Summary of Bridging Smoothness and Approximation: Theoretical Insights Into Over-smoothing in Graph Neural Networks, by Guangrui Yang et al.
Bridging Smoothness and Approximation: Theoretical Insights into Over-Smoothing in Graph Neural Networks
by Guangrui Yang, Jianfei Li, Ming Li, Han Feng, Ding-Xuan Zhou
First submitted to arxiv on: 1 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Functional Analysis (math.FA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the approximation theory of functions defined on graphs using Graph Convolutional Networks (GCNs). The study builds upon the approximation results derived from the K-functional, establishing a theoretical framework to assess the lower bounds of approximation for target functions. The analysis demonstrates how the high-frequency energy of GCN outputs decays, indicating over-smoothing. A lower bound is established for the approximation of target functions by GCNs, governed by the modulus of smoothness. Numerical experiments confirm the phenomenon of energy decay, supporting theoretical results on exponential decay order. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how to get close approximations of things defined on graphs using special kinds of neural networks called Graph Convolutional Networks (GCNs). They use a technique called K-functional to build upon what’s already known. The researchers show that these GCNs can sometimes make predictions that are too smooth, which is called over-smoothing. They also find a way to calculate how close an approximation will be based on the complexity of what they’re trying to approximate. This helps us understand what GCNs are good at and not so good at. |
Keywords
* Artificial intelligence * Gcn
