Related papers: Graph Reconstruction, Functorial Feynman Rules and…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…

Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…

We rewrite the loop equations of the hermitian matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological $1/N^2$ expansion, as residues on an hyperelliptical curve. Those residues, can be…

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 symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

Graph-structured data are pervasive in the real-world such as social networks, molecular graphs and transaction networks. Graph neural networks (GNNs) have achieved great success in representation learning on graphs, facilitating various…

It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…

We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…

When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…

We provide a mathematically and conceptually robust notion of quantum superpositions of graphs. We argue that, crucially, quantum superpositions of graphs require node names for their correct alignment, which we demonstrate through a…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…

We consider the perturbative renormalization of the Schwinger-Dyson functional, which is the generating functional of the expectation values of the products of the composite operator given by the field derivative of the action. It is argued…

In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for (supervised) machine learning with graphs and relational…

Recursive formulas extending some known $_{2}F_{1}$ and $_{3}F_{2}$ summation formulas by using contiguous relations have been obtained. On the one hand, these recursive equations are quite suitable for symbolic and numerical evaluation by…

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…

Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer science. They also provide a natural framework for the…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…