Graph Neural Networks built on the message-passing paradigm exchange information along a graph's edges, effectively learning from relational data while preserving structural symmetries. However, many real-world systems, such as social or biological networks, exhibit complex interactions better represented by higher-order topological domains. Geometric and Topological Deep Learning addresses this by leveraging such structures. Central to this field is the concept of lifting, which transforms data representations from basic graph forms to more expressive topologies before the application of graph models for learning.

In this work, we propose a structural lifting strategy based on Forman–Ricci curvature, an edge-based characteristic rooted in Riemannian geometry. Curvature reveals local and global graph properties, identifying network backbones, i.e., coarse, structure-preserving geometries connecting major communities. These backbones are most suitably represented as hyperedges, modeling information flow between distant clusters. Our approach assigns a curvature-based metric to each edge in an input graph and performs a structural lifting that maps this graph into a hypergraph representation, treating identified backbones as hyperedges and virtually shortening distances between relevant nodes for subsequent graph classification. Our approach thus offers a remedy to information distortion in message passing across long distances and graph bottlenecks, a phenomenon known as over-squashing.

We evaluate our method on multiple well-known graph learning benchmarks, including a large molecular property prediction dataset, e.g., NCI109 and OGBG-MolHIV. Using standard graph network models such as GCN and GAT, the lifted datasets consistently improve performance in 75% of test cases compared to non-lifted baselines. Notably, higher-order hypergraph models such as EDGNN and AllSetTransformer also benefit, showing improved performance in 80% of test cases when paired with our lifting step.