# Neuro-symbolic Rule Learning in Real-world Classification Tasks

arXiv: https://arxiv.org/abs/2303.16674 · HTML: https://mlsanity.com/paper/2303.16674/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Abductive Knowledge Induction From Raw Data](https://mlsanity.com/paper/2010.03514/) (2020)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [Inductive Logic Programming via Differentiable Deep Neural Logic Networks](https://mlsanity.com/paper/1906.03523/) (2019)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [Differentiable Logic Machines](https://mlsanity.com/paper/2102.11529/) (2021)
- [Logical Rule Induction and Theory Learning Using Neural Theorem Proving](https://mlsanity.com/paper/1809.02193/) (2018)
- [pix2rule: End-to-end Neuro-symbolic Rule Learning](https://mlsanity.com/paper/2106.07487/) (2021)

## Built on by (most cited first, 7 of 7)

- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [TELLER: A Trustworthy Framework for Explainable, Generalizable and Controllable Fake News Detection](https://mlsanity.com/paper/2402.07776/) (2024)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [Neural DNF-MT: A Neuro-symbolic Approach for Learning Interpretable and Editable Policies](https://mlsanity.com/paper/2501.03888/) (2025)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)
- [Disentangling Neural Disjunctive Normal Form Models](https://mlsanity.com/paper/2507.10546/) (2025)
- [Visual Perceptual to Conceptual First-Order Rule Learning Networks](https://mlsanity.com/paper/2604.07897/) (2026)

## Abstract (arXiv)

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.