Confidence Neural Logic Networks

Neural networks achieve strong predictive performance, but their decisions are often opaque, which is problematic in domains that require explicit, human-understandable reasoning. Neural rule learners address this by learning logical rules from data, yet they typically aggregate rules through a linear layer that has no formal logical meaning, leaving unclear what reasoning the trained network performs. We introduce Confidence Neural Logic Networks (CNLNet) and prove that conjunctive clauses followed by a linear layer exactly realize a weighted logic program: the forward pass performs weighted-satisfiability inference, and the predicted class provably coincides with the one favored by the program. Clause structure is learned end-to-end with differentiable $L_0$ gates. We extend this correspondence to depth with the Confidence Neural Logic Block, whose hidden units are themselves weighted-satisfiability decisions, so that deep networks remain layered logic programs, and we compose blocks into class-conditional chains that avoid gradient interference across classes. On $18$ tabular and image benchmarks with up to $11$M samples, CNLNet achieves a better average rank than interpretable baselines, including RRL (outperformed on $16$ datasets), C4.5, SATNet, and NeuroLogic, and is comparable to strong black-box models such as PLNN, LightGBM, and XGBoost.