Warped geometric information on the optimisation of Euclidean functions

arXiv:2308.08305v2 Announce Type: replace-cross
Abstract: We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in statistical inference. We use Riemannian geometry notions to redefine the optimisation problem of a function on the Euclidean space to a Riemannian manifold with a warped metric, and then find the function's optimum along this manifold. The warped metric chosen for …

abstract arxiv cs.lg distribution function functions geometry inference information logarithm loss machine optimisation probability space statistical stat.ml tasks type