# Transparent Classification with Multilayer Logical Perceptrons and Random Binarization

arXiv: https://arxiv.org/abs/1912.04695 · HTML: https://mlsanity.com/paper/1912.04695/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2019.

## Built on by (most cited first, 17 of 17)

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- [Finding Interpretable Class-Specific Patterns through Efficient Neural Search](https://mlsanity.com/paper/2312.04311/) (2023)
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- [Manifoldron: Direct Space Partition via Manifold Discovery](https://mlsanity.com/paper/2201.05279/) (2022)
- [Neural Logic Networks for Interpretable Classification](https://mlsanity.com/paper/2508.08172/) (2025)
- [RuDi: Explaining Behavior Sequence Models by Automatic Statistics Generation and Rule Distillation](https://mlsanity.com/paper/2208.07211/) (2022)
- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [Hamming Encoder: Mining Discriminative k-mers for Discrete Sequence Classification](https://mlsanity.com/paper/2310.10321/) (2023)
- [Interpretable Classification via a Rule Network with Selective Logical Operators](https://mlsanity.com/paper/2408.11918/) (2024)
- [Interpretable Responsibility Sharing as a Heuristic for Task and Motion Planning](https://mlsanity.com/paper/2409.05586/) (2024)
- [(Sometimes) Less is More: Mitigating the Complexity of Rule-based Representation for Interpretable Classification](https://mlsanity.com/paper/2509.22384/) (2025)
- [Deep Arguing](https://mlsanity.com/paper/2605.10569/) (2026)
- [Optimizing Sparse Boolean Rule Networks using Mixed Integer Linear Programming](https://mlsanity.com/paper/2610.20170/) (2026)

## Abstract (arXiv)

Models with transparent inner structure and high classification performance are required to reduce potential risk and provide trust for users in domains like health care, finance, security, etc. However, existing models are hard to simultaneously satisfy the above two properties. In this paper, we propose a new hierarchical rule-based model for classification tasks, named Concept Rule Sets (CRS), which has both a strong expressive ability and a transparent inner structure. To address the challenge of efficiently learning the non-differentiable CRS model, we propose a novel neural network architecture, Multilayer Logical Perceptron (MLLP), which is a continuous version of CRS. Using MLLP and the Random Binarization (RB) method we proposed, we can search the discrete solution of CRS in continuous space using gradient descent and ensure the discrete CRS acts almost the same as the corresponding continuous MLLP. Experiments on 12 public data sets show that CRS outperforms the state-of-the-art approaches and the complexity of the learned CRS is close to the simple decision tree. Source code is available at https://github.com/12wang3/mllp.