# Neural Logic Networks for Interpretable Classification

arXiv: https://arxiv.org/abs/2508.08172 · HTML: https://mlsanity.com/paper/2508.08172/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 52 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [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)
- [Learning Algorithms via Neural Logic Networks](https://mlsanity.com/paper/1904.01554/) (2019)
- [Transparent Classification with Multilayer Logical Perceptrons and Random Binarization](https://mlsanity.com/paper/1912.04695/) (2019)
- [Learning Interpretable Rules for Scalable Data Representation and Classification](https://mlsanity.com/paper/2310.14336/) (2023)
- [Learning Logistic Circuits](https://mlsanity.com/paper/1902.10798/) (2019)
- [Incorporating Relational Background Knowledge into Reinforcement Learning via Differentiable Inductive Logic Programming](https://mlsanity.com/paper/2003.10386/) (2020)
- [Optimal Decision Diagrams for Classification](https://mlsanity.com/paper/2205.14500/) (2022)
- [pix2rule: End-to-end Neuro-symbolic Rule Learning](https://mlsanity.com/paper/2106.07487/) (2021)

## Built on by (most cited first, 2 of 2)

- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [Training, Reading, and Editing Legible Transformers](https://mlsanity.com/paper/2607.08946/) (2026)

## Abstract (arXiv)

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a logical mechanism relating the inputs and outputs with AND and OR operations. We generalize these networks with NOT operations and biases that take into account unobserved data and develop a rigorous logical and probabilistic modeling in terms of concept combinations to motivate their use. We also propose a novel factorized IF-THEN rule structure for the model as well as a modified learning algorithm. Our method improves the state-of-the-art in Boolean networks discovery and is able to learn relevant, interpretable rules in tabular classification, notably on examples from the medical and industrial fields where interpretability has tangible value.