Most of the neural networks (NNs) learned via state-of-the-art machine learning techniques are black-box models. For a widespread success of machine learning in science and engineering, it is important to develop new NN architectures to effectively extract high-level mathematical knowledge from complex datasets. Motivated by this understanding, this paper develops a new NN architecture called the Gumbel-Max Equation Learner (GMEQL) network. Different from previously proposed Equation Learner (EQL) networks, GMEQL applies continuous relaxation to the network structure via the Gumbel-Max trick and introduces two types of trainable parameters: structure parameters and regression parameters. This paper also proposes a two-stage training process with new techniques to train structure parameters in both online and offline settings based on an elite repository. On 8 benchmark symbolic regression problems, GMEQL is experimentally shown to outperform several cutting-edge machine learning approaches.
The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；IIIS, Tsinghua University（清华大学交叉信息研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；Deepmind（深度思考）；MIT BCS（麻省理工学院脑与认知科学系）；CBMM（脑、心智与机器中心）
Language Models are Symbolic Learners in Arithmetic
Department of Computer Science（计算机科学系）；Rice University（里士满大学）；College of Computing（计算学院）；Georgia Institute of Technology（佐治亚理工学院）；Duke University（杜克大学）
Physics Symbolic Learner for Discovering Ground-Motion Models Via NGA-West2 Database
Beijing University of Technology（北京工业大学）；Institute of Geophysics, China Earthquake Administration（中国地震局地球物理研究所）；Institute of Geomechanics, Chinese Academy of Geological Sciences（中国地质科学院地质力学研究所）
Adaptive Protection for Evolutionary Feature Construction in Symbolic Regression with Application to Credit Classification
Centre for Data Science and Artificial Intelligence（数据科学与人工智能中心）；School of Engineering and Computer Science（工程与计算机科学学院）；Victoria University of Wellington（惠灵顿维多利亚大学）；Business School, Sichuan University（四川大学商学院）；Michigan State University（密歇根州立大学）
Weak-PDE-Net: Discovering Open-Form PDEs via Differentiable Symbolic Networks and Weak Formulation
School of Mathematical Sciences, East China Normal University（东华大学数学科学学院）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；Institute of Artificial Intelligence, Beihang University（北航人工智能研究所）；Shanghai Zhangjiang Institute of Mathematics（上海张江数学研究所）；Academy for Advanced Interdisciplinary Studies, Northeast Normal University（东北师范大学先进交叉学科研究院）
Massachusetts Institute of Technology（麻省理工学院）；Scripps Institution of Oceanography（斯克里普斯海洋研究所）；Paul Scherrer Institute（保罗·谢勒研究所）；University of California San Diego（加利福尼亚大学圣迭戈分校）
Gradient-Based Program Synthesis with Neurally Interpreted Languages
AMLab, University of Amsterdam（阿姆斯特丹大学AMLab）；Ndea；Department of Computing Science, University of Alberta（阿尔伯塔大学计算机科学系）；Alberta Machine Intelligence Institute (Amii), Edmonton, Canada（阿尔伯塔机器智能研究所（Amii），加拿大爱德蒙顿）
