Neurosymbolic (NeSy) AI studies the integration of neural networks (NNs) and symbolic reasoning based on logic. Usually, NeSy techniques focus on learning the neural, probabilistic and/or fuzzy parameters of NeSy models. Learning the symbolic or logical structure of such models has, so far, received less attention. We introduce neurosymbolic decision trees (NDTs), as an extension of decision trees together with a novel NeSy structure learning algorithm, which we dub NeuID3. NeuID3 adapts the standard top-down induction of decision tree algorithms and combines it with a neural probabilistic logic representation, inherited from the DeepProbLog family of models. The key advantage of learning NDTs with NeuID3 is the support of both symbolic and subsymbolic data (such as images), and that they can exploit background knowledge during the induction of the tree structure, In our experimental evaluation we demonstrate the benefits of NeSys structure learning over more traditonal approaches such as purely data-driven learning with neural networks.

本研究解决了神经符号人工智能中对符号或逻辑结构学习关注不足的问题。我们提出了神经符号决策树（NDT），并引入了一种新颖的结构学习算法NeuID3，该算法结合了传统的决策树算法与神经概率逻辑表示。实验结果显示，NDT在学习过程中能够同时支持符号和非符号数据，并在结构诱导中利用背景知识，展现了优于传统数据驱动学习方法的优势。