Related papers: Improved Upper Bound on the Network Function Compu…
Neural networks with rectified linear unit activations are essentially multivariate linear splines. As such, one of many ways to measure the "complexity" or "expressivity" of a neural network is to count the number of knots in the spline…
We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of…
Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…
We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
With the development of neural networks based machine learning and their usage in mission critical applications, voices are rising against the \textit{black box} aspect of neural networks as it becomes crucial to understand their limits and…
Tightening performance bounds of ring networks with cyclic dependencies is still an open problem in the literature. In this paper, we tackle such a challenging issue based on Network Calculus. First, we review the conventional timing…
This paper proves an abstract theorem addressing in a unified manner two important problems in function approximation: avoiding curse of dimensionality and estimating the degree of approximation for out-of-sample extension in manifold…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
We consider the multiple unicast problem under network coding over directed acyclic networks with unit capacity edges. There is a set of n source-terminal (s_i - t_i) pairs that wish to communicate at unit rate over this network. The…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
We introduce a new, "worst-case" model for an asynchronous communication network and investigate the simplest (yet central) task in this model, namely the feasibility of end-to-end routing. Motivated by the question of how successful a…
Network topology is critical for efficient parameter synchronization in distributed learning over networks. However, most existing studies do not account for bandwidth limitations in network topology design. In this paper, we propose a…
We study budget constrained network upgradeable problems. We are given an undirected edge weighted graph $G=(V,E)$ where the weight an edge $e \in E$ can be upgraded for a cost $c(e)$. Given a budget $B$ for improvement, the goal is to find…
The algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. This paper investigates the problem of accelerating the convergence of consensus processes by adding links to…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
The present paper considers leveraging network topology information to improve the convergence rate of ADMM for decentralized optimization, where networked nodes work collaboratively to minimize the objective. Such problems can be solved…