New method for Bayesian optimization without discretization, faster than existing methods.
problem Bayesian optimization with continuous domains and correlated priors.
method Discretization-free Knowledge Gradient method for continuous domains.
result Significantly faster performance compared to existing methods, especially with noisy evaluations.
New method constructs proper affine actions of groups in higher dimensions.
problem Finding proper affine actions of discrete groups in higher-dimensional spaces.
method Higher strip deformations and Margulis invariant for properness.
result Affine actions of convex cocompact groups and virtually free groups are constructed properly.
A new method for approximate inference using Wasserstein gradient flows.
problem Approximate inference for diffusion processes.
method Discretization-free inference method based on Wasserstein gradient flow.
result Performance comparable to state-of-the-art for nonlinear filtering tasks.
Let G=⟨A,B⟩ be a non-elementary two generator subgroup of the isometry group of H2, the hyperbolic plane. If G is discrete and free and geometrically finite, its quotient is a pair of pants and in prior work we produced a formula for the number of essential self intersections (ESIs) of a…
Algorithm determines discrete, free subgroups of SL2 over non-archimedean fields.
problem Identifying discrete, free subgroups of SL2 over non-archimedean fields.
method Ping Pong Lemma applied to Bruhat-Tits tree action.
result Algorithm determines if subgroup is discrete and free of rank two.
Bayesian optimization for expensive integrands achieves optimal performance.
problem Optimizing functions with expensive integrands in noisy conditions.
method Bayesian optimization with discretization-free value of information optimization.
result Achieves optimal performance in noisy and smooth conditions.
Unified framework for sampling from complex densities using PDEs and neural networks.
problem Sampling from complicated probability densities.
method Dynamical measure transport via PDEs and physics-informed neural networks (PINNs).
result Significantly better mode coverage and high accuracy in sampling.
Bayesian optimization learns from derivatives to improve performance.
problem Expensive function evaluations in optimization.
method Derivative-enabled knowledge-gradient (dKG) algorithm.
result dKG reduces the number of evaluations needed for good performance.
Unified analysis of Gaussian Process Thompson Sampling without discretization.
problem Sequential decision-making over continuous action spaces.
method Frequentist regret analysis based on fractional Gaussian process posteriors.
result Unified discretization-free regret bound for various kernel classes.
The paper proposes a method to sample quantum field configurations using neural operators and flows.
problem Sampling lattice field configurations from Boltzmann distributions in quantum field theories.
method Approximating a time-dependent neural operator to map between free and target theories, discretizing to a normalizing flow, and training to diffeomorphism.
result The method can generalize to larger lattice sizes when pre-trained on smaller ones, improving efficiency.
We prove the existence of positive lower bounds on the Cheeger constants of manifolds of the form X/Γ where X is a contractible Riemannian manifold and $Γ<\Isom(X)$ is a discrete subgroup, typically with infinite co-volume. The existence depends on the L2-Betti numbers of Γ, its subgroups and of a uniform latt…
VarNet solves PDEs with deep neural networks using variational loss.
problem Solving partial differential equations (PDEs) efficiently and accurately.
method VarNet uses a novel variational loss function and optimizes space-time samples for training deep neural networks.
result VarNet models are smooth, differentiable, and directly usable for PDE control and optimization.