Related papers: A simplified threshold dynamics algorithm for isot…

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton's method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or…

Weight thresholding is a simple technique that aims at reducing the number of edges in weighted networks that are otherwise too dense for the application of standard graph theoretical methods. We show that the group structure of real…

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

To increase the training speed of distributed learning, recent years have witnessed a significant amount of interest in developing both synchronous and asynchronous distributed stochastic variance-reduced optimization methods. However, all…

We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional diffusion phenomena. The time discretization consists of an…

Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of…

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…

The orthogonality constraints, including the hard and soft ones, have been used to normalize the weight matrices of Deep Neural Network (DNN) models, especially the Convolutional Neural Network (CNN) and Vision Transformer (ViT), to reduce…

The article proposes an algorithm to model the collision between arbitrary ellipsoids in viscous fluid. It is composed of several steps, each improving upon the standard procedure employed in the current literature. First, an efficient…

In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies…

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…

Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by…

We introduce a mesh-type approach for tackling discrete-time, finite-horizon Markov Decision Processes (MDPs) characterized by state and action spaces that are general, encompassing both finite and infinite (yet suitably regular) subsets of…

We study theoretical limits of \emph{descending} phase retrieval algorithms. Utilizing \emph{Random duality theory} (RDT) we develop a generic program that allows statistical characterization of various algorithmic performance metrics.…

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically…