18 citations · 34 across the 20 of their papers we have counts for
4 papers · 1 filter
The probabilistic method in real singularity theory
Antonio Lerario, Michele Stecconi
We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e. with total Betti number of the maximal possible orde…
How regularization affects the geometry of loss functions
Nathaniel Bottman, Y. Cooper, Antonio Lerario
What neural networks learn depends fundamentally on the geometry of the underlying loss function. We study how different regularizers affect the geometry of this function. One of t…
A proof of the Hamiltonian Thom Isotopy Lemma
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
In this note we present a complete proof of the fact that all the submanifolds of a one parameter family of compact symplectic submanifolds inside a compact symplectic manifold are…
What is the probability that a random symmetric tensor is close to rank-one?
Alberto Cazzaniga, Antonio Lerario, Andrea Rosana
We address the general problem of estimating the probability that a real symmetric tensor is close to rank-one tensors. Using Weyl's tube formula, we turn this question into a diff…