Complex Problem Solving in Large Language Models: A Statistical Control Survey and Diagnostic Framework

2026-09-17

AI Summary

本文通过构建一个统计控制框架解决大型语言模型在复杂问题解决中的错误放大等问题，方法包括明确状态表示、转换结构等五个组件。

Abstract

Complex problem solving (CPS) with large language models (LLMs) is often framed as a matter of stronger reasoning or longer generation. Yet early-step error amplification, prompt brittleness, and failures to revise incorrect commitments are difficult to explain by missing knowledge or expressive capacity alone. This survey interprets CPS as a sequential estimation-and-decision problem over a latent solution state. A controller maintains a belief about an unobserved solution trajectory, updates it as noisy intermediate evidence arrives, and decides whether to commit, verify, branch, roll back, or abstain to minimize expected loss. Reasoning supplies candidate transitions and interpretations, whereas process control shapes and evaluates those proposals and regulates subsequent transitions and observations. Within this framework, we organize existing methods around five components: explicit state representation, transition structuring, validation and constraint enforcement, search and rollback, and uncertainty management. We also interpret evaluation metrics according to the statistical quantities they estimate. The framework further yields a diagnostic hypothesis: interventions should be most effective when they target the error or uncertainty component implicated by an observed failure. We distinguish systematic, stochastic, and irreducible error together with epistemic and aleatoric uncertainty, and call this alignment problem-control fit and its failure control mismatch. For example, additional sampling may reduce sampling variability while leaving a shared systematic error unchanged. This perspective clarifies what current methods estimate and control, what remains uncontrolled, and why reliable validation, targeted recovery, calibrated uncertainty, and matched-budget evaluation are central open problems.

Problem

• Complex Problem Solving
• Large Language Models
• Error Amplification
• Prompt Brittleness
• Uncertainty Management

Innovation

• sequential estimation-and-decision problem
• latent solution state
• process control
• uncertainty management
• control mismatch