BIRDNet: Mining and Encoding Boolean Implication Knowledge Graphs as Interpretable Deep Neural Networks

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. We encode the resulting typed 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: at most 2/d of the weights in each BIR layer are active, where d is the input dimension. Second, the model is intrinsically 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, while using up to 95× fewer active parameters than an architecture-matched dense MLP. First-layer rules align with known biological signatures across multiple cancer subtypes and tissue types. Matched-topology controls show that the mined graph contributes symbolic meaning rather than predictive advantage: shuffled or random pairings match or improve AUROC but no longer correspond to mined implications. Data and code are available at: https://github.com/MAHI-Group/BIRDNet.