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We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…
In this paper, we present a detailed convergence analysis of a recently developed approximate Newton-type fully distributed optimization method for smooth, strongly convex local loss functions, called Network-GIANT, which has been…
We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable…
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
We analyse the asymptotic behaviour of random instances of the Maximum Set Packing (MSP) optimization problem, also known as Maximum Matching or Maximum Strong Independent Set on Hypergraphs. We give an analytical prediction of the MSPs…
In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimum cut. Our algorithm can compute $\lambda$ exactly in…
We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…
We investigate the maximum-entropy model $\mathcal{B}_{n,m,p}$ for random $n$-vertex, $m$-edge multi-hypergraphs with expected edge size $pn$. We show that the expected size of the minimization of $\mathcal{B}_{n,m,p}$, i.e., the number of…
A common approach for compressing NLP networks is to encode the embedding layer as a matrix $A\in\mathbb{R}^{n\times d}$, compute its rank-$j$ approximation $A_j$ via SVD, and then factor $A_j$ into a pair of matrices that correspond to…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\mu$, admits a density over $\mathbb{R}^d$. For a semi-concave cost function…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
In their breakthrough ICALP'15 paper, Bernstein and Stein presented an algorithm for maintaining a $(3/2+\epsilon)$-approximate maximum matching in fully dynamic {\em bipartite} graphs with a {\em worst-case} update time of…
Let P be a locally finite disk pattern on the complex plane C whose combinatorics are described by the one-skeleton G of a triangulation of the open topological disk and whose dihedral angles are equal to a function \Theta:E\to [0,\pi/2] on…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…
The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the…
The statistical leverage scores of a matrix $A$ are the squared row-norms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recently-popular…