CureLLM Boosts Graph Understanding with Edge-Aware Curvature Modeling

State-of-the-art graph-aware large language models (LLMs) typically align node representations from graph and textual views, but ignore edge-level structures. In a new paper, researchers from an undisclosed institution (authors include Zhenghong Lin, Zhibin Shi, et al.) conduct a rigorous theoretical analysis showing that this node-only alignment leads to suboptimal information propagation. Specifically, they prove for the first time that neglecting edge information causes negatively curved edges to create bottlenecks, inducing an over-squashing phenomenon between graph and textual views. This theoretical gap motivates their proposed framework, CureLLM (Curvature-enhanced Graph Representations for Large Language Models).

CureLLM injects edge signals into LLMs via two key innovations. First, it introduces a training-free textual prompt mechanism that generates outputs based on edge-aware prompts without requiring learnable parameters. Second, it employs a novel curvature-aware graph representation learning technique that restricts message passing between text and graph representations to only edges with positive curvature, effectively avoiding bottlenecks. The researchers evaluated CureLLM against 20 different methods on 11 real-world datasets across multiple domains, demonstrating consistent superiority in graph understanding tasks. This work provides both a theoretical foundation and a practical solution for integrating edge-level structure into LLM-based graph analysis.