提出强弱验证协同机制，智能判断何时用低成本自查、何时需人工确认。
When to Trust the Cheap Check: Weak and Strong Verification for Reasoning
- 设计双阈值策略，决定何时依赖快速自检、何时转为人工审查。
- 实验显示最优策略能有效控制误接受与误拒绝率，且无需假设模型或数据分布。
- 适用于需要高可靠性推理的场景，如医疗诊断、金融决策等关键领域。
大语言模型的推理过程日益依赖验证循环。内部采用自一致性或代理奖励等低成本检查（弱验证），外部则依赖用户反馈进行人工审查（强验证）。两者在成本与可靠性上差异显著：强验证可信但耗时，弱验证高效却易出错。本文形式化了弱-强验证策略，定义何时接受或拒绝结果、何时转入强验证。提出衡量错误接受、错误拒绝及强验证频率的指标。在总体层面证明最优策略具有双阈值结构，校准性与锐度决定弱验证价值。基于此，开发了一种在线算法，可在无查询流、模型或弱验证器假设下，严格控制接受与拒绝误差。
原文摘要 · Abstract (English)
Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through weak--strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier.
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