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

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a logical mechanism relating the inputs and outputs with AND and OR operations. We generalize these networks with NOT operations and biases that take into account unobserved data and develop a rigorous logical and probabilistic modeling in terms of concept combinations to motivate their use. We also propose a novel factorized IF-THEN rule structure for the model as well as a modified learning algorithm. Our method improves the state-of-the-art in Boolean networks discovery and is able to learn relevant, interpretable rules in tabular classification, notably on examples from the medical and industrial fields where interpretability has tangible value.

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.

Biological systems are governed by structured molecular interactions, where pathways, regulatory circuits, and functional gene relationships shape cellular behavior and disease progression. Much of this knowledge is naturally represented as graphs. However, most biomedical AI models cannot directly use graph-encoded biological knowledge and instead require compressed low-dimensional representations, which can lose important structure and reduce performance, especially in limited-sample clinical studies. Here, we introduce Graph-in-Graph (GiG), a knowledge graph-modulated deep learning framework for data-efficient clinical prediction. GiG represents each patient as a standalone modular graph, in which curated biological knowledge graphs define edges and patient-specific measurements, such as gene expression, define node features. This design allows multiple biological knowledge graphs to be integrated while preserving gene-gene interactions and pathway topology during patient-level representation learning. Across cohorts comprising nearly 9,700 patients and five clinical tasks, including liquid biopsy cancer detection, prostate cancer diagnosis, and 32-class pan-cancer classification, GiG consistently outperforms traditional and state-of-the-art methods, with the largest gains in limited-sample settings. On the challenging prostate cancer diagnosis task, GiG improves macro-F1 by up to 49 percentage points relative to competing methods. Control experiments replacing real pathway graphs with random topologies confirm that these gains arise from biologically grounded knowledge graph structure rather than graph modeling alone. These findings show that knowledge graph-modulated deep learning can improve robustness, interpretability, and sample efficiency in clinical data analysis, and provide a principled framework for integrating biological knowledge graphs into predictive modeling.