Related papers: Network Coding Capacity: A Functional Dependence B…
The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth…
We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
The aim of this thesis is to compare the capacity of different models of neural networks. We start by analysing the problem solving capacity of a single perceptron using a simple combinatorial argument. After some observations on the…
Secure network function computation is a critical research direction in network coding, which aims to ensure that the target function is correctly computed at the sink node while preventing the wiretapper from obtaining any information…
Inner and outer bounds are established on the capacity region of two-sender, two-receiver interference channels where one transmitter knows both messages. The transmitter with extra knowledge is referred to as being cognitive. The inner…
An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on…
Connectivity and layout of underlying networks largely determine the behavior of many environments. For example, transportation networks determine the flow of traffic in cities, or maps determine the difficulty and flow in games. Designing…
We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the…
A large amount of research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of isolated solutions.Though several concrete upper bounds…
Term Coding asks: given a finite system of term identities $\Gamma$ in $v$ variables, how large can its solution set be on an $n$--element alphabet, when we are free to choose the interpretations of the function symbols? This turns familiar…
We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…
Recent algorithmic developments have enabled computers to automatically determine and prove the capacity regions of small hypergraph networks under network coding. A structural theory relating network coding problems of different sizes is…
Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning.…
Recently, it has been shown that the max flow capacity can be achieved in a multicast network using network coding. In this paper, we propose and analyze a more realistic model for wireless random networks. We prove that the capacity of…
A sum-network is an instance of a network coding problem over a directed acyclic network in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a…
A capacity bounded grammar is a grammar whose derivations are restricted by assigning a bound to the number of every nonterminal symbol in the sentential forms. In the paper the generative power and closure properties of capacity bounded…