Related papers: Functorial Approach to Graph and Hypergraph Theory
We study graph parameters whose associated edge-connection matrices have exponentially bounded rank growth. Our main result is an explicit construction of a large class of graph parameters with this property that we call mixed partition…
Despite the promising results of disentangled representation learning in discovering latent patterns in graph-structured data, few studies have explored disentanglement for hypergraph-structured data. Integrating hyperedge disentanglement…
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,…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Graph-based learning is a rapidly growing sub-field of machine learning with applications in social networks, citation networks, and bioinformatics. One of the most popular models is graph attention networks. They were introduced to allow a…
We present the theory of multifunctions applied to graphs. Its interesting feature is that walks are recognized as iterations. We consider the graphs with arbitrary number of vertices which are determined by multifunctions. The mutually…
Heterogeneous graphs have multiple node and edge types and are semantically richer than homogeneous graphs. To learn such complex semantics, many graph neural network approaches for heterogeneous graphs use metapaths to capture multi-hop…
Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…
This study investigates a hybrid method for text classification that integrates deep feature extraction from large language models, multi-scale fusion through feature pyramids, and structured modeling with graph neural networks to enhance…
Graphs neural networks (GNNs) learn node features by aggregating and combining neighbor information, which have achieved promising performance on many graph tasks. However, GNNs are mostly treated as black-boxes and lack human intelligible…
In the standard Category of Graphs, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer…
We describe a category of Feynman graphs and show how it relates to compact symmetric multicategories (coloured modular operads) just as linear orders relate to categories and rooted trees relate to multicategories. More specifically we…
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly)…
Precategories generalize both the notions of strict $n$-category and sesquicategory: their definition is essentially the same as the one of strict $n$-categories, excepting that we do not require the various interchange laws to hold. Those…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
A major challenge in scene graph classification is that the appearance of objects and relations can be significantly different from one image to another. Previous works have addressed this by relational reasoning over all objects in an…
We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic…
This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may…