Seminarium Geometry, Algebra and Physics in Deep Neural Networks (GAPinDNNs)

Abstrakt finns enbart på engelska: Neural ODEs are geometric deep learning models based on the flows generated by vector fields. The ODEs corresponding to these flows describe the dynamics of information propagating through various geometries, and training amounts to learning the vector field that minimizes the loss in some machine learning application. Neural ODEs have been used to construct powerful generative models, in particular using the flow matching training paradigm, that can account for both the geometry and the symmetries of a problem, e.g., to generate 3D protein structures. In this talk I will discuss the NODE framework on manifolds and in particular some open problems that prompt us to revisit the role of geometry in these deep learning models, adding more geometrical structure to the manifolds or even moving beyond the manifold concept itself.