Conditional Performance Guarantee for Large Reasoning Models

2026-01-30

AI Summary

This work addresses the high computational cost of chain-of-thought reasoning in large reasoning models and the limitations of existing Probably Approximately Correct (PAC) inference, which offers only marginal risk guarantees and struggles to control conditional coverage. To overcome these challenges, the authors propose the G-PAC inference framework, which achieves group-level conditional risk control for the first time. By partitioning the input space, G-PAC is instantiated as Group PAC (G-PAC) when group structures are known and as Clustered PAC (C-PAC) when they are unknown, leveraging adaptive model switching and input clustering techniques. Experiments demonstrate that the method substantially reduces computational costs across multiple reasoning benchmarks while rigorously ensuring reliable inference performance for each group, thereby surpassing the constraints of traditional marginal PAC guarantees.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• conditional performance guarantee
• large reasoning models
• group-conditional risk control
• computational efficiency
• PAC reasoning

Innovation

• Group-conditional risk control
• PAC reasoning
• Large reasoning models
• Adaptive inference
• Efficiency-accuracy tradeoff