Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.
Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectives
Nanyang Technological University（南洋理工大学）；School of Social Sciences（社会科学学院）；School of Mechanical and Aerospace Engineering（机械与宇航工程学院）；School of Physical and Mathematical Sciences（物理与数学科学学院）
Geneva School for Business administration HES-SO（日内瓦商学院HES-SO）；University of Geneva（日内瓦大学）；Center for Artificial Intelligence and Robotics (CAIRO)（人工智能与机器人中心（CAIRO））；Technische Hochschule Würzburg-Schweinfurt (THWS)（维尔茨堡-施韦因富特应用科学大学（THWS））
Department of Computing, Imperial College London, UK（伦敦帝国学院计算机系）；Department of Mathematics, Imperial College London, UK（伦敦帝国学院数学系）；London School of Geometry（几何与数论研究所）
Symmetry-Aware Graph Metanetwork Autoencoders: Model Merging through Parameter Canonicalization
University of Amsterdam（阿姆斯特丹大学）；Informatics Institute, University of Amsterdam（阿姆斯特丹大学信息学院）；Amsterdam Machine Learning Lab (AMLab), University of Amsterdam（阿姆斯特丹大学机器学习实验室）
Learning to Optimize Permutation Flow Shop Scheduling via Graph-based Imitation Learning
The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)（香港中文大学（深圳））；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；National University of Singapore（新加坡国立大学）
HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
Guillermo Bernárdez University California Santa Barbara（Guillermo Bernárdez 卡尔弗大学圣巴bara分校）；Sapienza University of Rome（罗马萨皮恩扎大学）；Universitat Politèqnica de Catalunya（加泰罗尼亚理工大学）；University of Fribourg（弗里堡大学）；Aalto University（阿alto大学）；University California Santa Barbara（加州圣巴bara大学）；Intelligent Maintenance and Operations Systems, EPFL（EPFL智能维护与操作系统）
From Mice to Trains: Amortized Bayesian Inference on Graph Data
Department of Statistics, TU Dortmund University（统计系，多特蒙德技术大学）；School of Public Health, Imperial College London（公共卫生学院，伦敦帝国理工学院）；Department of Biology, University of Oxford（生物学系，牛津大学）；Department of Mechanical Engineering, Karlsruhe Institute of Technology（机械工程系，卡尔斯鲁厄理工学院）
