2023/11/24 by Lukas Fesser, Melanie Weber, Fesser, Lukas +1 · 3 citations
Computer Science · Engineering · Neuroscience · #Advanced Graph Neural Networks #Brain Tumor Detection and Classification #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Imaging and Analysis
paper · pdf · doi:10.48550/arxiv.2311.14864
openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.