Understanding Reasoning in Chain-of-Thought from the Hopfieldian View

TL;DR

This work reframes Chain-of-Thought reasoning in large language models through a Hopfieldian cognition lens, linking prompts (stimuli) to neural populations and low-dimensional representation spaces. It introduces the Representation-of-Thought (RoT) framework to enhance robustness and interpretability by manipulating representation-space directions, and provides a concrete method for localizing reasoning errors within these spaces. Across arithmetic, commonsense, and symbolic tasks, RoT demonstrates improved robustness and more controllable reasoning compared to standard CoT and base prompting, with detailed ablations illustrating the roles of sample selection, layer choice, and prompt design. Overall, the paper offers a principled, cognitive-science-informed pathway to diagnose and strengthen CoT reasoning in zero-shot and few-shot settings, with practical implications for more reliable reasoning in LLM-based systems.

Abstract

Large Language Models have demonstrated remarkable abilities across various tasks, with Chain-of-Thought (CoT) prompting emerging as a key technique to enhance reasoning capabilities. However, existing research primarily focuses on improving performance, lacking a comprehensive framework to explain and understand the fundamental factors behind CoT's success. To bridge this gap, we introduce a novel perspective grounded in the Hopfieldian view of cognition in cognitive neuroscience. We establish a connection between CoT reasoning and key cognitive elements such as stimuli, actions, neural populations, and representation spaces. From our view, we can understand the reasoning process as the movement between these representation spaces. Building on this insight, we develop a method for localizing reasoning errors in the response of CoTs. Moreover, we propose the Representation-of-Thought (RoT) framework, which leverages the robustness of low-dimensional representation spaces to enhance the robustness of the reasoning process in CoTs. Experimental results demonstrate that RoT improves the robustness and interpretability of CoT reasoning while offering fine-grained control over the reasoning process.

Figures (10)

• Figure 1: Illustration of the emergence of cognition in the brain and CoT reasoning from the Hopfieldian view.
• Figure 2: Larger scale
• Figure 3: Numbers of samples.
• Figure 4: Last layer
• Figure 6: A real case of reasoning error localization by using Llama-2-7B-Chat in a zero-shot scenario on GSM8K using Algorithm \ref{['alg:1']}. The green bar indicates that the reasoning snippet is correct, and the red bar means that the reasoning snippet may be wrong. The numbers in the bar are the scores calculated by Algorithm \ref{['alg:1']}.