arXiv research

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

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

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.

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…

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

We investigate the theoretical limits of pipeline parallel learning of deep learning architectures, a distributed setup in which the computation is distributed per layer instead of per example. For smooth convex and non-convex objective functions, we provide matching lower and upper complexity bounds and show that a na…

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

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

Novel method for shape optimization of non-smooth PDEs.

New algorithm for federated learning with non-smooth regularizers.

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

FedProx algorithm improved for non-smooth and heterogeneous data.

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

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic optimization procedures, both in expectation and with high probability, that have opti…

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…

Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions. Unfortunately, minimizing the Wasserstein distance between the data distribution and the gene…

Consistency models accelerate generation with theoretical guarantees.

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

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

Efficient algorithms for large Maxent models improve wildfire probability predictions.

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…

In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, d…

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

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme …

This work improves SGMs' convergence guarantees for semiconvex distributions with discontinuous gradients.

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…

EnCF improves data assimilation for implicit, non-smooth observations.

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

Improved model for non-smooth signals with complex spectra.

Paper uses deep learning to price and hedge options in incomplete markets.

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

New method uses machine learning to estimate sensitivity without binning.

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.

Whereas subriemannian geometry usually deals with smooth horizontal distributions, partially hyperbolic dynamical systems provide many examples of subriemannian geometries defined by non-smooth (namely, Hölder continuous) distributions. These distributions are of great significance for the behavior of the parent dynami…

Quantile Temporal-Difference learning proved convergent with proof.

Improves probability distribution compression with KT algorithm.

Adaptive data fusion boosts efficiency in multi-task optimization.

Paper proves CLT for quantile SGD with constant learning rate.

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

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

The paper develops bounds and regularity for minimal boundaries in non-smooth spaces with Ricci curvature.

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…