2 citations · 3 across the 9 of their papers we have counts for
10 papers
Quantifying Uncertainty In Wide Two-Layer Neural Networks: On The Law Of The Limiting Fluctuation Process
Arnaud Descours, Arnaud Guillin, Geoffrey Lacour +3
Uncertainty quantification in neural networks prediction is a main issue for usual applications. Our approach seeks at reducing computation costs by directly evaluating uncertainty…
Uniform-in-time concentration in two-layer neural networks via transportation inequalities
Arnaud Guillin, Boris Nectoux, Paul Stos
We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and t…
Quasi-stationarity of the Dyson Brownian motion with collisions
Arnaud Guillin, Boris Nectoux, Liming Wu
In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of…
Large deviations of the empirical measures of a strong-Feller Markov process inside a subset and quasi-ergodic distribution
Arnaud Guillin, Boris Nectoux, Liming Wu
In this work, we establish, for a strong Feller process, the large deviation principle for the occupation measure conditioned not to exit a given subregion. The rate function vanis…
Long time behavior of killed Feynman-Kac semigroups with singular Schr{ö}dinger potentials
Arnaud Guillin, D I Lu, Boris Nectoux +1
In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general sin…
Central Limit Theorem for Bayesian Neural Network trained with Variational Inference
Arnaud Descours, Tom Huix, Arnaud Guillin +3
In this paper, we rigorously derive Central Limit Theorems (CLT) for Bayesian two-layerneural networks in the infinite-width limit and trained by variational inference on a regress…
Generalized Langevin And Nos{é}-hoover Processes Absorbed At The Boundary Of A Metastable Domain
Arnaud Guillin, D I Lu, Boris Nectoux +1
In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential conver- gence towards the quasi-stationa…
Law of Large Numbers for Bayesian two-layer Neural Network trained with Variational Inference
Arnaud Descours, Tom Huix, Arnaud Guillin +3
We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case. We consider a regression problem with…
Recent advances in the long-time analysis of killed degenerate processes and their particle approximation
Bertrand Cloez, Lucas Journel, Pierre Monmarché +2
We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on th…
Law of large numbers and central limit theorem for wide two-layer neural networks: the mini-batch and noisy case
Arnaud Descours, Arnaud Guillin, Manon Michel +1
In this work, we consider a wide two-layer neural network and study the behavior of its empirical weights under a dynamics set by a stochastic gradient descent along the quadratic…