相关论文: Sensitivity and Dynamic Distance Oracles via Gener…

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…

We study second order and third order linear differential equations with analytic coefficients under the viewpoint of finding formal solutions and studying their convergence. We address some untouched aspects of Frobenius methods for second…

Graph Neural Networks (GNNs) have achieved remarkable success across various graph-based tasks but remain highly sensitive to distribution shifts. In this work, we focus on a prevalent yet under-explored phenomenon in graph generalization,…

In this paper, we introduce a fast row-stochastic decentralized algorithm, referred to as FRSD, to solve consensus optimization problems over directed communication graphs. The proposed algorithm only utilizes row-stochastic weights,…

Time series anomaly detection is extensively studied in statistics, economics, and computer science. Over the years, numerous methods have been proposed for time series anomaly detection using deep learning-based methods. Many of these…

The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…

We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i)…

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

We give offline algorithms for processing a sequence of $2$ and $3$ edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for $3$-edge and $3$-vertex…

In this article, we propose a new approach, optimize then agree for minimizing a sum $ f = \sum_{i=1}^n f_i(x)$ of convex objective functions over a directed graph. The optimize then agree approach decouples the optimization step and the…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

In the Distance Oracle problem, the goal is to preprocess $n$ vectors $x_1, x_2, \cdots, x_n$ in a $d$-dimensional metric space $(\mathbb{X}^d, \| \cdot \|_l)$ into a cheap data structure, so that given a query vector $q \in \mathbb{X}^d$…

We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test…

Let $G=(V, E)$ be an undirected $n$-vertices $m$-edges graph with non-negative edge weights. In this paper, we present three new algorithms for constructing a $(2k-1)$-stretch distance oracle with $O(n^{1+\frac{1}{k}})$ space. The first…

In many applications, gradient evaluations are inherently approximate, motivating the development of optimization methods that remain reliable under inexact first-order information. A common strategy in this context is adaptive evaluation,…

There has been a growing interest in developing diffusion-based Graph Neural Networks (GNNs), building on the connections between message passing mechanisms in GNNs and physical diffusion processes. However, existing methods suffer from…

Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and insertions. It is one of the most…

Graph neural networks are recognized for their strong performance across various applications, with the backpropagation algorithm playing a central role in the development of most GNN models. However, despite its effectiveness, BP has…

Recent years have seen extensive research on directed graph sparsification. In this work, we initiate the study of fast fully dynamic spectral and cut sparsification algorithms for directed graphs. We introduce a new notion of spectral…