• Corpus ID: 233423603

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

@article{Bronstein2021GeometricDL,
  title={Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges},
  author={Michael M. Bronstein and Joan Bruna and Taco Cohen and Petar Velivckovi'c},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.13478}
}

• M. Bronstein, Joan Bruna, +1 author Petar Velivckovi'c
• Published 27 April 2021
• Computer Science
• ArXiv

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.