11 papers
Universality of kernels on Riemannian symmetric spaces
Salem Said, Nathaël Da Costa, Franziskus Steinert +1
We investigate universality properties of continuous, positive-definite invariant kernels on Riemannian symmetric spaces, providing a unified harmonic-analytic characterization acr…
A theory of generalised coordinates for stochastic differential equations
Lancelot Da Costa, Nathaël Da Costa, Conor Heins +5
Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some…
Muon is Not That Special: Random or Inverted Spectra Work Just as Well
Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika +6
The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear min…
Closed-Form Last Layer Optimization
Alexandre Galashov, Nathaël Da Costa, Liyuan Xu +2
Neural networks are typically optimized with variants of stochastic gradient descent. Under a squared loss, however, the optimal solution to the linear last layer weights is known…
Rethinking Approximate Gaussian Inference in Classification
Bálint Mucsányi, Nathaël Da Costa, Philipp Hennig
In classification tasks, softmax functions are ubiquitously used as output activations to produce predictive probabilities. Such outputs only capture aleatoric uncertainty. To capt…
Sample Path Regularity of Gaussian Processes from the Covariance Kernel
Nathaël Da Costa, Marvin Pförtner, Lancelot Da Costa +1
Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive unders…