theorem-lemma-proof, plus pairwise comparison tie-breaks), and identify implicit scaling: larger candidate pools improve verification accuracy on ambiguous questions.

Key results

• Gemini v1.5 Pro with Verification@200 reaches 8/15 on AIME 2024 and 135/200 on LiveBench Math, versus 1/15 and 104/200 for Pass@1 and 4/15 and 118/200 for Consistency@200; o1-Preview scores 7/15 on AIME in the table.
• Tie-breaking comparisons raise Verification@200 on MATH from 457/500 to 467/500 and LiveBench Reasoning from 94/140 to 97/140.
• On a verification benchmark, GPT-4o and Claude 3.5 Sonnet perform only marginally better than random guessing on comparison tasks, while o1-preview fails to identify 20-30% of wrong responses.

Measured effects reported in the paper

Surprising findings

• Consistency@k saturates on AIME (Consistency@50 equals Consistency@10,000) while Verification@k keeps improving with power-law scaling.
• Frontier models including GPT-4o and Claude 3.5 Sonnet perform near random on the verification benchmark, and Consistency@5 often underperforms single-shot inference.

Limitations

• Each AIME result is a single run due to expense (about $200-650 per question), and the Olympiad LiveBench task shows no gain from verification.
• Verification relies on a closed Gemini model and LM-based answer scoring, with small benchmark sizes (e.g., 15 AIME questions).
• Prompts were explored only in a limited way and not optimized.

Experimental setup

Datasets: Berkeley MATH PRM800K AIME 2024 LiveBench MATH training split AIME 2023

Benchmarks: AIME 2024 Berkeley MATH LiveBench Math LiveBench Reasoning verification benchmark

Metrics: accuracy Pass@k Consistency@k Verification@k false positive rate false negative rate

Baselines: Consistency@200 Pass@1 o1-Preview Gemini v1.5 Flash GPT-4o Claude 3.5 Sonnet Gemini 2.0 Flash

Builds on: self-consistency chain-of-thought

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• Test-Time Scaling in the Wild: Why Exploitation, Not Exploration, Is the Bottleneck (NeurIPS 2026 · similarity 0.91)
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