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 $\mathcal{A}_H$.
arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.
arXiv:2608.25279v1 Announce Type: cross Abstract: The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Ca...
Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $γ$-uniformly stable algorithm with loss in $[0,L]$ has...
arXiv:2608.23094v1 Announce Type: new Abstract: One implicit DDIM inversion step is the cheapest probe of whether a pretrained diffusion model encodes local manifold geometry. It is the stationarity...
arXiv:2609.40193v1 Announce Type: new Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
arXiv:2608. 15337v1 Announce Type: cross Abstract: We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain $G$-equation should possess an effective burning velocity in cellular flows.
arXiv:2606. 00970v1 Announce Type: new Abstract: We study risk-neutral control in Markov decision processes with an absorbing catastrophic state.
arXiv:2607. 15702v2 Announce Type: replace-cross Abstract: We develop a non-asymptotic approximation, sampling, and finite-iteration optimization theory for variational physics-informed approximation of uniformly monotone nonlinear multiscale elliptic equations.
We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures.
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
arXiv:2609.06196v1 Announce Type: cross Abstract: We study the computational effort required for global optimization of a smooth, possibly nonconvex objective $\Gamma:\mathbb{R}^d\to\mathbb{R}$. An a...
arXiv:2602. 16966v2 Announce Type: replace-cross Abstract: Scalable methods for networked multi-agent reinforcement learning let each agent plan using only a small neighborhood of the agent graph.