In this study, we demonstrate that the linear combination of atomic orbitals (LCAO), an approximation of quantum physics introduced by Pauling and Lennard-Jones in the 1920s, corresponds to graph convolutional networks (GCNs) for molecules. However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT). We believe that the QDF model can be easily understood because it can be regarded as a single linear layer GCN. Moreover, it uses two vanilla feedforward neural networks to learn an energy functional and a Hohenberg--Kohn map that have nonlinearities inherent in quantum physics and the DFT. For molecular energy prediction tasks, we demonstrated the viability of an ``extrapolation,'' in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high extrapolation performance. This will lead to reliable and practical applications for discovering effective materials. The implementation is available at https://github.com/masashitsubaki/QuantumDeepField_molecule.
On the Equivalence of Decoupled Graph Convolution Network and Label Propagation
University of Science and Technology of China（中国科学技术大学）；National University of Singapore（新加坡国立大学）；North Carolina State University（北卡罗来纳州立大学）；Tsinghua University（清华大学）
Discovering alignment relations with Graph Convolutional Networks: a biomedical case study
Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；LORIA（洛林计算机科学与应用研究实验室）；Orange（Orange公司）；Ubisoft（育碧公司）；Inria Paris（法国国家信息与自动化研究所巴黎中心）；Centre de Recherche des Cordeliers（科德利耶研究中心）；Inserm（法国国家健康与医学研究院）；Université de Paris（巴黎大学）；Sorbonne Université（索邦大学）
Vision Transformers versus convolutional neural networks for fine-grained orchid genus identification in a species-rich, data-poor flora: a controlled benchmark on the Orchidaceae of New Guinea
James Cook University（詹姆斯库克大学）；Southwest Papua Natural Resources Conservation Agency, Ministry of Forestry, Indonesia（印度尼西亚林业部西南巴布亚自然资源保护局）；National Research and Innovation Agency (BRIN), Republic of Indonesia（印度尼西亚共和国国家研究与创新局（BRIN））；Royal Botanic Gardens, Kew（英国皇家植物园邱园）；Australian Tropical Herbarium（澳大利亚热带植物标本馆）；Commonwealth Industrial and Scientific Research Organisation (CSIRO)（澳大利亚联邦科学与工业研究组织（CSIRO））；Australian National Herbarium（澳大利亚国家植物标本馆）
Functional Equivalence in Attention: A Comprehensive Study with Applications to Linear Mode Connectivity
National University of Singapore（新加坡国立大学）；Center for AI Research, VinUniversity（Vin大学人工智能研究中心）；Independent Researcher（独立研究者）；Technical University of Munich（慕尼黑技术大学）
Deep Convolutional Networks are Hierarchical Kernel Machines
Center for Brains Minds and Machines, Massachusetts Institute of Technology（麻省理工学院脑、心智与机器中心）；Laboratory for Computational Learning, Istituto Italiano di Tecnologia（意大利理工学院计算学习实验室）；Massachusetts Institute of Technology（麻省理工学院）；DIBRIS, Universitá degli studi di Genova（热那亚大学DIBRIS）；Institute for Infocomm Research（信息通信研究院）
Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learning
Shenyang Institute of Automation, Chinese Academy of Sciences（中国科学院沈阳自动化研究所）；Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences（中国科学院机器人与智能制造创新研究院）；Xi’an Jiaotong University（西安交通大学）；University of Sydney（悉尼大学）
From Compass and Ruler to Convolution and Nonlinearity: On the Surprising Difficulty of Understanding a Simple CNN Solving a Simple Geometric Estimation Task
