arXiv research

MARINA-P improves non-smooth federated optimization with adaptive stepsizes.

Extends curve theory to non-smooth data with finite curvature and torsion.

AsylADMM improves gossip-based learning for non-smooth objectives.

Survey on preserving curvature bounds for non-smooth Ricci flow.

We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establishing an extension of the classical map of smooth functions to Hamiltonian vector fields to the setting of non-smooth geometry. For mildly sin…

The paper explores various stationarity concepts in non-smooth optimization.

New bounds explain deterministic non-smooth deep nets without large Lipschitz constants.

We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm…

Smoothness analysis of adversarial training reveals $L_\infty$ constraints cause more non-smoothness.

In the framework of Lorentzian warped products, we study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walke…

This work speeds up hyperparameter selection for non-smooth convex models using implicit differentiation.

New algorithms optimize non-smooth, non-convex objectives with improved complexity.

In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration compl…

Positive mass theorem for non-smooth metrics on flat manifolds with corners.

Paper tackles private optimization for non-smooth objectives efficiently.

We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. Our approach is based on smooth approximations of non-smooth space-times by families (or sequences…

Advances smooth over-parameterization for solving non-smooth optimization problems.

New methods improve convergence in non-convex non-smooth learning problems.

Adaptive data fusion boosts efficiency in multi-task optimization.

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics.

Abstracts a theorem for non-smooth maps in infinite dimensions.

New SPS variant improves non-smooth optimization without small gradients.

Stochastic approximation proves asymptotic normality for non-smooth problems.

Bayesian optimization tackles non-smooth tuning problems.

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(ε^{-4/5})$ iteration complexity, breaking the $O(ε^{-1})$ barrier so far present for previous methods. We arrive at a similar rate fo…

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern technique…

Safe-EF improves federated learning for non-smooth, constrained optimization.

We theoretically discuss why deep neural networks (DNNs) performs better than other models in some cases by investigating statistical properties of DNNs for non-smooth functions. While DNNs have empirically shown higher performance than other standard methods, understanding its mechanism is still a challenging problem.…

Modified perturbation method removes non-smoothness in solving Black-Scholes equations.

The study extends curvature bounds to non-smooth spaces and proves stability of mean curvature.

Expanding FCCO to non-smooth weakly-convex problems, improving deep learning performance.

Novel method for shape optimization of non-smooth PDEs.

Injectivity of X-ray transform proven for non-smooth metrics.

Timelike curvature and Brunn-Minkowski inequality linked in non-smooth spacetimes.

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth object…

New sampling algorithm for non-smooth potentials.

New method tackles non-smooth tensor data for better recovery.

Optimal private ERM and SCO with subquadratic gradient complexity.

We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Has…

Study generalizes Möbius energy to non-smooth sets in arbitrary dimensions.

The paper studies moduli spaces of non-smooth metric structures with non-negative Ricci curvature.

Paper proposes ZO-SMD for MERO, achieving optimal convergence rates.

FedProx algorithm improved for non-smooth and heterogeneous data.

New Morse theory for shapes at distances.

Consistency models accelerate generation with theoretical guarantees.

New algorithm for federated learning with non-smooth regularizers.

We prove the existence of non-smooth solutions to fully nonlinear uniformly elliptic equations.

The paper proposes a method to model non-smooth functions using clustering, classification, and Gaussian process modeling.