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2021 Geometric Deep Learning - Grids, Groups, Graphs, Geodesics, and Gauges

Last updated Aug 29, 2022

# Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges


  • CiteKey:: bronsteinGeometricDeepLearning2021
  • Type:: journalArticle
  • Author:: Michael Bronstein Joan Bruna Taco Cohen Petar Veličković
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  • Journal:: arXiv:2104.13478 [cs, stat]
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  • Year:: 2021
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  • Format:: PDF


The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach – such as computer vision, playing Go, or protein folding – are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a ‘geometric unification’ endeavour, in the spirit of Felix Klein’s Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.

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  • Keywords:: 📥, Geometric Deep Learning, Graphs, Grids
  • Collections:: Geometric DL

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# Imported: 2022-08-29 2:04 pm

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