Related papers: Are Graph Neural Networks Optimal Approximation Al…

Graph neural networks (GNN) have recently emerged as a vehicle for applying deep network architectures to graph and relational data. However, given the increasing size of industrial datasets, in many practical situations the message passing…

Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…

Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and…

Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…

In recent years, there has been notable interest in investigating combinatorial optimization (CO) problems by neural-based framework. An emerging strategy to tackle these challenging problems involves the adoption of graph neural networks…

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer),…

A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping…

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…

We explore the feasibility of combining Graph Neural Network-based policy architectures with Deep Reinforcement Learning as an approach to problems in systems. This fits particularly well with operations on networks, which naturally take…

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…

Graph transformer networks (GTN) are a variant of graph convolutional networks (GCN) that are targeted to heterogeneous graphs in which nodes and edges have associated type information that can be exploited to improve inference accuracy.…

We study the Sum of Squares (SoS) Hierarchy with a view towards combinatorial optimization. We survey the use of the SoS hierarchy to obtain approximation algorithms on graphs using their spectral properties. We present a simplified proof…

The control of high-dimensional systems, such as soft robots, requires models that faithfully capture complex dynamics while remaining computationally tractable. This work presents a framework that integrates Graph Neural Network…

Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…

The remarkable achievements of machine learning techniques in analyzing discrete structures have drawn significant attention towards their integration into combinatorial optimization algorithms. Typically, these methodologies improve…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

Graph Neural Networks (GNNs) have recently gained traction in transportation, bioinformatics, language and image processing, but research on their application to supply chain management remains limited. Supply chains are inherently…