Deep Learning and Geometry: advances in signal processing and imaging

This short post features a video and respective slides (PDF format) of a talk by DR. Michael M. Bronstein about the emerging topic of Geometric Deep Learning.

The field of deep learning just does not stop to surprise me in unexpected ways. Dr. Bronstein is a prominent pioneer in Geometric Deep Learning and his research is wonderfully full of good pieces of science & technology at the very edge of state-of-art in computer vision and pattern recognition. It intersects also with advanced mathematics, optimization and control and machine learning (Computational Learning Theory).

One of Dr. Bronstein latest paper on the subject of geometric deep learning is briefly depicted below the video with the respective abstract. The talk also displays an abstract in the Youtube channel of ACM student chapter Munich link, and it is very similar to the one I show below, so I won’t repeat it here for The Information Age. I hope new avenues of thought and imagination within the field of deep learning would open to as much as possible to anyone reading this post and watching Dr. Michael M. Bronstein talk. That is what this blog is about when online, posting to stay and hardly forgotten…

Video Slides: Geometric Deep Learning



Geometric deep learning: going beyond Euclidean data



Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of the social graph. Sensor networks are graph models of distributed interconnected sensors, whose readings are modelled as time-dependent signals on the vertices. In genetics, gene expression data are modeled as signals defined on the regulatory network. In neuroscience, graph models are used to represent anatomical and functional structures of the brain. Modeling data given as points in a high-dimensional Euclidean space using nearest neighbor graphs is an increasingly popular trend in data science, allowing practitioners access to the intrinsic structure of the data. In computer graphics and vision, 3D objects are modeled as Riemannian manifolds (surfaces) endowed with properties such as color texture. Even more complex examples include networks of operators, e.g., functional correspondences or difference operators in a collection of 3D shapes, or orientations of overlapping cameras in multi-view vision (“structure from motion”) problems. The complexity of geometric data and the availability of very large datasets (in the case of social networks, on the scale of billions) suggest the use of machine learning techniques. In particular, deep learning has recently proven to be a powerful tool for problems with large datasets with underlying Euclidean structure. The purpose of this paper is to overview the problems arising in relation to geometric deep learning and present solutions existing today for this class of problems, as well as key difficulties and future research directions.

featured image: ECCV Tutorial on Geometric Deep Learning

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