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Neural Logic Networks for Interpretable Classification

Vincent Perreault, Katsumi Inoue, Richard Labib, Alain Hertz

TL;DR

This work introduces Neural Logic Networks (NLNs) that integrate probabilistic reasoning with AND/OR logic to produce interpretable, rule-based classifications. By explicitly modeling unobserved data through biases and employing a two-layer DN F structure with dedicated input preprocessing, NLNs can learn concise, human-understandable rules while maintaining competitive predictive performance. The authors provide a rigorous probabilistic and fuzzy-logic foundation, outline a practical learning pipeline with rule resets and post-processing (discretization, pruning, bias adjustment), and demonstrate strong results on Boolean network discovery and tabular classification, including medical and industrial datasets. Overall, NLNs offer a scalable path toward interpretable, logic-grounded AI that can complement or partly replace black-box neural approaches in domains where transparency is critical.

Abstract

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.

Neural Logic Networks for Interpretable Classification

TL;DR

This work introduces Neural Logic Networks (NLNs) that integrate probabilistic reasoning with AND/OR logic to produce interpretable, rule-based classifications. By explicitly modeling unobserved data through biases and employing a two-layer DN F structure with dedicated input preprocessing, NLNs can learn concise, human-understandable rules while maintaining competitive predictive performance. The authors provide a rigorous probabilistic and fuzzy-logic foundation, outline a practical learning pipeline with rule resets and post-processing (discretization, pruning, bias adjustment), and demonstrate strong results on Boolean network discovery and tabular classification, including medical and industrial datasets. Overall, NLNs offer a scalable path toward interpretable, logic-grounded AI that can complement or partly replace black-box neural approaches in domains where transparency is critical.

Abstract

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.

Paper Structure

This paper contains 48 sections, 109 equations, 23 figures, 8 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Structure and Contributions
  4. Theory
  5. Probabilistic Modeling
  6. Fuzzy Logic Equivalency
  7. Logical Perspective
  8. Interpretation
  9. Machine Learning Pipeline
  10. Interpretable Structure
  11. Fully-Connected DNF Layers
  12. Input Pre-Processing Modules
  13. Input Encodings and Rule Modules
  14. Learning
  15. Training
  16. ...and 33 more sections

Figures (23)

  • Figure 1: Interpretability of the learned AND/OR networks on tic-tac-toe, when trying to predict if ${\times}$ wins from the end board configuration
  • Figure 2: Toy examples of interpretations for AND and OR concepts
  • Figure 3: Structure of an interpretable NLN
  • Figure 4: NLN structure used for learning
  • Figure 5: NLN initialization
  • ...and 18 more figures