Summary of Is Uniform Expressivity Too Restrictive? Towards Efficient Expressivity Of Graph Neural Networks, by Sammy Khalife et al.
Is uniform expressivity too restrictive? Towards efficient expressivity of graph neural networks
by Sammy Khalife, Josué Tonelli-Cueto
First submitted to arxiv on: 2 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Complexity (cs.CC); Logic in Computer Science (cs.LO)
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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 proves that Graph Neural Networks (GNNs) with Pfaffian activation functions, including sigmoid and tanh, cannot uniformly express GC2 queries without relying on input graph size. This limitation answers a question posed by Grohe (2021). While uniform expressivity is not possible, many GNNs can still efficiently express GC2 queries with logarithmic parameters dependent on the maximal degree of input graphs. A specific activation function choice enables a log-log dependency on degree, making it suitable for practical applications. Experiments confirm theoretical estimates. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies Graph Neural Networks (GNNs) and their ability to process data from large graphs. The authors show that some types of GNNs can’t handle certain kinds of queries without getting bigger as the graph gets larger. This is a problem because it means these networks would need to be adjusted each time they’re used with a new, larger graph. The researchers also find that other GNNs can still do well even if they don’t have this special ability, and they show how these networks might work in real-world situations. |
Keywords
» Artificial intelligence » Sigmoid » Tanh
