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

arXiv: https://arxiv.org/abs/2508.11390 · HTML: https://mlsanity.com/paper/2508.11390/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 15 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Understanding Oversquashing in GNNs through the Lens of Effective Resistance](https://mlsanity.com/paper/2302.06835/) (2023)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [Over-Squashing in Graph Neural Networks: A Comprehensive survey](https://mlsanity.com/paper/2308.15568/) (2023)
- [Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows](https://mlsanity.com/paper/1607.08654/) (2016)
- [Graph Rewiring in GNNs to Mitigate Over-Squashing and Over-Smoothing: A Survey](https://mlsanity.com/paper/2411.17429/) (2024)
- [ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain](https://mlsanity.com/paper/2409.05211/) (2024)

## Abstract (arXiv)

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.