Neural-Symbolic (NeSy) Artificial Intelligence has emerged as a promising approach for combining the learning capabilities of neural networks with the interpretable reasoning of symbolic systems. However, existing NeSy frameworks typically require either predefined symbolic policies or policies that are differentiable, limiting their applicability when domain expertise is unavailable or when policies are inherently non-differentiable. We propose a framework that addresses this limitation by enabling the concurrent learning of both non-differentiable symbolic policies and neural network weights through an evolutionary process. Our approach casts NeSy systems as organisms in a population that evolve through mutations (both symbolic rule additions and neural weight changes), with fitness-based selection guiding convergence toward hidden target policies. The framework extends the NEUROLOG architecture to make symbolic policies trainable, adapts Valiant's Evolvability framework to the NeSy context, and employs Machine Coaching semantics for mutable symbolic representations. Neural networks are trained through abductive reasoning from the symbolic component, eliminating differentiability requirements. Through extensive experimentation, we demonstrate that NeSy systems starting with empty policies and random neural weights can successfully approximate hidden non-differentiable target policies, achieving median correct performance approaching 100%. This work represents a step toward enabling NeSy research in domains where the acquisition of symbolic knowledge from experts is challenging or infeasible.
Discovering Continuous-Time Memory-Based Symbolic Policies using Genetic Programming
Department of Machine Learning and Neural Computing（机器学习与神经计算系）；Donders Institute for Brain, Cognition and Behaviour（大脑、认知与行为研究所）；Radboud University（拉德堡德大学）
Efficient Symbolic Policy Learning with Differentiable Symbolic Expression
SKL of Processors, Institute of Computing Technology, CAS（中国科学院计算技术研究所处理器芯片全国重点实验室）；Intelligent Software Research Center, Institute of Software, CAS（中国科学院软件研究所智能软件研究中心）；University of Science and Technology of China, USTC（中国科学技术大学）；Cambricon Technologies（寒武纪科技）；Shanghai Innovation Center for Processor Technologies, SHIC（上海处理器技术创新中心）；University of Chinese Academy of Sciences, UCAS（中国科学院大学）
Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction
Technical University of Darmstadt（达姆施塔特工业大学）；National Research Center for Applied Cybersecurity（国家应用网络安全研究中心）；Eindhoven University of Technology（埃因霍温理工大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）
BlendRL: A Framework for Merging Symbolic and Neural Policy Learning
Technical University of Darmstadt（达姆施塔特工业大学）；Eindhoven University of Technology（埃因霍温理工大学）；Hessian Center for Artificial Intelligence (hessian.AI)（黑森人工智能中心）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Centre for Cognitive Science, Technical University of Darmstadt（达姆施塔特工业大学认知科学中心）
Symbolic Imitation Learning: From Black-Box to Explainable Driving Policies
Department of Science and Engineering, the George Washington University（科学与工程系，乔治·华盛顿大学）；Autonomous Vehicles Lab, Department of Mechanical Engineering, University of Surrey（自主车辆实验室，机械工程系，萨里大学）
Automaton Distillation: Neuro-Symbolic Transfer Learning for Deep Reinforcement Learning
University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；University of Central Florida（中佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）；Florida International University（佛罗里达国际大学）；University of Colorado（科罗拉多大学）
Symbolic Regression Methods for Reinforcement Learning
Czech Institute of Informatics, Robotics, and Cybernetics, Czech Technical University in Prague（布拉格捷克理工大学信息学、机器人与控制论研究所）；Faculty of Electrical Engineering, Czech Technical University in Prague（布拉格捷克理工大学电气工程学院）；Cognitive Robotics, Delft University of Technology（代尔夫特理工大学认知机器人系）
