Riemannian optimisation leverages the geometry of smooth manifolds to reformulate and solve constrained optimisation problems as if they were unconstrained. By utilising techniques such as Riemannian ...

DeepSeek’s latest training research arrives at a moment when the cost of building frontier models is starting to choke off ...

Graph-based manifold learning and diffusion processes provide a powerful framework for extracting intrinsic geometric features from high-dimensional data. By constructing a graph where nodes represent ...

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...