Interpretable machine learning is essential in high-stakes domains like healthcare. Rule lists are a popular choice due to their transparency and accuracy, but learning them effectively remains a challenge. Existing methods require feature pre-discretization, constrain rule complexity or ordering, or struggle to scale. We present NeuRules, a novel end-to-end framework that overcomes these limitations. At its core, NeuRules transforms the inherently combinatorial task of rule list learning into a differentiable optimization problem, enabling gradient-based learning. It simultaneously discovers feature conditions, assembles them into conjunctive rules, and determines their order—without pre-processing or manual constraints. A key contribution here is a gradient shaping technique that steers learning toward sparse rules with strong predictive performance. To produce ordered lists, we introduce a differentiable relaxation that, through simulated annealing, converges to a strict rule list. Extensive experiments show that NeuRules consistently outperforms combinatorial and neural baselines on binary as well as multi-class classification tasks across a wide range of datasets.

Discovering patterns in data that best describe the differences between classes allows to hypothesize and reason about class-specific mechanisms. In molecular biology, for example, these bear the promise of advancing the understanding of cellular processes differing between tissues or diseases, which could lead to novel treatments. To be useful in practice, methods that tackle the problem of finding such differential patterns have to be readily interpretable by domain experts, and scalable to the extremely high-dimensional data. In this work, we propose a novel, inherently interpretable binary neural network architecture Diffnaps that extracts differential patterns from data. Diffnaps is scalable to hundreds of thousands of features and robust to noise, thus overcoming the limitations of current state-of-the-art methods in large-scale applications such as in biology. We show on synthetic and real world data, including three biological applications, that unlike its competitors, Diffnaps consistently yields accurate, succinct, and interpretable class descriptions.

Finding and describing sub-populations that are exceptional in terms of a target property has important applications in many scientific disciplines, from identifying disadvantaged demographic groups in census data to finding conductive molecules within gold nanoparticles. Current approaches to finding such subgroups require pre-discretized predictive variables, do not permit non-trivial target distributions, do not scale to large datasets, and struggle to find diverse results. To address these limitations, we propose SYFLOW, an end-to-end optimizable approach in which we leverage normalizing flows to model arbitrary target distributions and introduce a novel neural layer that results in easily interpretable subgroup descriptions. We demonstrate on synthetic data, real-world data, and via a case study, that SYFLOW reliably finds highly exceptional subgroups accompanied by insightful descriptions.