Beyond Words: A Mathematical Framework for Interpreting Large Language Models
This provides a formal tool for researchers and practitioners to advance safe and reliable generative AI in domains like healthcare and software engineering, though it is incremental as it offers a framework rather than a definitive solution.
The authors tackled the lack of a mathematical framework for systematically describing, comparing, and improving large language models (LLMs) by proposing Hex, a framework that clarifies key concepts like hallucinations and chain-of-thought reasoning, and establishes conditions for equivalence between chain-of-thought reasoning and prompting.
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.