Neural Network-Based Rule Models With Truth Tables

Abstract

Understanding the decision-making process of a machine/deep learning model is crucial, particularly in security-sensitive applications. In this study, we introduce a neural network framework that combines the global and exact interpretability properties of rule-based models with the high performance of deep neural networks. Our proposed framework, called $\textit{Truth Table rules}$ (TT-rules), is built upon $\textit{Truth Table nets}$ (TTnets), a family of deep neural networks initially developed for formal verification. By extracting the set of necessary and sufficient rules $\mathcal{R}$ from the trained TTnet model (global interpretability), yielding the same output as the TTnet (exact interpretability), TT-rules effectively transforms the neural network into a rule-based model. This rule-based model supports binary classification, multi-label classification, and regression tasks for tabular datasets. Furthermore, our TT-rules framework optimizes the rule set $\mathcal{R}$ into $\mathcal{R}_{opt}$ by reducing the number and size of the rules. To enhance model interpretation, we leverage Reduced Ordered Binary Decision Diagrams (ROBDDs) to visualize these rules effectively. After outlining the framework, we evaluate the performance of TT-rules on seven tabular datasets from finance, healthcare, and justice domains. We also compare the TT-rules framework to state-of-the-art rule-based methods. Our results demonstrate that TT-rules achieves equal or higher performance compared to other interpretable methods while maintaining a balance between performance and complexity. Notably, TT-rules presents the first accurate rule-based model capable of fitting large tabular datasets, including two real-life DNA datasets with over 20K features. Finally, we extensively investigate a rule-based model derived from TT-rules using the Adult dataset.