Interpretable neural network classification model using first-order logic rules

Over the past decade, the field of neural networks has made significant strides, particularly in deep learning. However, their limited interpretability has constrained their application in certain critical domains, drawing widespread criticism. Researchers have proposed various methods for explaining neural networks to address this challenge. This paper focuses on rule-based explanations for neural network classification problems. We propose IRCnet, a scalable classification model based on first-order logic rules. IRCnet consists of layers for learning conjunction and disjunction rules, utilizing binary logic activation functions to enhance interpretability. The model is initially trained using a continuous-weight version, which is later binarized to produce a discrete-weight version. During training, we innovatively employed gradient approximation method to handle the non-differentiable weight binarization function, thereby enabling the training of split matrices used for binarization. Finally, Conjunctive Normal Form (CNF) or Disjunctive Normal Form (DNF) rules are extracted from the model’s discrete-weight version. Experimental results indicate that our model achieves the highest or near-highest performance across various classification metrics in multiple structured datasets while demonstrating significant scalability. It effectively balances classification accuracy with the complexity of the generated rules. • We propose an interpretable classification model grounded in First-Order Logic (FOL), which is both scalable and capable of achieving state-of-the-art or near state-of-the-art classification performance across diverse datasets. • The model includes two versions: one with continuous weights that directly uses binary logic activation functions to learn the features of the data, aiming to improve the model’s classification performance. The other version uses binary weights, where a gradient approximation method is employed to train the split matrix. The continuous weights are then binarized using the trainable split matrix to obtain a binarized weight matrix, from which FOL rules are extracted to explain the model’s decisions. • We disentangle the training phase from the rule extraction process by implementing a bifurcated training methodology. Rule extraction is performed modularly, with subsequent integration according to logical junctions. We further streamline the integrated rules using first-order logic representations.