Neural Rule Lists: Learning Discretizations, Rules, and Order in One Go

Sascha Xu, Nils Philipp Walter, Jilles Vreeken

Advances in Neural Information Processing Systems 38 (NeurIPS 2025) Main Conference Track

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.