  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.
