Handling Over-Smoothing and Over-Squashing in Graph Convolution With Maximization Operation

D Shen, C Qin, Q Zhang, H Zhu… - IEEE Transactions on …, 2024 - ieeexplore.ieee.org
Recent years have witnessed the great success of the applications of graph convolutional
networks (GCNs) in various scenarios. However, due to the challenging over-smoothing and …

Design your own universe: A physics-informed agnostic method for enhancing graph neural networks

D Shi, A Han, L Lin, Y Guo, Z Wang, J Gao - arXiv preprint arXiv …, 2024 - arxiv.org
Physics-informed Graph Neural Networks have achieved remarkable performance in
learning through graph-structured data by mitigating common GNN challenges such as over …

Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges

D Shi, A Han, L Lin, Y Guo, J Gao - arXiv preprint arXiv:2311.07073, 2023 - arxiv.org
Graph-based message-passing neural networks (MPNNs) have achieved remarkable
success in both node and graph-level learning tasks. However, several identified problems …

Effective Structural Encodings via Local Curvature Profiles

L Fesser, M Weber - arXiv preprint arXiv:2311.14864, 2023 - arxiv.org
Structural and Positional Encodings can significantly improve the performance of Graph
Neural Networks in downstream tasks. Recent literature has begun to systematically …

Exploiting Data Geometry in Machine Learning

M Weber - Proceedings of the AAAI Conference on Artificial …, 2024 - ojs.aaai.org
A key challenge in Machine Learning (ML) is the identification of geometric structure in high-
dimensional data. Most algorithms assume that data lives in a high-dimensional vector …

Unitary convolutions for learning on graphs and groups

BT Kiani, L Fesser, M Weber - arXiv preprint arXiv:2410.05499, 2024 - arxiv.org
Data with geometric structure is ubiquitous in machine learning often arising from
fundamental symmetries in a domain, such as permutation-invariance in graphs and …

When Graph Neural Networks Meet Dynamic Mode Decomposition

D Shi, L Lin, A Han, Z Wang, Y Guo, J Gao - arXiv preprint arXiv …, 2024 - arxiv.org
Graph Neural Networks (GNNs) have emerged as fundamental tools for a wide range of
prediction tasks on graph-structured data. Recent studies have drawn analogies between …

Foundations and Frontiers of Graph Learning Theory

Y Huang, M Zhou, M Yang, Z Wang, M Zhang… - arXiv preprint arXiv …, 2024 - arxiv.org
Recent advancements in graph learning have revolutionized the way to understand and
analyze data with complex structures. Notably, Graph Neural Networks (GNNs), ie neural …

Joint Graph Rewiring and Feature Denoising via Spectral Resonance

J Linkerhägner, C Shi, I Dokmanić - arXiv preprint arXiv:2408.07191, 2024 - arxiv.org
Graph neural networks (GNNs) take as input the graph structure and the feature vectors
associated with the nodes. Both contain noisy information about the labels. Here we …

Graph Pooling via Ricci Flow

A Feng, M Weber - arXiv preprint arXiv:2407.04236, 2024 - arxiv.org
Graph Machine Learning often involves the clustering of nodes based on similarity structure
encoded in the graph's topology and the nodes' attributes. On homophilous graphs, the …