Large reasoning models have shown strong performance through extended chain-of-thought reasoning, yet their computational cost remains significant. Probably approximately correct (PAC) reasoning provides statistical guarantees for efficient reasoning by adaptively switching between thinking and non-thinking models, but the guarantee holds only in the marginal case and does not provide exact conditional coverage. We propose G-PAC reasoning, a practical framework that provides PAC-style guarantees at the group level by partitioning the input space. We develop two instantiations: Group PAC (G-PAC) reasoning for known group structures and Clustered PAC (C-PAC) reasoning for unknown groupings. We prove that both G-PAC and C-PAC achieve group-conditional risk control, and that grouping can strictly improve efficiency over marginal PAC reasoning in heterogeneous settings. Our experiments on diverse reasoning benchmarks demonstrate that G-PAC and C-PAC successfully achieve group-conditional risk control while maintaining substantial computational savings.

翻译：大型推理模型通过扩展的思维链推理展现出强大的性能，但其计算成本仍然高昂。近似正确（PAC）推理通过自适应地在思考模型与非思考模型之间切换，为高效推理提供了统计保证，但该保证仅在边际情况下成立，无法提供精确的条件覆盖。我们提出G-PAC推理，一种通过在输入空间划分组别来实现组级别PAC式保证的实用框架。我们开发了两种具体实现：针对已知组结构的组PAC（G-PAC）推理，以及针对未知分组的聚类PAC（C-PAC）推理。我们证明G-PAC与C-PAC均能实现组条件风险控制，并且在异质场景下分组策略能严格提升相对于边际PAC推理的效率。我们在多样化推理基准上的实验表明，G-PAC与C-PAC在保持显著计算节约的同时，成功实现了组条件风险控制。