4 citations · 4 across the 6 of their papers we have counts for
8 papers
Affine Geometry of Gaussian ReLU Networks via Conditional Kac-Rice Formulas
Recep Özkan, Christian Hirsch
We study how the affine geometry of finite ReLU networks is created at random initialization and reorganized by supervised training. We call a sign-changing zero of a hidden preact…
Local large deviations for linear-region growth in random piecewise-linear networks
Recep Özkan, Christian Hirsch
We study a random compositional model for the growth of affine regions in deep piecewise-linear networks. The model is generated by i.i.d.\ perturbations of the symmetric height-on…
Stable and Fréchet limit theorem for subgraph functionals in the hyperbolic random geometric graph
Christian Hirsch, Takashi Owada, Ruiting Tong
We study the fluctuations of subgraph counts in hyperbolic random geometric graphs on the -dimensional Poincaré ball in the heterogeneous, heavy-tailed degree regime. In a hyper…
Normal approximation of stabilizing Poisson pair functionals with column-type dependence
Hanna Döring, Adélie Garin, Christian Hirsch +1
In this paper, we study two specific types of -dimensional Poisson functionals: a double-sum type and a sum-log-sum type, both over pairs of Poisson points. On these functionals…
Normal approximation for subgraph counts in age-dependent random connection models
Christian Hirsch, Raphaël Lachièze-Rey, Takashi Owada
We study normal approximation of subgraph counts in a model of spatial scale-free random networks known as the age-dependent random connection model. In the light-tailed regime whe…
Large Deviation Analysis for Canonical Gibbs Measures
Christian Hirsch, Martina Petráková
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We stud…
Functional central limit theorem for topological functionals of Gaussian critical points
Christian Hirsch, Raphaël Lachièze-Rey
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivati…
Large deviations of one-hidden-layer neural networks
Christian Hirsch, Daniel Willhalm
We study large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. We derive a quenched large deviation principle, wh…