Conformal Thinking: Risk Control for Reasoning on a Compute Budget

2026-02-03

AI Summary

This work addresses the key challenge of balancing inference accuracy and error risk control under limited computational budgets in large language model reasoning. The authors reformulate the computational budget allocation problem as an adaptive stopping decision task under explicit risk constraints and propose a dynamic termination mechanism based on dual confidence thresholds. By parameterizing a lower threshold to early-exit hopeless samples and integrating a distribution-free risk control method to optimize the stopping policy, the approach ensures rigorous adherence to user-specified risk limits. Furthermore, an efficiency loss metric is introduced to select the optimal exit strategy across multiple criteria. Experimental results demonstrate that the proposed method significantly improves computational efficiency across diverse tasks and models while strictly satisfying prescribed risk upper bounds.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Large language models for search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Reasoning Large Language Models (LLMs) enable test-time scaling, with dataset-level accuracy improving as the token budget increases, motivating adaptive reasoning -- spending tokens when they improve reliability and stopping early when additional computation is unlikely to help. However, setting the token budget, as well as the threshold for adaptive reasoning, is a practical challenge that entails a fundamental risk-accuracy trade-off. We re-frame the budget setting problem as risk control, limiting the error rate while minimizing compute. Our framework introduces an upper threshold that stops reasoning when the model is confident (risking incorrect output) and a novel parametric lower threshold that preemptively stops unsolvable instances (risking premature stoppage). Given a target risk and a validation set, we use distribution-free risk control to optimally specify these stopping mechanisms. For scenarios with multiple budget controlling criteria, we incorporate an efficiency loss to select the most computationally efficient exiting mechanism. Empirical results across diverse reasoning tasks and models demonstrate the effectiveness of our risk control approach, demonstrating computational efficiency gains from the lower threshold and ensemble stopping mechanisms while adhering to the user-specified risk target.

Problem

• risk control
• compute budget
• adaptive reasoning
• token budget
• error rate

Innovation

• risk control
• adaptive reasoning
• compute budget
• conformal prediction
• early stopping