Related papers: Homogeneity vs. Adjacency: generalising some graph…

As deep learning applications continue to become more diverse, an interesting question arises: Can general problem solving arise from jointly learning several such diverse tasks? To approach this question, deep multi-task learning is…

Modular meta-learning is a new framework that generalizes to unseen datasets by combining a small set of neural modules in different ways. In this work we propose abstract graph networks: using graphs as abstractions of a system's subparts…

I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…

We consider the problem of configuration formation in modular robot systems where a set of modules that are initially in different configurations and located at different locations are required to assume appropriate positions so that they…

This article develops a new theoretical basis for decomposing signals that are formed by the linear superposition of a finite number of modes. Each mode depends nonlinearly upon several parameters; we seek both these parameters and the…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…

This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…

Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…

Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the…

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…

The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for combinatorial designs, and some generalizations, was…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

A theta is a graph formed by three paths between the same pair of distinct vertices so that the union of any two of the paths induces a hole. A wheel is a graph formed by a hole and a node that has at least 3 neighbors in the hole. In this…

An old idea in optimization theory says that since the gradient is a dual vector it may not be subtracted from the weights without first being mapped to the primal space where the weights reside. We take this idea seriously in this paper…

The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lov\'asz and Plummer developed a decomposition theory for graphs with perfect…

A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…

In this paper, we propose a framework under which the decentralized optimization algorithms suggested in \cite{JKJJ,MA, NO,NO2} can be treated in a unified manner. More precisely, we show that the distributed subgradient descent algorithms…