Understanding Chain-of-Thought in LLMs through Information Theory (2411.11984v1)

Abstract: LLMs have shown impressive performance in complex reasoning tasks through Chain-of-Thought (CoT) reasoning, allowing models to break down problems into manageable sub-tasks. However, existing CoT evaluation techniques either require annotated CoT data or fall short in accurately assessing intermediate reasoning steps, leading to high rates of false positives. In this paper, we formalize CoT reasoning in LLMs through an information-theoretic lens. Specifically, our framework quantifies the `information gain' at each reasoning step, enabling the identification of failure modes in LLMs without the need for expensive annotated datasets. We demonstrate the efficacy of our approach through extensive experiments on toy and GSM-8K data, where it significantly outperforms existing outcome-based methods by providing more accurate insights into model performance on individual tasks.

• The paper introduces a formal framework that quantifies information gain at each reasoning step in LLMs.
• It employs a Bayesian network to detect unidentifiable tasks and assess sub-task contributions without annotated data.
• Empirical validation on toy data and GSM-8K shows improved pinpointing of failure points compared to traditional metrics.

An Information-Theoretic Framework for Evaluating Chain-of-Thought in LLMs

The paper "Understanding Chain-of-Thought in LLMs through Information Theory" presents an innovative framework designed to assess the Chain-of-Thought (CoT) reasoning in LLMs using information theory. The approach provides an alternative to existing methodologies, which largely depend on annotated data or evaluate only the final outcomes of reasoning tasks, often leading to inaccuracies and false positives in understanding model performance.

Formalizing Chain-of-Thought Reasoning

The paper acknowledges the significant role of CoT reasoning, which breaks down complex problems into manageable sub-tasks, mirroring cognitive processes. Despite its effectiveness, assessing CoT remains a challenge due to the high cost of annotation and the lack of granularity in existing evaluation metrics. The authors propose a formal framework that quantifies the information gain at each reasoning step, providing insights into the intermediate stages of problem solving that are often overlooked in conventional assessments.

Framework and Methodology

The core contribution of this work is the development of a theoretical framework based on information theory. This framework quantifies the information gain at each reasoning step without relying on annotated step-by-step data. It enables the detection of failure modes in LLMs by identifying sub-tasks that do not contribute meaningful information towards the final answer.

Key Contributions:

1. Identification of Unidentifiable Tasks: The authors introduce the concept of unidentifiability to describe tasks that an LLM cannot infer or perform effectively because these tasks weren't part of its training data. This is formalized through a Bayesian network illustrating how unidentifiable steps lead to zero information gain about the final output once encountered within a reasoning sequence.
2. Information-Theoretic Evaluation: The authors develop a practical algorithm that quantifies information gain, thereby assessing task performance without annotated datasets. This involves calculating the mutual information between intermediate steps and the final output conditioned on previous steps, highlighting sub-tasks that fail to add predictive value.
3. Empirical Validation: The framework is validated using toy data and a subset of the GSM-8K dataset. The results underscore its capability to pinpoint failure points more precisely than traditional baselines like outcome reward modeling and Math-Shepherd, which rely heavily on final accuracy and tend to produce false positives.

Implications and Future Directions

This paper lays the groundwork for a new class of evaluation metrics that could be particularly useful for enhancing the explainability and reliability of LLMs. The ability to identify and rectify specific CoT failures without extensive annotations could streamline the development of more efficient training regimes and improve the robustness of LLMs across different problem domains. Additionally, by providing a more granular understanding of reasoning processes, this work opens avenues for extending CoT capabilities to more complex decision-making tasks.

In future developments, the authors could explore the possibility of integrating in-context learning techniques to further optimize the framework, reducing computational demands and increasing adaptability. Additionally, extending this framework to other types of reasoning beyond arithmetic and logic, such as natural language understanding, could provide a comprehensive toolkit for assessing LLM reasoning capabilities at a fine-grained level.

In conclusion, the paper proposes a significant step forward in understanding and evaluating CoT reasoning in LLMs through an innovative application of information theory, promising to enhance both practical implementations and theoretical understanding of LLMs' intricate reasoning processes.