Related papers: Universal Function Approximation on Graphs

Graph learning has become essential in various domains, including recommendation systems and social network analysis. Graph Neural Networks (GNNs) have emerged as promising techniques for encoding structural information and improving…

In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…

Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…

The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…

We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A…

Real-world networks often benefit from capturing both local and global interactions. Inspired by multi-modal analysis in brain imaging, where structural and functional connectivity offer complementary views of network organization, we…

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…

Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the…

Hypergraph, an expressive structure with flexibility to model the higher-order correlations among entities, has recently attracted increasing attention from various research domains. Despite the success of Graph Neural Networks (GNNs) for…

Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the…

Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…

We establish a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. At the center of this framework lies the concept of a $\leqslant$-parametric graph:…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…

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…

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Graph filters that transform prior node values to posterior scores via edge propagation often support graph mining tasks affecting humans, such as recommendation and ranking. Thus, it is important to make them fair in terms of satisfying…

We study the problem of learning features through self-supervision that are generalisable to multiple graphs. State-of-the-art graph self-supervision restricts training to only one graph, resulting in graph-specific models that are…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…