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Geometric Deep Learning

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30 April 2021


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Geometric Deep Learning

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 –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 talk 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.

Bio

Petar Velikovi is a Senior Research Scientist at DeepMind. He holds a PhD in Computer Science from the University of Cambridge (Trinity College), obtained under the supervision of Pietro Liò. His research interests involve devising neural network architectures that operate on nontrivially structured data (such as graphs), and their applications in algorithmic reasoning and computational biology. He has published relevant research in these areas at both machine learning venues (NeurIPS, ICLR, ICML-W) and biomedical venues and journals (Bioinformatics, PLOS One, JCB, PervasiveHealth). In particular, he is the first author of Graph Attention Networks—a popular convolutional layer for graphs—and Deep Graph Infomax—a scalable local/global unsupervised learning pipeline for graphs (featured in ZDNet). Further, his research has been used in substantially improving the travel-time predictions in Google Maps (covered by outlets including the CNBC, Endgadget, VentureBeat, CNET, the Verge and ZDNet).


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