4 citations · 9 across the 5 of their papers we have counts for
4 papers · 1 filter
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…
Lower large deviations for geometric functionals in sparse, critical and dense regimes
Christian Hirsch, Daniel Willhalm
We prove lower large deviations for geometric functionals in sparse, critical and dense regimes. Our results are tailored for functionals with nonexisting exponential moments, for…
Limit theory of sparse random geometric graphs in high dimensions
Gilles Bonnet, Christian Hirsch, Daniel Rosen +1
We study topological and geometric functionals of -random geometric graphs on the high-dimensional torus in a sparse regime, where the expected number of neighbors decays…
Upper large deviations for power-weighted edge lengths in spatial random networks
Christian Hirsch, Daniel Willhalm
We study the large-volume asymptotics of the sum of power-weighted edge lengths in Poisson-based spatial random networks. In the regime , we provide a s…