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

Abstract

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 $95\times$ 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.