Related papers: On the Gap between Scalar and Vector Solutions of …
Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…
Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes,…
We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare…
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…
We present a framework to study linear deterministic interference networks over finite fields. Unlike the popular linear deterministic models introduced to study Gaussian networks, we consider networks where the channel coefficients are…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
This paper reviews graph convolutional neural networks (GCNNs) through the lens of edge-variant graph filters. The edge-variant graph filter is a finite order, linear, and local recursion that allows each node, in each iteration, to weigh…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…
We give a polynomial time reduction from vector scheduling problem (VS) to generalized load balancing problem (GLB). This reduction gives the first non-trivial online algorithm for VS where vectors come in an online fashion. The online…
We introduce a technique based on the singular vector canonical correlation analysis (SVCCA) for measuring the generality of neural network layers across a continuously-parametrized set of tasks. We illustrate this method by studying…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…
Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…
Consider a graph G with an assignment of costs to vertices. Even if G and all its subgraphs admit balanced separators of sublinear size, G may only admit a balanced separator of sublinear cost after deleting a small set Z of exceptional…
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification…
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…