Neural Symbolic Logical Rule Learner for Interpretable Learning

Abstract

Rule-based neural networks stand out for enabling interpretable classification by learning logical rules for both prediction and interpretation. However, existing models often lack flexibility due to the fixed model structure. Addressing this, we introduce the Normal Form Rule Learner (NFRL) algorithm, leveraging a selective discrete neural network, that treat weight parameters as hard selectors, to learn rules in both Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF) for enhanced accuracy and interpretability. Instead of adopting a deep, complex structure, the NFRL incorporates two specialized Normal Form Layers (NFLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Normal Form Constraint (NFC) to streamline neuron connections. We also show the novel network architecture can be optimized using adaptive gradient update together with Straight-Through Estimator to overcome the gradient vanishing challenge. Through extensive experiments on 11 datasets, NFRL demonstrates superior classification performance, quality of learned rules, efficiency and interpretability compared to 12 state-of-the-art alternatives. Code and data are available at \url{https://anonymous.4open.science/r/NFRL-27B4/}.