23 citations · 65 across the 9 of their papers we have counts for
9 papers
Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations
Giuseppe Gaeta, Roman Kozlov, Francesco Spadaro
We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochas…
Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances
Berfin Şimşek, François Ged, Arthur Jacot +4
We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with layers of minimal wi…
Kernel Alignment Risk Estimator: Risk Prediction from Training Data
Arthur Jacot, Berfin Şimşek, Francesco Spadaro +2
We study the risk (i.e. generalization error) of Kernel Ridge Regression (KRR) for a kernel with ridge and i.i.d. observations. For this, we introduce two objects: the Si…
On the construction of discrete fermions in the FK-Ising model
Francesco Spadaro
We consider many-point correlation functions of discrete fermions in the two-dimensional FK-Ising model and show that, despite not being commuting observable, they can be realized…
Symmetry classification of scalar Ito equations with multiplicative noise
Giuseppe Gaeta, Francesco Spadaro
We provide a symmetry classification of scalar stochastic equations with multiplicative noise. These equations can be integrated by means of the Kozlov procedure, by passing to sym…
Implicit Regularization of Random Feature Models
Arthur Jacot, Berfin Şimşek, Francesco Spadaro +2
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF m…
Recent advances in symmetry of stochastic differential equations
Giuseppe Gaeta, Claudia Lunini, Francesco Spadaro
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete o…
Random Lie-point symmetries of stochastic differential equations
Giuseppe Gaeta, Francesco Spadaro
We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic dif…
A countable number of homoclinic loops as an ω-limit set for a planar vector field
Francesco Spadaro
We construct an example of a smooth, non analytic planar vector field with an ω-limit set consisting of a countable number of homoclinic loops.