Related papers: Homomorphism Counts for Graph Neural Networks: All…

Foundation Models (FMs) serve as a general class for the development of artificial intelligence systems, offering broad potential for generalization across a spectrum of downstream tasks. Despite extensive research into self-supervised…

In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index…

Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…

Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…

Graph Neural Networks (GNNs) often assume strong homophily for graph classification, seldom considering heterophily, which means connected nodes tend to have different class labels and dissimilar features. In real-world scenarios, graphs…

Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open…

Graph foundation models (GFMs) have recently attracted interest due to the promise of graph neural network (GNN) architectures that generalize zero-shot across graphs of arbitrary scales, feature dimensions, and domains. While existing work…

This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use…

Graph neural networks (GNNs) are a widely used class of machine learning models for graph-structured data, based on local aggregation over neighbors. GNNs have close connections to logic. In particular, their expressive power is linked to…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests…

We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

The expressive limitations of message-passing Graph Neural Networks (GNNs) have motivated a wide range of more powerful graph learning architectures. We advocate Deep Homomorphism Networks (DHNs) as a model particularly well-suited for…

Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs. Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform. In an attempt to avert…

Hypergraph neural networks have been promising tools for handling learning tasks involving higher-order data, with notable applications in web graphs, such as modeling multi-way hyperlink structures and complex user interactions. Yet, their…