Conditional Performance Guarantee for Large Reasoning Models

TL;DR

This paper introduces G-PAC and C-PAC reasoning frameworks that provide group-level probabilistic guarantees for large reasoning models, improving efficiency while maintaining risk control in diverse tasks.

Contribution

It develops novel PAC-style reasoning methods that offer group-conditional guarantees and demonstrate efficiency gains over traditional marginal approaches.

Findings

G-PAC and C-PAC achieve group-conditional risk control.

Both methods maintain performance while reducing computational costs.

Experiments show effectiveness across diverse reasoning benchmarks.

Abstract

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.