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Geometric Deep Learning


1 February 2018

Geometric Deep Learning

  • Michael Bronstein

As part of the 2017–2018 Fellows’Presentation Series at the Radcliffe Institute for Advanced Study, Michael Bronstein RI’18 discusses the past, present, and potential future of technologies implementing computer vision—a scientific field in which machines are given the remarkable capability to extract and analyze information from digital images with a high degree of understanding.

Geometric Deep Learning on Graphs and Manifolds

The purpose of the proposed tutorial is to introduce the emerging field of geometric deep learning on graphs and manifolds, overview existing solutions and applications for this class of problems, as well as key difficulties and future research directions.

Michael Bronstein · Joan Bruna · arthur szlam · Xavier Bresson · Yann LeCun

Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs

  • Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodolà, Jan Svoboda, Michael M. Bronstein
  • Paper


Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures currently produce state-of-the-art performance on a variety of image analysis tasks such as object detection and recognition. Most of deep learning research has so far focused on dealing with 1D, 2D, or 3D Euclidean-structured data such as acoustic signals, images, or videos. Recently, there has been an increasing interest in geometric deep learning, attempting to generalize deep learning methods to non-Euclidean structured data such as graphs and manifolds, with a variety of applications from the domains of network analysis, computational social science, or computer graphics. In this paper, we propose a unified framework allowing to generalize CNN architectures to non-Euclidean domains (graphs and manifolds) and learn local, stationary, and compositional task-specific features. We show that various non-Euclidean CNN methods previously proposed in the literature can be considered as particular instances of our framework. We test the proposed method on standard tasks from the realms of image-, graph- and 3D shape analysis and show that it consistently outperforms previous approaches.

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