Related papers: Universal Function Approximation on Graphs

Graph neural networks (GNNs) have been extensively studied for prediction tasks on graphs. As pointed out by recent studies, most GNNs assume local homophily, i.e., strong similarities in local neighborhoods. This assumption however limits…

Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real…

The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable…

Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical…

This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…

Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

As graph representations of data emerge in multiple domains, data analysts need to be able to intelligently select among a magnitude of different data graphs based on the effects different graph operators have on them. Exhaustive execution…

The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors…

We present a novel methodology to jointly perform multi-task learning and infer intrinsic relationship among tasks by an interpretable and sparse graph. Unlike existing multi-task learning methodologies, the graph structure is not assumed…

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

In traditional graph retrieval tools, graph matching is commonly used to retrieve desired graphs from extensive graph datasets according to their structural similarities. However, in real applications, graph nodes have numerous attributes…

The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…

We target open-world feature extrapolation problem where the feature space of input data goes through expansion and a model trained on partially observed features needs to handle new features in test data without further retraining. The…

Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…

The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…

Graph neural networks (GNN) are powerful models for many graph-structured tasks. Existing models often assume that the complete structure of the graph is available during training. In practice, however, graph-structured data is usually…