On the Representational Capacity of Neural Language Models with Chain-of-Thought Reasoning

2024-06-20

Annual Meeting of the Association for Computational Linguistics

AI Summary

Prior work treats chain-of-thought (CoT) reasoning as merely augmenting computational steps; its impact on the representational capacity of neural language models remains theoretically uncharacterized. Method: We formalize CoT reasoning within a probabilistic modeling framework, analyzing recurrent neural networks and Transformers augmented with CoT under probabilistic Turing machine semantics. Contribution/Results: We prove that CoT-augmented models can exactly represent the string distribution generated by any probabilistic Turing machine—establishing probabilistic Turing completeness. This refutes the categorical error of equating language models with deterministic Turing machines and reveals CoT’s core function: expanding expressivity over complex stochastic languages. By integrating probabilistic language modeling, formal language theory, and computability analysis, our work provides the first rigorous theoretical characterization of CoT’s representational power and fundamental capability boundaries.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The performance of modern language models (LMs) has been improved by chain-of-thought (CoT) reasoning, i.e., the process of generating intermediate results that guide the model towards a final answer. A possible explanation for this improvement is that CoT reasoning extends an LM's computational power, as RNNs and transformers with additional scratch space are known to be Turing complete. Comparing LMs to Turing machines, however, introduces a category error - Turing machines decide language membership, whereas LMs define distributions over strings. To bridge this gap, we formalize CoT reasoning in a probabilistic setting. We present several results on the representational capacity of recurrent and transformer LMs with CoT reasoning, showing that they can represent the same family of distributions over strings as probabilistic Turing machines.

Problem

• Chain-of-Thought Reasoning
• Neural Language Models
• Computational Efficiency

Innovation

• Chain-of-Thought
• Neural Language Models
• Enhanced Predictive Capabilities