The paper tackles gradual domain adaptation with manifold-constrained DRO, showing error bounds across distributions.
problem Gradual domain adaptation challenge with manifold-constrained data distributions.
method Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius.
result Theoretical bounds on classification error across distributions, demonstrating error propagation dynamics.
MAGI-X learns unknown dynamics from data without numerical integration.
problem Difficult to propose ODEs in closed-form for complex systems.
method MAGI-X uses neural networks within a manifold-constrained Gaussian process framework.
result MAGI-X achieves competitive accuracy in fitting and forecasting with reduced computational time.
Accelerates Birkhoff projection for manifold-constrained hyper-connections with high accuracy and speed.
problem Inaccurate and slow Birkhoff projection in mHC implementations.
method Dual formulation, Newton's method, implicit differentiation, warp-level CUDA kernel.
result Substantial speedups and accuracy improvements in doubly stochastic projections.
Study Lipschitz regularity for manifold-constrained ROF model on curved surfaces.
problem Lipschitz regularity for manifold-constrained ROF model on curved surfaces.
method Generalization of ROF model, existence and uniqueness of minimizers, regularity results on PDE system.
result Lipschitz regularity of minimizers without convexity requirements.
NucleusDiff models atomic nuclei interactions to prevent separation violations in drug design.
problem Maintaining minimum pairwise distance between atoms to avoid separation violations in drug design.
method Enforces distance constraint between atomic nuclei and manifolds in a diffusion model.
result Reduces separation violations by up to 100.00% and enhances binding affinity by up to 22.16%.
We consider minimizing a nonconvex, smooth function f on a Riemannian manifold M. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manifold). The rate of convergence depends as 1/ε2 o…
Magnetic manifold HMC improves sampling on constrained manifolds.
problem Sampling from distributions restricted to embedded manifolds.
method Introduces magnetic manifold HMC, a generalization of HMC for constrained manifolds.
result Magnetic manifold HMC outperforms canonical manifold-constrained HMC.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the Riemannian manifold of symmetric positive definite (SPD) matrices they belong to. In…
New method predicts spatial events like hurricanes and earthquakes with uncertainty.
problem Quantifying uncertainty in natural hazard predictions.
method Representing spatial point clouds as empirical measures, constraining prediction sets to spatial data manifold, using Wasserstein distance.
result Achieves near-nominal coverage and lower energy/manifold distances compared to baselines.
Novel methods improve Bayesian analysis of chaotic dynamical systems.
problem Bayesian parameter inference and trajectory reconstruction of chaotic systems with sparse and noisy data.
method Pilot MAGI (pMAGI) and Pilot MAGI Sequential Prediction (PMSP) methods.
result pMAGI and PMSP significantly outperform existing methods in accuracy and computational efficiency.
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature …
Statistical methods remain relevant for ODE inverse problems, especially with sparse data.
problem The relevance of statistical methods in the era of deep learning for ODE inverse problems.
method Employed physics-informed neural networks (PINN) and manifold-constrained Gaussian process inference (MAGI) to compare statistical and deep learning approaches.
result Statistically principled methods outperform deep learning models in tasks like parameter inference and trajectory reconstruction.
A new diffusion sampling method combines Krylov subspace and diffusion models for faster and more efficient inverse problems.
problem Efficiently solving large-scale inverse problems in high-performance computing.
method Proposes a novel diffusion sampling strategy that integrates Krylov subspace methods with diffusion models.
result Demonstrates significant speedup (80x faster inference time) and improved reconstruction quality on real-world medical imaging problems.
PLoM learns stochastic solutions to PDEs with limited data.
problem Synthesizing solutions to nonlinear PDEs with scarce data.
method Probabilistic Learning on Manifolds constrained by PDEs.
result Learned stochastic solutions minimize PDE residuals.
The paper refines classical covariance asymptotics using geometric information geometry.
problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.