Higher-Order Deep Learning: Learning to analyze & generate multi-way data of arbitrary underlying Geometry

Machine learning has become a crucial part of scientific fields and industries that produce a massive amount of data and that are in dire need of scalable tools to make sense of it automatically.

Unfortunately, classical statistical modeling has often become impractical when dealing with datasets consisting of multiple, heterogeneous modalities that possibly have different underlying geometries. The promise of this project is a new paradigm, called higher-order deep learning, which fulfills the current needs of multimodal/multiway machine learning by developing a mathematically principled and unified framework capable of learning to analyze and generate multi-way data of arbitrary geometry with unprecedented accuracy. We will explore some of the most challenging problems in different realms (computer vision and graphics, medical imaging, computational neuroscience, and climate monitoring and earth observation) where such data are used. We strive to achieve a quantitative breakthrough in performance in known, challenging problems and to unleash qualitatively new applications.