Avoiding unsafe sets when training with Langevin Dynamics
arXiv:2607.07538v1 Announce Type: new Abstract: Training a model with noisy gradient descent can be idealized as overdamped Langevin dynamics on the loss landscape, and a natural safety question is to bound the probability $\nu_t(\mathcal{A}_H) = \mathbb{P}(Q_t \in \mathcal{A}_H)$ that the trajectory lies in a designated failure region $\mathcal{A}_H$. We study this for a smooth, strongly convex loss in $d$ dimensions and a failure region separated from the minimizer by an energy gap. Three boun