Related papers: On the Gap between Scalar and Vector Solutions of …
Motivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank $r$ and with bounded subdeterminants. In particular, we study the…
In this paper, we study the problem of constructing a network by observing ordered connectivity constraints, which we define herein. These ordered constraints are made to capture realistic properties of real-world problems that are not…
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…
Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear…
Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…
The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities…
We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…
The network scale-up method enables researchers to estimate the size of hidden populations, such as drug injectors and sex workers, using sampled social network data. The basic scale-up estimator offers advantages over other size estimation…
We study the problem of finding the largest number $T(n, m)$ of ternary vectors of length $n$ such that for any three distinct vectors there are at least $m$ coordinates where they pairwise differ. For $m = 1$, this is the classical…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyond the classical problem of identifying…
Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…
This manuscript describes the notions of blocker and interdiction applied to well-known optimization problems. The main interest of these two concepts is the capability to analyze the existence of a combinatorial structure after some…
This paper studies a layered coding framework with a relaxed hierarchical structure. Advances in wired/wireless communication and consumer electronic devices have created a requirement for serving the same content at different quality…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…