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.

翻译：神经符号（NeSy）人工智能已成为一种前景广阔的方法，它将神经网络的学习能力与符号系统的可解释推理相结合。然而，现有的NeSy框架通常需要预定义的符号策略或可微分的策略，这限制了其在领域专业知识不可用或策略本身不可微分情况下的适用性。我们提出了一个框架，通过进化过程实现不可微分符号策略和神经网络权重的协同学习，从而解决这一局限。我们的方法将NeSy系统视为种群中的有机体，通过变异（包括符号规则添加和神经权重改变）进行进化，基于适应度的选择引导系统向隐藏的目标策略收敛。该框架扩展了NEUROLOG架构以使符号策略可训练，将Valiant的可进化性框架适配到NeSy情境，并采用机器辅导语义来实现可变的符号表示。神经网络通过符号组件的溯因推理进行训练，消除了可微分性要求。通过大量实验，我们证明从空策略和随机神经权重开始的NeSy系统能够成功逼近隐藏的不可微分目标策略，中位数正确性能接近100%。这项工作推动了NeSy研究在难以或无法从专家获取符号知识的领域中的应用。