Clustering as Reasoning: A $k$-Means Interpretation of Chain-of-Thought Graph Learning

2026-05-24

AI Summary

Existing chain-of-thought (CoT) approaches on graphs struggle to achieve dynamic interaction and interpretability between semantic content and topological structure due to their decoupled architectures and static graph representations. This work proposes KCoT, a unified framework that reframes graph CoT reasoning as a clustering process, uncovering a mathematical correspondence between Transformer blocks and the k-means algorithm. By introducing semantic-discriminative prompts and a structure-alignment strategy, KCoT enables dynamic and interpretable fusion of semantics and topology during reasoning. Extensive experiments demonstrate that KCoT consistently outperforms state-of-the-art methods across standard graph benchmarks, validating the efficacy of clustering mechanisms as a foundational principle for graph-based CoT reasoning.

Abstract

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as reasoning, offering a $k$-means interpretation of how iterative reasoning operates over graph-structured data. We observe that existing graph CoT methods rely on disjoint architectures and fixed graph representations, limiting step-by-step semantic-topological interaction and interpretability. To overcome this limitation, we propose a unified framework named KCoT that integrates CoT reasoning with graph representation learning. Our key theoretical result reveals a formal mathematical correspondence between a Transformer block and the $k$-means algorithm, allowing reasoning to be interpreted as iterative assignment and update steps. Based on this insight, we introduce a Semantic Discriminating Prompt that explicitly formulates these steps as structured CoT reasoning, together with a structure-grounded alignment strategy to fuse topological priors with evolving thought-conditioned representations. Experiments on standard benchmarks demonstrate consistent improvements over state-of-the-art methods, validating clustering as a principled mechanism for CoT-based graph learning.

Problem

• Chain-of-Thought
• graph learning
• clustering
• reasoning
• interpretability

Innovation

• clustering as reasoning
• k-means interpretation
• Chain-of-Thought
• graph representation learning
• Transformer-k-means correspondence