When to Trust the Cheap Check: Weak and Strong Verification for Reasoning

<p>This paper explores <strong>weak-strong verification policies</strong> for large language models, presenting a framework that balances the affordability of scalable internal checks with the precision of resource-intensive external validation. To address the trade-off between <strong>type-I errors</strong>, <strong>type-II errors</strong>, and <strong>verification frequency</strong>, the authors introduce <strong>Selective Strong Verification (SSV)</strong>, an online calibration algorithm that operates without prior distributional assumptions. Through experiments on <strong>mathematical reasoning</strong> and <strong>sequential puzzle-solving</strong>, the researchers demonstrate that this method effectively maintains target error rates while significantly reducing computational overhead.</p>