7 papers
Born Discrete, Made Smooth: Variational Formulation of Shallow Neural Networks
Matej Benko, Pierre Bousquet, Iwona Chlebicka +1
Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochasti…
Operator splitting algorithm for structured population models on metric spaces
Carolin Lindow, Christian Düll, Piotr Gwiazda +2
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of…
Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations
Matej Benko, Iwona Chlebicka, Jørgen Endal +1
We study the spatially homogeneous granular medium equation \[\partial_tμ=\rm{div}(μ\nabla V)+\rm{div}(μ(\nabla W \ast μ))+Îμ\,,\] within a large and natural class of the con…
Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
MichaÅ Borowski, Pierre Bousquet, Iwona Chlebicka +2
We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_Î…
Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz DÄbiec, Piotr Gwiazda, BÅażej Miasojedow +3
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive rela…
Convergence of projected stochastic approximation algorithm
MichaÅ Borowski, BÅażej Miasojedow
We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the…