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

TL;DR

This paper formalizes how chain-of-thought reasoning enhances neural language models' ability to represent complex distributions, aligning their capabilities with those of probabilistic Turing machines.

Contribution

It introduces a probabilistic formalization of CoT reasoning and demonstrates that LMs with CoT can represent the same distributions as probabilistic Turing machines.

Findings

Recurrent and transformer LMs with CoT can represent the same distributions as probabilistic Turing machines.

Formalization bridges the gap between LM computational power and Turing completeness.

Results suggest CoT reasoning extends the representational capacity of neural language models.

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.