Related papers: Randomized Communication and Implicit Representati…
Semantic communication, enabled by deep joint source-channel coding (DeepJSCC), is widely expected to inherit the vulnerability of deep learning to adversarial perturbations. This paper challenges this prevailing belief and reveals a…
We provide a counterexample to a recent conjecture that the minimum rank of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a…
We analyze and improve low rank representation (LRR), the state-of-the-art algorithm for subspace segmentation of data. We prove that for the noiseless case, the optimization model of LRR has a unique solution, which is the shape…
Capacity-achieving signaling strategies for the Gaussian wiretap MIMO channel are investigated without the degradedness assumption. In addition to known solutions, a number of new rank-deficient solutions for the optimal transmit covariance…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…
In this paper, we characterize graphs with circular chromatic number less than 3 in terms of certain balancing labellings studied in the context of signed graphs. In fact, we construct a signed graph which is universal for all such…
As NNs permeate various scientific and industrial domains, understanding the universality and reusability of their representations becomes crucial. At their core, these networks create intermediate neural representations, indicated as…
An index coding problem with $n$ messages has symmetric rate $R$ if all $n$ messages can be conveyed at rate $R$. In a recent work, a class of index coding problems for which symmetric rate $\frac{1}{3}$ is achievable was characterised…
A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…
Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is…
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly…
It has been observed that message-passing graph neural networks (GNN) sometimes struggle to maintain a healthy balance between the efficient/scalable modeling of long-range dependencies across nodes while avoiding unintended consequences…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…
We develop lower bounds on communication in the memory hierarchy or between processors for nested bilinear algorithms, such as Strassen's algorithm for matrix multiplication. We build on a previous framework that establishes communication…
We study the problem of randomized Leader Election in synchronous distributed networks with indistinguishable nodes. We consider algorithms that work on networks of arbitrary topology in two settings, depending on whether the size of the…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
Semantic communication is a novel communication paradigm that focuses on the transportation and delivery of the \emph{meaning} of messages. Recent results have verified that a graphical structure provides the most expressive and…
Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P,…
Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable…