# Neuro-Symbolic Rule Lists

arXiv: https://arxiv.org/abs/2411.06428 · HTML: https://mlsanity.com/paper/2411.06428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 10 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [Scalable Bayesian Rule Lists](https://mlsanity.com/paper/1602.08610/) (2016)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Learning Accurate and Interpretable Decision Rule Sets from Neural Networks](https://mlsanity.com/paper/2103.02826/) (2021)
- [Do Not Trust Additive Explanations](https://mlsanity.com/paper/1903.11420/) (2019)
- [Interpretable multiclass classification by MDL-based rule lists](https://mlsanity.com/paper/1905.00328/) (2019)
- [Finding Interpretable Class-Specific Patterns through Efficient Neural Search](https://mlsanity.com/paper/2312.04311/) (2023)
- [Learning Exceptional Subgroups by End-to-End Maximizing KL-divergence](https://mlsanity.com/paper/2402.12930/) (2024)

## Built on by (most cited first, 1 of 1)

- [RLIE: Rule Generation with Logistic Regression, Iterative Refinement, and Evaluation for Large Language Models](https://mlsanity.com/paper/2510.19698/) (2025)

## Abstract (arXiv)

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.