21 citations · 50 across the 10 of their papers we have counts for
10 papers
Neural Networks Efficiently Learn Low-Dimensional Representations with SGD
Alireza Mousavi-Hosseini, Sejun Park, Manuela Girotti +2
We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input is Gaus…
Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation
Manuela Girotti, Tamara Grava, Robert Jenkins +2
We analyze the case of a dense mKdV soliton gas and its large time behaviour in the presence of a single trial soliton. We show that the solution can be expressed in terms of Fredh…
Convergence Analysis and Implicit Regularization of Feedback Alignment for Deep Linear Networks
Manuela Girotti, Ioannis Mitliagkas, Gauthier Gidel
We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rat…
A Study of Condition Numbers for First-Order Optimization
Charles Guille-Escuret, Baptiste Goujaud, Manuela Girotti +1
The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothness and strong convexity. These metrics ar…
Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes
Mattia Cafasso, Tom Claeys, Manuela Girotti
We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in…
Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles
Tom Claeys, Manuela Girotti, Dries Stivigny
We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large.…
Asymptotics of the Tacnode process: a transition between the gap probabilities from the Tacnode to the Airy process
Manuela Girotti
We study the gap probabilities of the single-time Tacnode process. Through steepest descent analysis of a suitable Riemann-Hilbert problem, we show that under appropriate scaling r…
Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach
Manuela Girotti
We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process…
Riemann-Hilbert approach to gap probabilities for the Bessel process
Manuela Girotti
We consider the gap probability for the Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process can be expr…
Time relaxation of a phase-field model with entropy balance
Manuela Girotti
We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations:…