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A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…

We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical…

Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network…

The Transformer architecture has achieved remarkable success in a number of domains including natural language processing and computer vision. However, when it comes to graph-structured data, transformers have not achieved competitive…

We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…

Recently, there have been some breakthroughs in graph analysis by applying the graph neural networks (GNNs) following a neighborhood aggregation scheme, which demonstrate outstanding performance in many tasks. However, we observe that the…

Graph Neural Networks (GNNs) are increasingly important given their popularity and the diversity of applications. Yet, existing studies of their vulnerability to adversarial attacks rely on relatively small graphs. We address this gap and…

In this work we propose a random graph model that can produce graphs at different levels of sparsity. We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on…

Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network…

We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…

Graph Neural Networks (GNNs) are a new and increasingly popular family of deep neural network architectures to perform learning on graphs. Training them efficiently is challenging due to the irregular nature of graph data. The problem…

Graph neural networks (GNNs) have demonstrated remarkable success in graph representation learning, and various sampling approaches have been proposed to scale GNNs to applications with large-scale graphs. A class of promising GNN training…

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…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infinite reduction has a well defined limit allowing us to treat…

In this paper, we explore the limits of graphics processors (GPUs) for general purpose parallel computing by studying problems that require highly irregular data access patterns: parallel graph algorithms for list ranking and connected…

Graph representation learning has recently been applied to a broad spectrum of problems ranging from computer graphics and chemistry to high energy physics and social media. The popularity of graph neural networks has sparked interest, both…

Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…

Graph neural networks (GNNs) have been widely adopted for semi-supervised learning on graphs. A recent study shows that the graph random neural network (GRAND) model can generate state-of-the-art performance for this problem. However, it is…

In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery,…