Related papers: Hypergraph Horn functions
Shannon entropy is a polymatroidal set function and lies at the foundation of information theory, yet the class of entropic polymatroids is strictly smaller than the class of all submodular functions. In parallel, submodular and…
This paper stands at the intersection of two distinct lines of research. One line is "holographic algorithms," a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is "normal factor…
Document classification is a challenging task with important applications. The deep learning approaches to the problem have gained much attention recently. Despite the progress, the proposed models do not incorporate the knowledge of the…
Hypergraphs are a generalized data structure of graphs to model higher-order correlations among entities, which have been successfully adopted into various research domains. Meanwhile, HyperGraph Neural Network (HGNN) is currently the…
We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models…
Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in…
Context-aware Human Activity Recognition (CHAR) is challenging due to the need to recognize the user's current activity from signals that vary significantly with contextual factors such as phone placements and the varied styles with which…
Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…
Holonomic functions play an essential role in Computer Algebra since they allow the application of many symbolic algorithms. Among all algorithmic attempts to find formulas for power series, the holonomic property remains the most important…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…
An algebra denoted $m\mathfrak{H}$ with three generators is introduced and shown to admit embeddings of the Hahn algebra and the rational Hahn algebra. It has a real version of the deformed Jordan plane as a subalgebra whose connection with…
We give closed forms for several families of Heun functions related to classical entropies. By comparing two expressions of the same Heun function, we get several combinatorial identities generalizing some classical ones.
Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent…
We discuss some properties of linear functionals on topological hyperbolic and topological bicomplex modules. The hyperbolic and bicomplex analogues of the uniform boundedness principle, the open mapping theorem, the closed graph theorem…
Graph Neural Nets (GNNs) have received increasing attentions, partially due to their superior performance in many node and graph classification tasks. However, there is a lack of understanding on what they are learning and how sophisticated…
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…
This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and…