Related papers: Wireless Network Simplification : Beyond Diamond N…
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…
We consider the well-studied problem of learning a linear combination of $k$ ReLU activations with respect to a Gaussian distribution on inputs in $d$ dimensions. We give the first polynomial-time algorithm that succeeds whenever $k$ is a…
In this paper, the capacity of wireless channels is characterized based on electromagnetic and antenna theories with only minimal assumptions. We assume the transmitter can generate an arbitrary current distribution inside a spherical…
In this paper, joint designs of data routes and resource allocations are developed for generic half-duplex multicarrier wireless networks in which each subcarrier can be reused by multiple links. Two instances are considered. The first…
The capacity scaling of a Wi-Fi network with fixed transmit power is investigated. The 802.11 MAC appears to impose a hard limit on the area capacity by enforcing single transmissions in overlapped cell coverage areas. However due to the…
The significant progress in constructing graph spanners that are sparse (small number of edges) or light (low total weight) has skipped spanners that are everywhere-sparse (small maximum degree). This disparity is in line with other network…
We prove the following results regarding the linear solvability of networks over various alphabets. For any network, the following are equivalent: (i) vector linear solvability over some finite field, (ii) scalar linear solvability over…
In recent years, LEO satellite constellations have become envisioned as a core component of the next-generation wireless communication networks. The successive establishment of mega satellite constellations has triggered further demands for…
In Francis and Steel (2015), it was shown that there exists non-trivial networks on $4$ leaves upon which the distance metric affords a metric on a tree which is not the base tree of the network. In this paper we extend this result in two…
We study the approximation of the median of $d$ inputs using ReLU neural networks. We present depth-width tradeoffs under several settings, culminating in a constant-depth, linear-width construction that achieves exponentially small…
Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
In a series of four papers we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every $\alpha>0$ there exists a number $k_0$ such that for every $k>k_0$ every $n$-vertex graph $G$ with at least $(\frac12+\alpha)n$…
Motivated by the design of low-complexity low-power coding solutions for the Gaussian relay channel, this work presents an upper bound on the minimum energy-per-bit achievable on the Gaussian relay channel using rank-1 linear relaying. Our…
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks. First, we emphatically show that it is unsurprising…
Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer…
A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary…
A family of equivalence tools for bounding network capacities is introduced. Part I treats networks of point-to-point channels. The main result is roughly as follows. Given a network of noisy, independent, memoryless point-to-point…
This paper introduces an extended notion of expansion suitable for radio networks. A graph $G=(V,E)$ is called an $(\alpha_w, \beta_w)$-{wireless expander} if for every subset $S \subseteq V$ s.t. $|S|\leq \alpha_w \cdot |V|$, there exists…
Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However most of the proposed solutions require distributed space-time coding…