Interpretable Classification via a Rule Network with Selective Logical Operators

Abstract

We introduce the Rule Network with Selective Logical Operators (RNS), a novel neural architecture that employs \textbf{selective logical operators} to adaptively choose between AND and OR operations at each neuron during training. Unlike existing approaches that rely on fixed architectural designs with predetermined logical operations, our selective logical operators treat weight parameters as hard selectors, enabling the network to automatically discover optimal logical structures while learning rules. The core innovation lies in our \textbf{selective logical operators} implemented through specialized Logic Selection Layers (LSLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Heterogeneous Connection Constraint (HCC) to streamline neuron connections. We demonstrate that this selective logical operator framework can be effectively optimized using adaptive gradient updates with the Straight-Through Estimator to overcome gradient vanishing challenges. Through extensive experiments on 13 datasets, RNS demonstrates superior classification performance, rule quality, and efficiency compared to 25 state-of-the-art alternatives, showcasing the power of RNS in rule learning. Code and data are available at https://anonymous.4open.science/r/RNS_-3DDD.