no code implementations • 10 Jul 2023 • Arnaud Descours, Tom Huix, Arnaud Guillin, Manon Michel, Éric Moulines, Boris Nectoux
We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case.
no code implementations • 15 Dec 2020 • Tony Lelièvre, Dorian Le Peutrec, Boris Nectoux
We consider the first exit point distribution from a bounded domain $\Omega$ of the stochastic process $(X_t)_{t\ge 0}$ solution to the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t$$ starting from deterministic initial conditions in $\Omega$, under rather general assumptions on $f$ (for instance, $f$ may have several critical points in $\Omega$).
Analysis of PDEs Mathematical Physics Mathematical Physics Probability