Deep learning techniques have achieved impressive performance in computer vision, natural language processing and speech analysis. These tasks focus on data that lie on Euclidean domains, and mathematical tools for these domains, such as convolution, downsampling, multi-scale, and locality, are well-defined and benefit from fast computational hardware like GPUs. However, many essential data and tasks deal with non-Euclidean domains for which deep learning methods were not originally designed. Examples include 3D point clouds and 3D shapes in computer graphics, functional MRI signals on the brain structural connectivity network, the DNA of the gene regulatory network in genomics, drugs design in quantum chemistry, neutrino detection in high energy physics, and knowledge graph for common sense understanding of visual scenes. This major limitation has pushed the research community in recent years to generalize neural networks to arbitrary geometric domains like graphs and manifolds. Fundamental operations such as convolution, coarsening, multi-resolution, causality have been redefined through spectral and spatial approaches. Recent results for these non-Euclidean data analysis problems show promising and exciting new tools for applications in many fields.
The goals of this workshop are to 1) bring together mathematicians, machine learning scientists and domain experts to establish the current state of these emerging techniques, 2) discuss a framework for the analysis of these new deep learning techniques, 3) establish new research directions and applications of these techniques in neuroscience, social science, computer vision, natural language processing, physics, chemistry, and 4) discuss new computer processing architecture beyond GPU adapted to non-Euclidean domains.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.