Large language models (LLMs) are powerful AI tools that can generate and
comprehend natural language text and other complex information. However, the
field lacks a mathematical framework to systematically describe, compare and
improve LLMs. We propose Hex a framework that clarifies key terms and concepts
in LLM research, such as hallucinations, alignment, self-verification and
chain-of-thought reasoning. The Hex framework offers a precise and consistent
way to characterize LLMs, identify their strengths and weaknesses, and
integrate new findings. Using Hex, we differentiate chain-of-thought reasoning
from chain-of-thought prompting and establish the conditions under which they
are equivalent. This distinction clarifies the basic assumptions behind
chain-of-thought prompting and its implications for methods that use it, such
as self-verification and prompt programming.
Our goal is to provide a formal framework for LLMs that can help both
researchers and practitioners explore new possibilities for generative AI. We
do not claim to have a definitive solution, but rather a tool for opening up
new research avenues. We argue that our formal definitions and results are
crucial for advancing the discussion on how to build generative AI systems that
are safe, reliable, fair and robust, especially in domains like healthcare and
software engineering.

大语言模型领域缺乏描述、比较和改进的数学框架，因此我们提出了 Hex 框架，该框架可以清晰地描述大语言模型研究中的关键术语和概念，如幻觉、对齐、自我验证和思考链。该框架为表征大语言模型、识别其优势和劣势以及整合新发现提供了精确和一致的方法。我们利用 Hex 将思考链推理与思考链提示区分开，并确定了它们等价的条件。这一区分澄清了思考链提示背后的基本假设及其对使用它的方法（如自我验证和提示编程）的影响。我们的目标是为大语言模型提供形式化框架，以帮助研究人员和从业者探索生成型人工智能的新可能性。我们并不声称拥有终极解决方案，而是提供了一个开启新研究方向的工具。我们认为，我们的形式定义和结果对于推动如何构建安全、可靠、公正和健壮的生成型人工智能系统的讨论至关重要，尤其是在医疗保健和软件工程等领域。