arXiv research

Study smooth convergence of metric flows from $\mathbb{F}$-limits.

This paper improves convergence guarantees for SGD algorithms in non-convex smooth functions.

We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the Moebius Energy of the smooth knot as the polygons converge to the smooth knot. However, the polygons must converge in a ``nice'' way, and th…

New shuffling methods improve convergence without Lipschitz smoothness.

The article calculates the $\mathbb{F}$-convergence rate for Ricci flows with closed and smooth tangent flows.

Smooth convergence shown for curve diffusion flows.

Smooth DNNs mitigate the curse of dimensionality in uniform convergence for various regression tasks.

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …

OSGM uses online learning to adapt stepsize for faster convergence.

Study revisits AdaGrad convergence with relaxed noise assumptions.

This paper analyzes the convergence of Federated Average under relaxed assumptions.

New method for faster convergence in non-convex optimization with unbounded smoothness.

A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.

New method improves convergence for smooth games.

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

Study analyzes label smoothing in deep learning optimization.

AdaGrad fails to adapt to Hölder-smoothness in composite optimization problems.

Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to …

In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the Extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of $O(1/T)$ (Nemirovski, 2004). In this paper, we show that the last…

FedProx algorithm improved for non-smooth and heterogeneous data.

This work accelerates gradient descent with anytime convergence guarantees.

New bounds for agnostic learning with average smoothness.

Armijo line-search speeds up gradient descent for various functions.

New method improves simulation efficiency in high dimensions.

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to generalize the concept of Lipschitz smoothness condition to the relative smoothn…

Gradient descent with logistic loss can interpolate deep networks with smoothed ReLU activations under certain conditions.

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

The paper examines convergence of currents and forms under smooth diffeomorphisms.

Establishes smooth Ricci flows from convex surfaces in 3D space.

New algorithm for differentially private distributed optimization of smooth, non-convex problems.

Paper proposes an algorithm for sampling from complex mixture distributions without requiring smoothness.

New algorithm tackles nonconvex machine learning problems with adaptive normalization and independent sampling.

The paper provides a uniform convergence bound for smooth calibration error and its relationship with functional gradient.

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze what happens when one blows up the surfaces near a point where…

Study confirms conjecture about Kähler metrics on smooth minimal models.

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…

New convergence guarantees for SGDA and SCO under expected co-coercivity.

Step decay schedules improve convergence in non-convex optimization.

Preserves scalar curvature bounds under weak convergence of 3-manifolds.

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

The paper provides convergence guarantees for multicalibration gradient boosting.

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a p…

Quantifies scalar curvature under $C^0$ convergence, proving a refined version in all dimensions.

The paper studies the convergence of elastic flows of curves into manifolds, proving smooth convergence under certain conditions.

Paper provides GOT convergence guarantees for sub-gamma distributions and dependent samples.

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…

Paper solves a complex equation for smooth domains.

The study proves leafwise flat forms for Gauduchon metrics on Inoue-Bombieri surfaces.