Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Girotti, Manuela"'
Autor:
Mousavi-Hosseini, Alireza, Park, Sejun, Girotti, Manuela, Mitliagkas, Ioannis, Erdogdu, Murat A.
We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a multiple-index model,
Externí odkaz:
http://arxiv.org/abs/2209.14863
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 Fredholm determinants as well as in terms of a Riemann-Hilbert problem. We
Externí odkaz:
http://arxiv.org/abs/2205.02601
We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete dynamics.
Externí odkaz:
http://arxiv.org/abs/2110.10815
Publikováno v:
International Conference on Artificial Intelligence and Statistics. PMLR, 2021. p. 1261-1269
The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothness and strong convexity. These metrics are used to tune the hyperparameters of FOA. We introduce a class of per
Externí odkaz:
http://arxiv.org/abs/2012.05782
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 various random matrix and statistical physics models. We show that the
Externí odkaz:
http://arxiv.org/abs/1902.05595
We analytically study the long time and large space asymptotics of a new broad class of solutions of the KdV equation introduced by Dyachenko, Zakharov, and Zakharov. These solutions are characterized by a Riemann--Hilbert problem which we show arise
Externí odkaz:
http://arxiv.org/abs/1807.00608
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. Their limit distributions can be expressed as Fredholm determinants of
Externí odkaz:
http://arxiv.org/abs/1612.01916
Autor:
Girotti, Manuela
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 regimes the gap probability of the Tacnode process degenerates into a p
Externí odkaz:
http://arxiv.org/abs/1401.5446
Autor:
Girotti, Manuela
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 can be expressed in terms of determinants of Its-Izergin-Korepin-Slav
Externí odkaz:
http://arxiv.org/abs/1309.7015
Autor:
Girotti, Manuela
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 expressed in terms of determinants of integrable kernels \`a la Its-Izergi
Externí odkaz:
http://arxiv.org/abs/1306.5663