Machine learning models deployed in sensitive areas such as healthcare must be interpretable to ensure accountability and fairness. Rule lists (if Age < 35 $\wedge$ Priors > 0 then Recidivism = True, else if Next Condition . . . ) offer full transparency, making them well-suited for high-stakes decisions. However, learning such rule lists presents significant challenges. Existing methods based on combinatorial optimization require feature pre-discretization and impose restrictions on rule size. Neuro-symbolic methods use more scalable continuous optimization yet place similar pre-discretization constraints and suffer from unstable optimization. To address the existing limitations, we introduce NeuRules, an end-to-end trainable model that unifies discretization, rule learning, and rule order into a single differentiable framework. We formulate a continuous relaxation of the rule list learning problem that converges to a strict rule list through temperature annealing. NeuRules learns both the discretizations of individual features, as well as their combination into conjunctive rules without any pre-processing or restrictions. Extensive experiments demonstrate that NeuRules consistently outperforms both combinatorial and neuro-symbolic methods, effectively learning simple and complex rules, as well as their order, across a wide range of datasets.

翻译：在医疗保健等敏感领域部署的机器学习模型必须具备可解释性，以确保问责制与公平性。规则列表（例如：若年龄<35岁∧前科次数>0则再犯风险=真，否则若下一条件……）提供了完全透明性，使其特别适用于高风险决策。然而，学习此类规则列表存在显著挑战。现有基于组合优化的方法需要特征预离散化，并对规则规模施加限制。神经符号方法采用更具扩展性的连续优化，但仍需类似的预离散化约束，且存在优化不稳定的问题。为克服现有局限，我们提出NeuRules——一种端到端可训练模型，将离散化、规则学习和规则排序统一在单个可微分框架中。我们构建了规则列表学习问题的连续松弛形式，通过温度退火收敛至严格规则列表。NeuRules无需任何预处理或限制，既能学习单个特征的离散化，也能将其组合为合取规则。大量实验表明，NeuRules在多种数据集上持续优于组合优化与神经符号方法，能有效学习简单规则、复杂规则及其排序关系。