Summary of The Role Of Fibration Symmetries in Geometric Deep Learning, by Osvaldo Velarde et al.
The Role of Fibration Symmetries in Geometric Deep Learning
by Osvaldo Velarde, Lucas Parra, Paolo Boldi, Hernan Makse
First submitted to arxiv on: 28 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 Geometric Deep Learning (GDL) is a framework for machine learning techniques that incorporate problem-specific inductive biases like Graph Neural Networks (GNNs). The current formulation of GDL is limited to global symmetries, which are not common in real-world problems. Our research proposes relaxing GDL to allow for local symmetries, specifically fibration symmetries in graphs, to leverage regularities in realistic instances. We demonstrate that GNNs apply the inductive bias of fibration symmetries and derive a tighter upper bound for their expressive power. Additionally, we show that identifying symmetries in networks can collapse network nodes, increasing computational efficiency during inference and training of deep neural networks. Our mathematical extension applies beyond graphs to manifolds, bundles, and grids, enabling the development of models with inductive biases induced by local symmetries, which can lead to better generalization. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine a way to teach machines to learn from patterns in data. Geometric Deep Learning (GDL) is like a framework for doing this. Right now, GDL only works with big patterns that apply everywhere. We want to make it work with smaller patterns that are specific to certain parts of the data. Our research shows how we can do this by looking at local symmetries in graphs and using them to improve machine learning models. This can help machines learn faster and more accurately from complex data sets. |
Keywords
» Artificial intelligence » Deep learning » Generalization » Inference » Machine learning
