Xuan Son Nguyen, ETIS, MIDI.
Abstract: Data lying on matrix manifolds are commonly encountered in various applied areas such as medical imaging, shape analysis, drone classification, image recognition, human behavior analysis. Due to the non-Euclidean nature of these data, traditional optimization algorithms usually fail to obtain good results in the matrix manifold setting. While a number of approaches has been developed to generalize traditional optimization algorithms to this setting, there is still a lack of works that translate the language of differential geometry to basic operations on matrix manifolds so that they can be used in computational building blocks of neural network models on these manifolds just as basic operations on Euclidean spaces are used in deep neural networks. In this talk, I will present an approach for building neural networks on matrix manifolds based on the theory of gyrogroups and gyrovector spaces.