A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition the space has imperfections, \textit{e}.\textit{g}., the compromised interpretability for complex models, the inflexibility in decision boundary construction due to the generic character of the model, and the risk of being trapped into shortcut solutions. In contrast, although the non-parameterized models can adorably avoid or downplay these issues, they are usually insufficiently powerful either due to over-simplification or the failure to accommodate the manifold structures of data. In this context, we first propose a new type of machine learning models referred to as Manifoldron that directly derives decision boundaries from data and partitions the space via manifold structure discovery. Then, we systematically analyze the key characteristics of the Manifoldron such as manifold characterization capability and its link to neural networks. The experimental results on 4 synthetic examples, 20 public benchmark datasets, and 1 real-world application demonstrate that the proposed Manifoldron performs competitively compared to the mainstream machine learning models. We have shared our code in \url{https://github.com/wdayang/Manifoldron} for free download and evaluation.
GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks
L3S Research Center, Leibniz University Hannover（莱布尼茨汉诺威大学L3S研究中心）；Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed)（下萨克森州人工智能与因果医学方法中心（CAIMed））；Institute for Causal and Explainable Artificial Intelligence in Life Sciences（生命科学因果与可解释人工智能研究所）；Center for Computational Life Sciences（计算生命科学中心）；RWTH Aachen University（亚琛工业大学）
Causal Discovery with Fewer Conditional Independence Tests
Eric and Wendy Schmidt Center, Broad Institute（埃里克和温迪·施密特中心，布罗德研究所）；Laboratory for Information & Decision Systems, Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts
The University of Texas at El Paso（德克萨斯大学埃尔帕索分校）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；Clarkson University（克拉克森大学）；Texas A&M University in Kingsville（德克萨斯农工大学金斯维尔分校）
Ensuring the Robustness and Reliability of Data-Driven Knowledge Discovery Models in Production and Manufacturing
University of Applied Sciences Upper Austria（上奥地利应用科学大学）；Tampere University（坦佩雷大学）；Institute of Biosciences and Medical Technology（生物科学与医疗技术研究所）；UMIT-The Health and Life Science University（UMIT-健康与生命科学大学）；Nankai University（南开大学）
Hamiltonian Graph Inference Networks: Joint structure discovery and dynamics prediction for lattice Hamiltonian systems from trajectory data
School of Mathematics and Statistics（数学与统计学学院）；University of Massachusetts（马萨诸塞大学）；Seoul National University（首尔国立大学）；Northeast Normal University（东北师范大学）；Great Bay University（大贝大学）
Machine Learning Discovery of Optimal Quadrature Rules for Isogeometric Analysis
BCAM – Basque Center for Applied Mathematics（巴斯克应用数学中心（BCAM））；CUNEF University（CUNEF大学）；University of the Basque Country (UPV/EHU)（巴斯克大学（UPV/EHU））；Ikerbasque – Basque Foundation for Sciences（巴斯克科学基金会（Ikerbasque））
