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

Problem
This paper addresses the gap in leveraging Boolean implication relationships (BIRs) in tabular data from knowledge-rich domains, particularly in the context of interpretability and sparsity in neural networks. The authors propose a novel architecture, BIRDNet, which is designed to mine and encode these relationships directly from the data, rather than relying on an external rule base. This work is presented as a preprint and has not yet undergone peer review.

Method
BIRDNet is constructed by first mining Boolean implications using a sparse-exception binomial test, resulting in a directed graph that represents the mined implications as a propositional rule base of 2-literal clauses. The architecture of BIRDNet is layered, where each hidden unit corresponds to a mined rule and connects exclusively to its two associated features. This design ensures sparsity, with at most (2/d) of the weights in each BIR layer being active, where (d) is the input dimension. The model’s interpretability is enhanced as each unit retains a stable symbolic identity, allowing for direct extraction of rules without the need for surrogate models. The training process and specific compute requirements are not disclosed in the paper.

Results
BIRDNet was evaluated on six benchmarks related to transcriptomic and proteomic data. The model achieved an area under the receiver operating characteristic (AUROC) score within 0.02 of the strongest dense baseline, indicating competitive performance with a minimal accuracy trade-off. Notably, BIRDNet utilized up to (96\times) fewer active parameters compared to a dense multi-layer perceptron (MLP) of equivalent architecture. The first-layer rules identified by BIRDNet successfully recovered known biological signatures across various cancer subtypes and tissue types, including canonical amplicons, lineage-defining co-expression modules, and immune-infiltration markers.

Limitations
The authors acknowledge that while BIRDNet demonstrates strong performance and interpretability, it may be limited by the quality and completeness of the mined Boolean implications. Additionally, the reliance on a specific type of data (transcriptomic and proteomic) may restrict the generalizability of the findings to other domains. The paper does not discuss potential scalability issues or the computational efficiency of the mining process itself.

Why it matters
The implications of this work are significant for the fields of interpretable machine learning and bioinformatics. By integrating mined Boolean implications into a neural network architecture, BIRDNet offers a novel approach to enhance model interpretability while maintaining competitive performance. This could facilitate the discovery of biologically relevant patterns in complex datasets, ultimately aiding in the understanding of disease mechanisms and the development of targeted therapies. Furthermore, the approach may inspire future research into the integration of symbolic reasoning with deep learning, particularly in domains where interpretability is crucial.

Authors: Tirtharaj Dash
Source: arXiv:2605.28739
URL: https://arxiv.org/abs/2605.28739v1