Neuro-symbolic rule learning has attracted lots of attention as it offers better interpretability than pure neural models and scales better than symbolic rule learning. A recent approach named pix2rule proposes a neural Disjunctive Normal Form (neural DNF) module to learn symbolic rules with feed-forward layers. Although proved to be effective in synthetic binary classification, pix2rule has not been applied to more challenging tasks such as multi-label and multi-class classifications over real-world data. In this paper, we address this limitation by extending the neural DNF module to (i) support rule learning in real-world multi-class and multi-label classification tasks, (ii) enforce the symbolic property of mutual exclusivity (i.e. predicting exactly one class) in multi-class classification, and (iii) explore its scalability over large inputs and outputs. We train a vanilla neural DNF model similar to pix2rule's neural DNF module for multi-label classification, and we propose a novel extended model called neural DNF-EO (Exactly One) which enforces mutual exclusivity in multi-class classification. We evaluate the classification performance, scalability and interpretability of our neural DNF-based models, and compare them against pure neural models and a state-of-the-art symbolic rule learner named FastLAS. We demonstrate that our neural DNF-based models perform similarly to neural networks, but provide better interpretability by enabling the extraction of logical rules. Our models also scale well when the rule search space grows in size, in contrast to FastLAS, which fails to learn in multi-class classification tasks with 200 classes and in all multi-label settings.

翻译：神经符号规则学习因其相比纯神经模型具有更好的可解释性，且比符号规则学习具有更好的扩展性而备受关注。近期提出的pix2rule方法采用神经析取范式（neural DNF）模块，通过前馈层学习符号规则。尽管该方法在合成二元分类任务中被证明有效，但pix2rule尚未应用于更具挑战性的任务，例如基于真实数据实现多标签和多类别分类。本文通过扩展神经DNF模块来解决上述局限性，具体包括：(i) 支持真实世界中多类别和多标签分类任务的规则学习；(ii) 在多类别分类中强制实现互斥性（即预测且仅预测一个类别）的符号属性；(iii) 探索该方法在大规模输入输出场景下的可扩展性。我们训练了一个类似pix2rule神经DNF模块的原始神经DNF模型用于多标签分类，并提出了一个名为neural DNF-EO（Exactly One）的新型扩展模型，该模型在多类别分类中强制实现互斥性。我们评估了基于神经DNF模型的分类性能、可扩展性和可解释性，并将其与纯神经模型及当前最先进的符号规则学习器FastLAS进行了比较。结果表明，基于神经DNF的模型与神经网络性能相当，但通过支持逻辑规则提取提供了更优的可解释性。此外，我们的模型在规则搜索空间扩大时仍具有良好扩展性，而FastLAS在包含200个类别的多类别分类任务及所有多标签设定中均无法完成学习。