Neural Logic Networks for Interpretable Classification

Tabular data in knowledge-rich domains often carries a latent prior in the form of Boolean implication relationships (BIRs) between pairs of features. We mine such relationships with a sparse-exception binomial test. The mined implications form a typed directed graph, equivalent to a propositional rule base of 2-literal clauses. We encode this graph as the connectivity of a layered neural network, called BIRDNet, in which each hidden unit corresponds to one mined rule and binds only to its two features. We show two consequences of this design: First, the architecture is sparse by construction: at most $2/d$ of the weights in each BIR layer are active, where $d$ is the input dimension. Second, the model is interpretable: every trained unit keeps a stable symbolic identity, so rules can be read off the network without surrogate models. Unlike most neurosymbolic models, BIRDNet does not consume an external rule base; its structural prior is mined from the data. We evaluate BIRDNet on six transcriptomic and proteomic benchmarks. Our results show that BIRDNet stays within 0.02 AUROC of the strongest dense baseline, at a small accuracy cost, while using up to $96\times$ fewer active parameters than an architecture-matched dense MLP. First-layer rules recover known biological signatures across multiple cancer subtypes and tissue types, including canonical amplicons, lineage-defining co-expression modules, and immune-infiltration markers. Data and code are available at: https://github.com/MAHI-Group/BIRDNet.

Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that simultaneously achieve high predictive performance and low, human-understandable complexity remains challenging. To address this, we introduce TT-Sparse, a flexible neural building block that leverages differentiable truth tables as nodes to learn sparse, effective connections. A key contribution of our approach is a new soft TopK operator with straight-through estimation for learning discrete, cardinality-constrained feature selection in an end-to-end differentiable manner. Crucially, the forward pass remains sparse, enabling efficient computation and exact symbolic rule extraction. As a result, each node (and the entire model) can be transformed exactly into compact, globally interpretable DNF/CNF Boolean formulas via Quine-McCluskey minimization. Extensive empirical results across 28 datasets spanning binary, multiclass, and regression tasks show that the learned sparse rules exhibit superior predictive performance with lower complexity compared to existing state-of-the-art methods.

Black-box models limit the adoption of artificial intelligence in medicine because their predictions are difficult to interpret and reproduce. We present a statistically grounded framework for interpretable, rule-based clinical classification using the Bernoulli Naïve Bayes (BNB) model. Supervised chi-square-guided binarization converts continuous variables into binary indicators by selecting thresholds that maximize association with the clinical outcome within the training folds, which allows BNB to operate on continuous medical data without sacrificing transparency. On three benchmark datasets, Pima Indians Diabetes, Wisconsin Breast Cancer, and Heart Failure Prediction, the framework reached areas under the receiver operating characteristic curve of 0.800, 0.984, and 0.919, respectively. Probabilistic reliability was assessed with a leakage-safe cross-validated calibration analysis reporting Brier score and calibration intercept and slope, and post-hoc beta calibration improved probability calibration across datasets. These results indicate that an interpretable, statistically motivated framework can perform comparably to more complex models while providing explicit decision rules expressed in clinical units and calibrated risk estimates. A complete worked example further shows that model inference can be reproduced from a printed reference table using only basic arithmetic, without software or proprietary tools, supporting trustworthy and auditable use of artificial intelligence in clinical settings.