arXiv research

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

Improved model for non-smooth signals with complex spectra.

This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on gra…

The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach requires looking for a good representation that reveals the signal structure, and sol…

Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a generative model. We search and constrain on latent variable space to make the m…

New method uses machine learning to estimate sensitivity without binning.

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

New algorithm solves non-convex, non-differentiable min-max games.

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…

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…

Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed dictionary. Unfortunately, inference in this model involves solving non-smooth op…

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.

MLShrink integrates machine learning with wavelet shrinkage for denoising.

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 propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is $L_1$ regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. $L_1$ regularization impedes the …

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.

The study analyzes convergence rates for sparse pivotal estimators in high-dimensional regression.

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.

This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph signal, defined over some graph (network) structure intrinsic to the dataset. Follo…

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…

LocalKMeans parallelizes Lloyd's algorithm for distributed data.

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.…

In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by many applications in which the local objective function is the sum of smooth but po…

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.

Example of non-smooth isotopy using K3 surfaces.

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…