Deep Learning approaches such as convolutional and recurrent neural networks have been successfully applied to a broad range of problems within fields such as computer vision and speech recognition. Research on these approaches has mainly focused on data defined on Euclidean spaces, that is, high-dimensional and regular grids. In numerous application domains such as Biology, the Material Sciences, and Physics, however, data is more suitably represented on non-Euclidean spaces. For instance, biomedical networks modeling genes, drugs, and their side-effects can be represented as a multi-relational and irregular graph. My group’s research is concerned with the development of learning techniques for relational data, that is, data that can be represented as graphs and on manifolds. Our work also addresses the problem of learning structure from data where it is missing, combining discrete probabilistic models with continuous gradient-based learning. The talk will also cover some biomedical applications and future research directions.