arXiv research

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

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

A new algorithm improves both computational efficiency and statistical optimality for robust low-rank matrix and tensor estimation.

We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex optimization. In each time window, we assume the data follow a linear model parameterized …

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

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

Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.

Adaptive data fusion boosts efficiency in multi-task optimization.

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

We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order methods: (1) they allow using two different extrapolation points to evaluate the grad…

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

On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius. The deficit between the diameters of the mani…

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

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

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…

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…

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.

FedProx algorithm improved for non-smooth and heterogeneous data.

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.

Efficient algorithms for large Maxent models improve wildfire probability predictions.

The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3-manifold with non-negative scalar curvature which has zero total mass is isometric to (R^3, delta_{ij}). In this paper, we quantify this statement using spinors and prove that if a complete, asymptotically flat manifold with non-negative…

Paper improves learning efficiency by focusing on effective dimensionality.

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.

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.

Consistency models accelerate generation with theoretical guarantees.

Smooth bundles with rough data maintain Hodge kernel isomorphism.

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

Adaptive NN method improves matrix completion for non-smooth data.

New bounds for online portfolio selection without smoothness assumptions.

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…

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.…

Improved model for non-smooth signals with complex spectra.

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.