Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have recently been proposed, in large part building upon precursors from the more traditional graph neural network (GNN) literature. Somewhat differently, in this paper we begin by presenting an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings that, when paired with a parameterized classifier, can be trained end-to-end via a supervised bilevel optimization process. Later, we draw parallels between the implicit architecture of the predictive models emerging from the proposed bilevel hypergraph optimization, and existing GNN architectures in common use. Empirically, we demonstrate state-of-the-art results on various hypergraph node classification benchmarks. Code is available at https://github.com/yxzwang/PhenomNN.
HWL-HIN: A Hypergraph-Level Hypergraph Isomorphism Network as Powerful as the Hypergraph Weisfeiler-Lehman Test with Application to Higher-Order Network Robustness
Stability and Generalization of Hypergraph Collaborative Networks
Institute of Data Science, The University of Hong Kong（香港大学数据科学学院）；College of Information Science and Technology, Jinan University（暨南大学信息科学技术学院）；The University of Hong Kong（香港大学）
HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problems
School of Mathematical Sciences, University of Chinese Academy of Science（中国科学院大学数学科学学院）；Zhongguancun Laboratory（中关村实验室）；School of Automation Science and Electrical Engineering, Beihang University（北京航空航天大学自动化科学与电气工程学院）
LHNN: Lattice Hypergraph Neural Network for VLSI Congestion Prediction
The Chinese University of Hong Kong（香港中文大学）；Shenzhen Institutes of Advanced Technology（深圳先进技术研究院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Huawei Hisilicon（华为海思）；Peking University（北京大学）
Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger
Beijing University of Posts and Telecommunications（北京邮电大学）；North China Electric Power University（华北电力大学）；University of Kent（肯特大学）；Beihang University（北航）；University of Illinois（伊利诺伊大学）
UniG-Encoder: A Universal Feature Encoder for Graph and Hypergraph Node Classification
Fudan University（复旦大学）；Institute of AI and Robotics, Academy for Engineering and Technology, Fudan University（复旦大学工程与应用技术研究院人工智能与机器人研究所）；Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂体系研究院）
Heterogeneous Directed Hypergraph Neural Network over abstract syntax tree (AST) for Code Classification
School of Computer Science and Technology, East China Normal University（计算机科学与技术学院，东华大学）；NPPA Key Laboratory of Publishing Integration Development, ECNUP（出版集成发展关键实验室，ECNUP）
Dynamic Hypergraph-Enhanced Prediction of Sequential Medical Visits
University of Southern California（南加州大学）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Texas Tech University（德克萨斯理工大学）；Southern Methodist University（南卫理公会大学）
Multi-Granular Attention based Heterogeneous Hypergraph Neural Network
School of Computer Science, Hubei University（湖北大学计算机学院）；Hubei Key Laboratory of Big Data Intelligent Analysis and Application (Hubei University)（湖北大学大数据智能分析与应用重点实验室）；Discipline of Business Analytics, The University of Sydney（悉尼大学商业分析学科）；Key Laboratory of Intelligent Sensing System and Security (Hubei University), Ministry of Education（智能感知系统与安全重点实验室（湖北大学），教育部）
HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes
Department of Electrical and Computer Engineering, The University of Texas at Dallas（电子与计算机工程系，德克萨斯大学达拉斯分校）；Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute（电子、计算机与系统工程系，伦塞拉尔理工大学）
A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures
Department of Mechanical Engineering, The University of British Columbia（不列颠哥伦比亚大学机械工程系）；Department of Mechanical Engineering, University of California, Berkeley（加州大学伯克利分校机械工程系）
POSTECH（浦项科技大学）；Center for Geometry and Physics, Institute for Basic Science (IBS)（基础科学研究院几何与物理中心）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing
School of Mathematics and Statistics, Shandong University（山东大学数学与统计学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）
Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets
Institute for Financial Services Analytics, University of Delaware（特拉华大学金融服务分析研究所）；Department of Applied Economics and Statistics, University of Delaware（特拉华大学应用经济学与统计学系）；Department of Electrical and Computer Engineering, University of Kentucky（肯塔基大学电气与计算机工程系）；Department of Electrical and Computer Engineering, University of Delaware（特拉华大学电气与计算机工程系）
From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks
School of Mathematics and Statistics, Shandong University, Weihai（山东大学（威海）数学与统计学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
