# ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming

arXiv: https://arxiv.org/abs/2605.04193 · HTML: https://mlsanity.com/paper/2605.04193/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [Differentiable Inductive Logic Programming for Structured Examples](https://mlsanity.com/paper/2103.01719/) (2021)
- [Inductive Logic Programming via Differentiable Deep Neural Logic Networks](https://mlsanity.com/paper/1906.03523/) (2019)
- [Learning First-Order Rules with Differentiable Logic Program Semantics](https://mlsanity.com/paper/2204.13570/) (2022)
- [Minimalist Softmax Attention Provably Learns Constrained Boolean Functions](https://mlsanity.com/paper/2505.19531/) (2025)
- [Symbolic Imitation Learning: From Black-Box to Explainable Driving Policies](https://mlsanity.com/paper/2309.16025/) (2023)
- [Integrating Neurosymbolic AI in Advanced Air Mobility: A Comprehensive Survey](https://mlsanity.com/paper/2508.07163/) (2025)

## Abstract (arXiv)

Inductive Logic Programming (ILP) aims to learn interpretable first-order rules from data, but existing symbolic and neuro-symbolic approaches struggle to scale to noisy and probabilistic settings. Classical ILP relies on discrete combinatorial rule search and is brittle under uncertainty, while differentiable ILP methods typically depend on predefined rule templates or inaccurate fuzzy operators that suffer from vanishing gradients or poor approximation of logical structure when reasoning over probabilistic predicate valuations. This paper proposes an Attention-based Neuro-symbolic Differentiable Rule Extractor (ANDRE), a novel ILP framework that learns first-order logic programs by optimizing over a continuous rule space with attention-based logical operators. ANDRE replaces both rule templates and logical operators with fully differentiable, attention-driven conjunction and disjunction operators that approximate logical min-max semantics, enabling accurate, stable, and interpretable reasoning over probabilistic data. By softly selecting, negating, or excluding predicates within each rule, ANDRE supports flexible rule induction while preserving symbolic structure. Extensive experiments on classical ILP benchmarks, large-scale knowledge bases, and synthetic datasets with probabilistic predicates and noisy supervision demonstrate that ANDRE achieves competitive or superior predictive performance while reliably recovering correct symbolic rules under uncertainty. In particular, ANDRE remains robust to moderate label noise, substantially outperforming existing differentiable ILP methods in both rule extraction quality and stability.