One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with the ability of deep learning to learn from raw data. However, most current approaches require manually engineered symbolic knowledge, and where end-to-end training is considered, such approaches are either restricted to learning definite programs, or are restricted to training binary neural networks. In this paper, we introduce Neuro-Symbolic Inductive Learner (NSIL), an approach that trains a general neural network to extract latent concepts from raw data, whilst learning symbolic knowledge that maps latent concepts to target labels. The novelty of our approach is a method for biasing the learning of symbolic knowledge, based on the in-training performance of both neural and symbolic components. We evaluate NSIL on three problem domains of different complexity, including an NP-complete problem. Our results demonstrate that NSIL learns expressive knowledge, solves computationally complex problems, and achieves state-of-the-art performance in terms of accuracy and data efficiency. Code and technical appendix: https://github.com/DanCunnington/NSIL

翻译：人工智能的终极目标之一是辅助人类进行复杂决策。实现这一目标的一个有前景的方向是神经符号AI，它旨在结合符号技术可解释性与深度学习从原始数据中学习的能力。然而，当前大多数方法需要人工构建符号知识，而即便在考虑端到端训练的情况下，此类方法要么局限于学习确定性程序，要么只能训练二值神经网络。本文提出神经符号归纳学习器（NSIL），该方法训练通用神经网络从原始数据中提取潜在概念，同时学习将潜在概念映射到目标标签的符号知识。该方法的核心创新在于一种基于神经网络与符号组件训练中性能来偏置符号知识学习的机制。我们在三个不同复杂度的问题域上评估了NSIL，包括一个NP完全问题。实验结果表明，NSIL能够学习具有表达力的知识，解决计算复杂问题，并在准确率和数据效率方面达到了最先进水平。代码和技术附录见：https://github.com/DanCunnington/NSIL