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Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
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.
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.
160 pages, ebook
Published May 4, 2021
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Displaying 1 - 2 of 2 reviews
August 17, 2022
A fantastic book that tries to obtain systematization of the field of Deep Learning.
The knowledge in this book will allow you to derive popular deep learning architectures from first principles. And because machine learning is such a fast-paced field where new architectures come out on a daily basis, that knowledge can help you make better connections between new model architectures and the old ones, and that will result in a faster and easier learning process.
The knowledge in this book will allow you to derive popular deep learning architectures from first principles. And because machine learning is such a fast-paced field where new architectures come out on a daily basis, that knowledge can help you make better connections between new model architectures and the old ones, and that will result in a faster and easier learning process.
April 22, 2023
By far my favorite ML-related paper (book?) to come out of the past 5 years. Actually lays out a principled way to design networks, and it does it all with geometric tools. Would especially recommend to those excited by mathematical physics
Displaying 1 - 2 of 2 reviews