# Rewiring Networks for Graph Neural Network Training Using Discrete Geometry

arXiv: https://arxiv.org/abs/2207.08026 · HTML: https://mlsanity.com/paper/2207.08026/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 16 Jul 2022.

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

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Geometric Sampling of Networks](https://mlsanity.com/paper/2010.15221/) (2020)
- [Curved Markov Chain Monte Carlo for Network Learning](https://mlsanity.com/paper/2110.03413/) (2021)

## Built on by (most cited first, 14 of 14)

- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)
- [Probabilistically Rewired Message-Passing Neural Networks](https://mlsanity.com/paper/2310.02156/) (2023)
- [Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching](https://mlsanity.com/paper/2312.16560/) (2023)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [Joint Graph Rewiring and Feature Denoising via Spectral Resonance](https://mlsanity.com/paper/2408.07191/) (2024)
- [The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisited](https://mlsanity.com/paper/2407.09381/) (2024)
- [Content Augmented Graph Neural Networks](https://mlsanity.com/paper/2311.12741/) (2023)
- [Deep Learning as Ricci Flow](https://mlsanity.com/paper/2404.14265/) (2024)
- [Causally-guided Regularization of Graph Attention Improves Generalizability](https://mlsanity.com/paper/2210.10946/) (2022)
- [Foundations and Frontiers of Graph Learning Theory](https://mlsanity.com/paper/2407.03125/) (2024)
- [Towards Precise Prediction Uncertainty in GNNs: Refining GNNs with Topology-grouping Strategy](https://mlsanity.com/paper/2412.14223/) (2024)
- [Structural Invariance Matters: Rethinking Graph Rewiring through Graph Metrics](https://mlsanity.com/paper/2510.20556/) (2025)
- [Pair-Centric Graph Rewiring for Over-Squashing via Optimal Transport-Guided Communication Alignment](https://mlsanity.com/paper/2608.10619/) (2026)

## Abstract (arXiv)

Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks. It is an important problem that is known to significantly impact the training of graph neural networks (GNNs), as the receptive field of a node grows exponentially. To mitigate this problem, a preprocessing procedure known as rewiring is often applied to the input network. In this paper, we investigate the use of discrete analogues of classical geometric notions of curvature to model information flow on networks and rewire them. We show that these classical notions achieve state-of-the-art performance in GNN training accuracy on a variety of real-world network datasets. Moreover, compared to the current state-of-the-art, these classical notions exhibit a clear advantage in computational runtime by several orders of magnitude.