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.

本研究解决了机器学习模型在敏感领域（如医疗保健）中的可解释性问题。创新性地提出了NeuRules，这是一种端到端可训练的模型，统一了离散化、规则学习和规则顺序，避免了对特征的预先离散化限制。实验结果表明，NeuRules在多种数据集上显著优于现有方法，能够有效学习简单和复杂的规则及其顺序。

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