7 papers
Functional Scaling Limits of Interpolated Correlated Random Walks in Hölder Topology
Felix Benning, Ivan Nourdin
We prove functional scaling limits for interpolated random walks whose increments are functions of a stationary Gaussian sequence. In this setting, the classical Dobrushin-Major-Ta…
Measure Theory of Conditionally Independent Random Function Evaluation
Felix Benning
In sequential design strategies, common in geostatistics and Bayesian optimization, the selection of a new observation point of a random function is informed…
A Distributional View of High Dimensional Optimization
Felix Benning
This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical o…
Schoenberg characterization of continuous non-stationary isotropic positive definite kernels
Felix Benning, Max David Schölpple
We characterize the continuous isotropic positive definite kernels on , where isotropy refers to invariance under the orthogonal group but not necessarily stat…
In almost all shallow analytic neural network optimization landscapes, efficient minimizers have strongly convex neighborhoods
Felix Benning, Steffen Dereich
Whether or not a local minimum of a cost function has a strongly convex neighborhood greatly influences the asymptotic convergence rate of optimizers. In this article, we rigorousl…
Random Function Descent
Felix Benning, Leif Döring
Classical worst-case optimization theory neither explains the success of optimization in machine learning, nor does it help with step size selection. In this paper we demonstrate t…