Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
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- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges M.M. Bronstein, J. Bruna, T. Cohen, P. VeliÄkoviÄ 2021 š« NA reading citation Print:: ā Zotero Link:: NA PDF:: NA Files:: arXiv.org Snapshot; Bronstein et al_2021_Geometric Deep Learning.pdf
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> [!Excerpt] Abstract
> Abstract
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 ā such as computer vision, playing Go, or protein folding ā 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 āgeometric unificationā endeavour, in the spirit of Felix Kleinās 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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