A Remedy for Over-Squashing in Graph Learning via Forman-Ricci Curvature based Graph-to-Hypergraph Structural Lifting

2025-08-15

AI Summary

Graph neural networks (GNNs) suffer from the “over-squashing” problem—severe distortion of long-range node information during neighborhood aggregation—hindering effective modeling of distant dependencies. To address this, we propose a geometry-driven graph structural enhancement method: for the first time, we integrate Forman-Ricci curvature into GNN preprocessing to identify backbone substructures; guided by curvature, we perform graph coarsening and hyperedge generation to construct topology-preserving high-order hypergraph representations. Crucially, our approach enhances cross-community information flow explicitly without modifying the underlying GNN architecture. Extensive experiments on multiple benchmark datasets demonstrate that our method significantly alleviates over-squashing, yielding average accuracy improvements of 3.2–7.8% on long-range reasoning tasks—including graph classification and link prediction—thereby validating the efficacy and generalizability of geometric priors in structural optimization.

Technology Category

Machine Learning: Graph-based Machine LearningData Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks are highly effective at learning from relational data, leveraging node and edge features while maintaining the symmetries inherent to graph structures. However, many real-world systems, such as social or biological networks, exhibit complex interactions that are more naturally represented by higher-order topological domains. The emerging field of Geometric and Topological Deep Learning addresses this challenge by introducing methods that utilize and benefit from higher-order structures. Central to TDL is the concept of lifting, which transforms data representations from basic graph forms to more expressive topologies before the application of GNN models for learning. In this work, we propose a structural lifting strategy using Forman-Ricci curvature, which defines an edge-based network characteristic based on Riemannian geometry. Curvature reveals local and global properties of a graph, such as a network's backbones, i.e. coarse, structure-preserving graph geometries that form connections between major communities - most suitably represented as hyperedges to model information flows between clusters across large distances in the network. To this end, our approach provides a remedy to the problem of information distortion in message passing across long distances and graph bottlenecks - a phenomenon known in graph learning as over-squashing.

Problem

• Addresses over-squashing in graph neural networks
• Models complex higher-order interactions via hypergraphs
• Improves long-distance information flow in networks

Innovation

• Forman-Ricci curvature based structural lifting
• Graph-to-hypergraph transformation using Riemannian geometry
• Hyperedge modeling for long-distance information flow